Nuevas funciones package descomponer 1.2
Francisco Parra Rodríguez
Documento tecnico:
http://econometria.wordpress.com/2013/07/29/estimacion-con-parametros-dependientes-del-tiempo/
Niveles de significación para el test de Durbin(1969) :
X0.1 <- c(0.4 ,0.35044 ,0.35477 ,0.33435 ,0.31556 ,0.30244 ,0.28991 ,0.27828 ,0.26794 ,0.25884 ,0.25071 ,0.24325 ,0.23639 ,0.2301 ,0.2243 ,0.21895 ,0.21397 ,0.20933 ,0.20498 ,0.20089 ,0.19705 ,0.19343 ,0.19001 ,0.18677 ,0.1837 ,0.18077 ,0.17799 ,0.17037 ,0.1728 ,0.17037 ,0.16805 ,0.16582 ,0.16368 ,0.16162 ,0.15964 ,0.15774 ,0.1559 ,0.15413 ,0.15242 ,0.15076 ,0.14916 ,0.14761 ,0.14011 ,0.14466 ,0.14325 ,0.14188 ,0.14055 ,0.13926 ,0.138 ,0.13678 ,0.13559 ,0.13443 ,0.133 ,0.13221 ,0.13113 ,0.13009 ,0.12907 ,0.12807 ,0.1271 ,0.12615 ,0.12615 ,0.12431 ,0.12431 ,0.12255 ,0.12255 ,0.12087 ,0.12087 ,0.11926 ,0.11926 ,0.11771 ,0.11771 ,0.11622 ,0.11622 ,0.11479 ,0.11479 ,0.11341 ,0.11341 ,0.11208 ,0.11208 ,0.11079 ,0.11079 ,0.10955 ,0.10955 ,0.10835 ,0.10835 ,0.10719 ,0.10719 ,0.10607 ,0.10607 ,0.10499 ,0.10499 ,0.10393 ,0.10393 ,0.10291 ,0.10291 ,0.10192 ,0.10192 ,0.10096 ,0.10096 ,0.10002)
X0.05 <- c(0.45,0.44306,0.41811,0.39075 ,0.37359 ,0.35522 ,0.33905 ,0.32538 ,0.31325 ,0.30221 ,0.29227 ,0.2833 ,0.27515 ,0.26767 ,0.26077 ,0.25439 ,0.24847 ,0.24296 ,0.23781 ,0.23298 ,0.22844 ,0.22416 ,0.22012 ,0.2163 ,0.21268 ,0.20924 ,0.20596 ,0.20283 ,0.19985 ,0.197 ,0.19427 ,0.19166 ,0.18915 ,0.18674 ,0.18442 ,0.18218 ,0.18003 ,0.17796 ,0.17595 ,0.17402 ,0.17215 ,0.17034 ,0.16858 ,0.16688 ,0.16524 ,0.16364 ,0.16208 ,0.16058 ,0.15911 ,0.15769 ,0.1563 ,0.15495 ,0.15363 ,0.15235 ,0.1511 ,0.14989 ,0.1487 ,0.14754 ,0.14641 ,0.1453 ,0.1453 ,0.14361 ,0.14361 ,0.14112 ,0.14112 ,0.13916 ,0.13916 ,0.13728 ,0.13728 ,0.13548 ,0.13548 ,0.13375 ,0.13375 ,0.13208 ,0.13208 ,0.13048 ,0.13048 ,0.12894 ,0.12894 ,0.12745 ,0.12745 ,0.12601 ,0.12601 ,0.12464 ,0.12464 ,0.12327 ,0.12327 ,0.12197 ,0.12197 ,0.12071 ,0.12071 ,0.11949 ,0.11949 ,0.11831 ,0.11831 ,0.11716 ,0.11716 ,0.11604 ,0.11604 ,0.11496)
X0.025 <- c(0.475 ,0.50855 ,0.46702 ,0.44641 ,0.42174 ,0.40045 ,0.38294 ,0.3697 ,0.35277 ,0.34022 ,0.32894 ,0.31869 ,
0.30935 ,0.30081 ,0.29296 ,0.2857 ,0.27897 ,0.2727 ,0.26685 ,0.26137 ,0.25622 ,0.25136 ,0.24679 ,0.24245 ,0.23835 ,0.23445 ,0.23074 ,0.22721 ,0.22383 ,0.22061 ,0.21752 ,0.21457 ,0.21173 ,0.20901 ,0.20639 ,0.20337 ,0.20144 ,0.1991 ,0.19684 ,0.19465 ,0.19254 ,0.1905 ,0.18852 ,0.18661 ,0.18475 ,0.18205 ,0.1812 ,0.1795 ,0.17785 ,0.17624 ,0.17468 ,0.17361 ,0.17168 ,0.17024 ,0.16884 ,0.16748 ,0.16613 ,0.16482 ,0.16355 ,0.1623 ,0.1623 ,0.1599 ,0.1599 ,0.1576 ,0.1576 ,0.1554 ,0.1554 ,0.15329 ,0.15329 ,0.15127 ,0.15127 ,0.14932 ,0.14932 ,0.14745 ,0.14745 ,0.14565 ,0.14565 ,0.14392 ,0.14392 ,0.14224 ,0.14224 ,0.14063 ,0.14063 ,0.13907 ,0.13907 ,0.13756 ,0.13756 ,0.1361 ,0.1361 ,0.13468 ,0.13468 ,0.13331 ,0.13331 ,0.13198 ,0.13198 ,0.1307 ,0.1307 ,0.12944 ,0.12944 ,0.12823)
X0.01 <- c( 0.49 ,0.56667 ,0.53456 ,0.50495 ,0.47629 ,0.4544 ,0.43337 ,0.41522 ,0.39922 ,0.38481 ,0.37187 ,0.36019 ,0.34954 ,0.3398 ,0.33083 ,0.32256 ,0.31489 ,0.30775 ,0.30108 ,0.29484 ,0.28898 ,0.28346 ,0.27825 ,0.27333 ,0.26866 ,0.26423 ,0.26001 ,0.256 ,0.25217 ,0.24851 ,0.24501 ,0.24165 ,0.23843 ,0.23534 ,0.23237 ,0.22951 ,0.22676 ,0.2241 ,0.22154 ,0.21906 ,0.21667 ,0.21436 ,0.21212 ,0.20995 ,0.20785 ,0.20581 ,0.20383 ,0.2119 ,0.20003 ,0.19822 ,0.19645 ,0.19473 ,0.19305 ,0.19142 ,0.18983 ,0.18828 ,0.18677 ,0.18529 ,0.18385 ,0.18245 ,0.18245 ,0.17973 ,0.17973 ,0.17713 ,0.17713 ,0.17464 ,0.17464 ,0.17226 ,0.17226 ,0.16997 ,0.16997 ,0.16777 ,0.16777 ,0.16566 ,0.16566 ,0.16363 ,0.16363 ,0.16167 ,0.16167 ,0.15978 ,0.15978 ,0.15795 ,0.15795 ,0.15619 ,0.15619 ,0.15449 ,0.15449 ,0.15284 ,0.15284 ,0.15124 ,0.15124 ,0.1497 ,0.1497 ,0.1482 ,0.1482 ,0.14674 ,0.14674 ,0.14533 ,0.14533 ,0.14396)
X0.005 <- c(0.495 ,0.59596 ,0.579 ,0.5421 ,0.51576 ,0.48988 ,0.4671 ,0.44819 ,0.43071 ,0.41517 ,0.40122 ,0.38856 ,0.37703 ,0.36649 ,0.35679 ,0.34784 ,0.33953 ,0.33181 ,0.32459 ,0.31784 ,0.31149 ,0.30552 ,0.29989 ,0.29456 ,0.28951 ,0.28472 ,0.28016 ,0.27582 ,0.27168 ,0.26772 ,0.26393 ,0.2603 ,0.25348 ,0.25348 ,0.25027 ,0.24718 ,0.24421 ,0.24134 ,0.23857 ,0.23589 ,0.2331 ,0.23081 ,0.22839 ,0.22605 ,0.22377 ,0.22377 ,0.21943 ,0.21753 ,0.21534 ,0.21337 ,0.21146 ,0.20961 ,0.2078 ,0.20604 ,0.20432 ,0.20265 ,0.20101 ,0.19942 ,0.19786 ,0.19635 ,0.19635 ,0.19341 ,0.19341 ,0.19061 ,0.19061 ,0.18792 ,0.18792 ,0.18534 ,0.18534 ,0.18288 ,0.18288 ,0.18051 ,0.18051 ,0.17823 ,0.17823 ,0.17188 ,0.17188 ,0.17392 ,0.17392 ,0.17188 ,0.17188 ,0.16992 ,0.16992 ,0.16802 ,0.16802 ,0.16618 ,0.16618 ,0.1644 ,0.1644 ,0.16268 ,0.16268 ,0.16101 ,0.16101 ,0.1594 ,0.1594 ,0.15783 ,0.15783 ,0.15631 ,0.15631 ,0.15483)
TestD <- data.frame(X0.1,X0.05,X0.025,X0.01,X0.005)Packages necesarios:
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## prewhitenFunción gdf(a)
Transforma los datos del dominio del tiempo al dominio de la frecuencia pre-multiplicandolos por la matriz ortogonal,\(W\), sugerida por Harvey (1978)
Nerlove (1964) y Granger (1969) fueron los primeros investigadores en aplicar el analisis espectral a las series de tiempo en economía. El uso del analisis espectral requiere un cambio en el modo de ver las series económicas, al pasaser de la perspectiva del tiempo al dominio de la frecuencia. El analisis espectral parte de la supsición de que cuanquier serie {Xt}, puede ser transformada en ciclos formados con senos u cosenos:
\(X_t=\eta+\sum_{j=1}^N[a_j\cos(2\pi\frac{ft}n)+b_j\sin(2\pi\frac{ft}n)]\) (1)
donde \(\eta\) es la media de la serie, \(a_j\) y \(b_j\) son su amplitud,\(f\) son las frecuencias que del conjunto de las \(n\) observaciones,\(t\) es un indice de tiempo que va de 1 a N, siendo N el numero de periodos para los cuales tenemos observaciones en el conjunto de datos, el cociente \(\frac{ft}n)\) convierte cada valor de \(t\) en escala de tiempo en proporciones de \(2n\) y rango \(j\) desde \(1\) hasta \(n\) siendo \(n=\frac{N}2\) (es decir, 0,5 ciclos por intervalo de tiempo). Las dinámica de las altas frecuencias (los valores más altos de f) corresponden a los ciclos cortos en tanto que la dinámica de la bajas frecuencias (pequeños valores de f) van a corresponder con los ciclos largos. Si nosotros hacemos que \(\frac{ft}n=w\) la ecuación (1) quedaría, asi :
\(X_t=\eta+\sum_{j=1}^N[a_j\cos(\omega_j)+b_j\sin(\omega_j)]\)(2)
El analisis espectral puede utilizarse para identificar y cuantificar en procesos aparentemente aperiodicos, sucesiones de cicos de periodo de corto y largo plazo. Una serie dada \({X_t}\) puede contener diversos ciclos de diferentes frecuencias y amplitudes, y esa combinación de frecuencias y amplitudes de carcter cíclico la hacer aparecer como un serie no periodica e irregular. De hecho la ecuación (2), muestra que cada observación \(t\) de una serie de tiempo, es el resultado sumar los valores en \(t\) que resultan de \(N\) ciclos de diferente longitud y amplitud, a los que habría que añadir si cabe un termino de error.
Una manera practica de pasar desde el dominio del tiempo al dominio de la frecuencia es pre-multiplicando los datos originales por una matriz ortogonal, \(W\), sugerida por Harvey (1978), con el elemento (j,t)th :
\[\begin{equation} w_{jt} = \left\lbrace\begin{array}{ll}\left(\frac{1}T\right) ^\frac{1}2 & \forall j=1\\ \left(\frac{2}T\right) ^\frac{1}2 \cos\left[\frac{\pi j(t-1)}T\right] & \forall j=2,4,6,..\frac{(T-2)}{(T-1)}\\ \left(\frac{2}T\right) ^\frac{1}2 \sin\left[\frac{\pi (j-1)(t-1)}T\right] & \forall j=3,5,7,..\frac{(T-2)}T\\ \left(\frac{1}T\right) ^\frac{1}2 (-1)^{t+1} & \forall j=T\end{array}\right.\end{equation}\] (3)
La matriz \(W\) tiene la ventaja de ser ortogonal por lo que \(WW^T=I\).
Matriz \(W\)
MW <- function(n) {
# Author: Francisco Parra Rodr?guez
# Some ideas from: Harvey, A.C. (1978), Linear Regression in the Frequency Domain, International Economic Review, 19, 507-512.
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
uno <- as.numeric (1:n)
A <- matrix(rep(sqrt(1/n),n), nrow=1)
if(n%%2==0){
for(i in 3:n-1){
if(i%%2==0) {
A1 <- matrix(sqrt(2/n)*cos(pi*(i)*(uno-1)/n), nrow=1)
A <- rbind(A,A1)}
else {
A2 <- matrix(sqrt(2/n)*sin(pi*(i-1)*(uno-1)/n), nrow=1)
A <- rbind(A,A2)
}}
AN <- matrix(sqrt(1/n)*(-1)^(uno+1), nrow=1)
A <- rbind(A,AN)
A
} else {
for(i in 3:n-1){
if(i%%2==0) {
A1 <- matrix(
sqrt(2/n)*cos(pi*(i)*(uno-1)/n), nrow=1)
A <- rbind(A,A1)}
else {
A2 <- matrix(sqrt(2/n)*sin(pi*(i-1)*(uno-1)/n), nrow=1)
A <- rbind(A,A2)
}}
AN <- matrix(
sqrt(2/n)*sin(pi*(n-1)*(uno-1)/n), nrow=1)
A <- rbind(A,AN)
}
}gdf <- function(y) {
a <- matrix(y,nrow=1)
n <- length(y)
A <- MW(n)
A%*%t(a)
}Función gdt(a)
Transforma los datos del dominio de frecuencias al dominio del tiempo pre-multiplicandolos por la matriz ortogonal, A, sugerida por Harvey (1978)
gdt <- function(y) {
# Author: Francisco Parra Rodr?guez
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
a <- matrix(y,nrow=1)
n <- length(y)
A <- MW(n)
t(A)%*%t(a)
}Función cdf(a)
Otiene la matriz auxiliar para operaciones con vectores en dominio de tiempo y dominio de la frecuencia, pre-multiplica un vector por la matriz ortogonal, \(W\) y por su transpuesta, Parra F. (2013) La multiplicación de dos series armónicas de diferente frecuencia:
\([a_j\cos (\omega_j)+b_j\sin (\omega_j)]x [a_i\cos (\omega_i)+b_i\sin (\omega_i)]\)
da como resultado la siguiente suma: \[\begin{equation} \begin{array}{c} a_ja_i\cos(\omega_j)\cos(\omega_i)+a_jb_i\cos (\omega_j)\sin (\omega_i)\\ +a_ib_j\sin (\omega_j)\cos (\omega_i)b_i\sin (\omega_i)+b_jb_i\sin(\omega_j)\sin(\omega_i) \end{array} \end{equation}\]
considerando las identidades del producto de senos y cosenos, quedaría:
\[\begin{equation} \begin{array}{c} \frac{a_ja_i+b_jb_i}{2} \cos(\omega_j- \omega_i)+\frac{b_ja_i-b_ja_j}{2}\sin(\omega_j- \omega_i)\\ +\frac{a_ja_i-b_jb_i}{2}\cos(\omega_j+ \omega_i)+\frac{b_ja_i+b_ja_i}{2}\sin(\omega_j+ \omega_i) \end{array} \end{equation}\]
La circularidad de \(\omega\) determina que la serie producto de dos series en \(t\), resulte una nueva serie cuyos coeficientes de Fourier sean una combinación lineal de los coeficientes de Fourier de las series multiplos.
Partiendo de las dos series siguientes:
\[\begin{equation} \begin{array} {cc} y_t=\eta^y+a_0^y\cos(\omega_0)+b_0^y\sin(\omega_0)+a_1^y\cos(\omega_1)+b_1^y\sin(\omega_1)+ a_2^y\cos(\omega_2)+b_2^y\sin(\omega_2)+a_3^y\cos(\omega_3)\\ x_t=\eta^x+a_0^x\cos(\omega_0)+b_0^x\sin(\omega_0)+a_1^x\cos(\omega_1)+b_1^x\sin(\omega_1)+ a_2^x\cos(\omega_2)+b_2^x\sin(\omega_2)+a_3^x\cos(\omega_3) \end{array} \end{equation}\]
Dada una matriz \(\Theta^{\dot x\dot x}\) de tamaño 8x8 :
\[ \Theta^{\dot x\dot x} = \eta^x I_8+\frac{1}2\left( \begin{array}{cccccccc} 0& a_0^x& b_0^x & a_1^x & b_1^x & a_2^x & b_2^x& 2a_3^x \\ 2a_0^x& a_1^x& b_1^x & a_0^x+a_2^x & b_0^x+b_2^x & a_1^x+2a_3^x & b_1^x& 2a_2^x \\ 2b_0^x& b_1^x&- a_1^x & -b_0^x+b_2^x & a_0^x-a_2^x &- b_1^x &a_1^x- a_3^x &- 2b_2^x \\ 2a_1^x& a_0^x+a_2^x&- b_0^x+b_2^x & 2a_3^x &0 & a_0^x+a_2^x & b_0^x-b_2^x& 2a_1^x \\ 2b_1^x& a_0^x+b_2^x&- b_0^x-a_2^x &0& -2a_3^x & -b_0^x+b_2^x & a_0^x-a_2^x& -2b_1^x \\ 2a_2^x& a_1^x+2a_3^x&- b_1^x & a_0^x+a_2^x &-b_0^x-b_2^x & a_1^x &- b_1^x& 2a_0^x \\ 2b_2^x& b_1^x& a_1^x-2a_3^x & b_0^x-b_2^x &a_0^x-a_2^x & -b_1^x &- a_1^x& -2b_0^x \\ 2a_3^x& a_2^x& -b_2^x & a_1^x &- b_1^x & a_0^x & -b_0^x& 0 \end{array} \right) \] Se demuestra que:
\(\dot z=\Theta^{\dot x\dot x}\dot y\)
donde \(\dot y = Wy\),\(\dot x = Wx\), y \(\dot z = Wz\).
En el dominio del tiempo:
\(z_t= x_t y_t=W^T\dot x W^T\dot y=W^T Wx_t W^T\dot y=x_tI_nW^T\dot y\)
\(W^T\dot z=x_tI_nW^T\dot y\)
\(\dot z=Wx_tI_nW^T\dot y\)
Entonces:
\(\Theta^{\dot x\dot x}=W^Tx_tI_nW\)
La matriz cuadrada \(\Theta^{\dot x\dot x}\) puede ser utilizada para obtener los resultados en el dominio de la frecuencia de diversas funciones de series de tiempo . Por ejemplo, si se desea obtener el desarrollo de los coeficientes en fourier de \(z_t=x_t^2\), entonces:
\(\dot z= Wx_tI_nW^T\dot x\)
En consecuencia, si \(z_t=x_t^n\)
\(\dot z= Wx_t^{n-1}I_nW^T\dot x\)
Si ahora queremos obtener el desarrollo en coeficientes de fourier de \(z_t=\frac{x_t}{y_t}\), entonces:
\(\dot z= W[\frac{1}y_t]I_nW^T\dot x\)
cdf <- function(y) {
# Author: Francisco Parra Rodr?guez
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
a <- matrix(y, nrow=1)
n <- length(y)
uno <- as.numeric (1:n)
A <- MW(n)
I<- diag(c(a))
B <- A%*%I
B%*%t(A)
}Función periodograma (a)
Calcula y presenta el espectro de la serie “a”
Sea \(a\) un vector n x 1 el modelo transformado en el dominio de la frecuencia esta dado por:
\(\hat a= Wa\)
Denominando \(p_j\) el ordinal del periodograma de \(\hat a\) en la frecuencia \(\lambda_j=2\pi j/n\), y \(\hat a_j\) el j-th elemento de \(\hat a\), entonces
\[ \left\lbrace \begin{array}{ll} p_j=\hat a_{2j}^{2}+\hat a_{2j+1}^{2} & \forall j = 1,...\frac{n-1}{2}\\ p_j=\hat a_{2j}^{2}& \forall j = \frac{n}{2}-1 \end{array} \right . \]
\[p_0=\hat a_{1}^{2}\]
Entonces el cuadrado del \(\hat a\) puede ser utilizado como un estimador consistente del periodograma de \(a\).
periodograma <- function(y) {
# Author: Francisco Parra Rodr?guez
# Some ideas from Gretl
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
cf <- gdf(y)
n <- length(y)
if (n%%2==0) {
m1 <- c(0)
m2 <- c()
for(i in 1:n){
if(i%%2==0) m1 <-c(m1,cf[i]) else m2 <-c(m2,cf[i])}
m2 <-c(m2,0)
frecuencia <- seq(0:(n/2))
frecuencia <- frecuencia-1
omega <- pi*frecuencia/(n/2)
periodos <- n/frecuencia
densidad <- (m1^2+m2^2)/(4*pi)
tabla <- data.frame(omega,frecuencia, periodos,densidad)
tabla$densidad[(n/2+1)] <- 4*tabla$densidad[(n/2+1)]
data.frame(tabla[2:(n/2+1),])}
else {m1 <- c(0)
m2 <- c()
for(i in 1:(n-1)){
if(i%%2==0) m1 <-c(m1,cf[i]) else m2 <-c(m2,cf[i])}
m2 <-c(m2,cf[n])
frecuencia <- seq(0:((n-1)/2))
frecuencia <- frecuencia-1
omega <- pi*frecuencia/(n/2)
periodos <- n/frecuencia
densidad <- (m1^2+m2^2)/(4*pi)
tabla <- data.frame(omega,frecuencia, periodos,densidad)
data.frame(tabla[2:((n+1)/2),])}
}Función gperiodogrma (a)
Presenta gráficamente el espectro de la variabe a
gperiodograma <- function(y) {
# Author: Francisco Parra Rodríguez
# Some ideas from Gretl
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
tabla <- periodograma(y)
plot(tabla$frecuencia,tabla$densidad,
main = "Espectro",
ylab = "densidad",
xlab="frecuencia",type = "l",
col="#ff0000")}Función td (y,significance)
Realiza una prueba estadística para estudiar la dependencia serial sobre el periodograma acumulado de a, con una significación de 0,1(significance=1); 0,05(significance=2); 0,025(significance=3); 0,01(significance=4) y 0,005 (significance=5) (Durbin; 1969)
El test de Durbin esta basado en el siguiente estadistico: \(s_j=\frac{\sum_{r=1} ^j p_r}{\sum_{r=1}^m p_r}\)
donde \(m=\frac{1}{2}n\) para \(n\) par y \(\frac{1}{2}(n-1)\) para \(n\) impar.
El estadístico \(s_j\) ha en encontrarse entre unos límites inferior y superior de valores críticos que han sido tabulados por Durbin (1969). Si bien hay que tener presente que el valor \(p_o\) no se considera en el cálculo del estadístico esto es, \(p_o=\hat v_1=0\)
td <- function(y,significance) {
# Author: Francisco Parra Rodríguez
# Some ideas from:
#Harvey, A.C. (1978), Linear Regression in the Frequency Domain, International Economic Review, 19, 507-512.
# DURBIN, J., "Tests for Serial Correlation in Regression Analysis based on the Periodogram ofLeast-Squares Residuals," Biometrika, 56, (No. 1, 1969), 1-15.
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
per <- periodograma(y)
p <- as.numeric(per$densidad)
n <- length(p)
s <- p[1]
t <- 1:n
for(i in 2:n) {s1 <-p[i]+s[(i-1)]
s <- c(s,s1)
s2 <- s/s[n]
}
while (n > 100) n <- 100
if (significance==1) c<- c(TestD[n,1]) else {if (significance==2) c <- c(TestD[n,2]) else {if (significance==3) c <- c(TestD[n,3]) else {if (significance==4) c <- c(TestD[n,4])
c <- c(TestD[n,5])}}}
min <- -c+(t/length(p))
max <- c+(t/length(p))
data.frame(s2,min,max)
} Fuction gtd (a,b)
Presenta graficamente los resultados de la prueba de Durbin (Durbin; 1969) :
gtd <- function (y,significance) {
S <- td(y,significance)
plot(ts(S), plot.type="single", lty=1:3,main = "Test Durbin",
ylab = "densidad acumulada",
xlab="frecuencia")
}Función rbs (a,b,A)
Realiza la regresión band spectrum del vector de datos “a”" con el vector de datos “b” con el filtro de frecuencias “A”. “A” debe ser un vector de tamaño \(n\) con 0 en las frecuencias de senos y cosenos que se desean eliminar.
Hannan (1963) fue quien propuso la regresión en dominio de la frecuencia (regresión band spectrum). Engle (1974), demostró que dicha regresión no alteraba los supuestos básicos de la regresión clásica, cuyos estimadores eran Estimadores Lineales Insesgados y Optimos (ELIO).
\[\begin{equation} y=X\beta+u \end{equation}\] (4)
donde \(X\) es una matriz \(n x k\) de observaciones de \(k\) variables independientes, \(\beta\) es un vecto \(k x I\) de parámetros, \(y\) es un vecto \(n x 1\) de observaciones de la variable dependiente, y \(u\) en un vector \(n x I\) de pertubacciones de media cero y varianza constante, \(\sigma^2\).
El modelo puese expresarse en el dominio de la frecuencia aplicando una transformación lineal a las variables dependiente e independientes,por ejemplo, premultiplicando todas las variables por la matriz ortogonal \(W\). La técnica de la “regresión band spectrum”,consiste en realizar el analisis de regresión en el dominio de la frecuencia pero omitinedo determinadas oscilaciones periodicas. Con este procedimiento pueden tratarse problemas derivados de la estacionalidad de las series o de autocorrelación en los residuos. Engle (1974) muesta que si los residuos están correlacionados serialmente y son generados por un procieso estacionario estocastico, la regresión en el dominio de la frecuencia es el estimador asintóticamente más eficiente de \(\beta\).
La transformación de la ecuación (4) del dominio del tiempo al dominio de la frecuencia en Engle (1974), se basa en la matriz \(W\), cuyo elemento \((t, s)\) esta dado por:
\(w_{ts}=\frac{1}{\sqrt n} e^{i\lambda_t s}\),\(s= 0,1,...,n-1\)
donde \(\lambda_t = 2\pi \frac{t}n\), \(t=0,1,...,n-1\), y \(i=\sqrt{-1}\).
Premultiplicando las observaciones de (4) por \(W\), obtenemos: \[\begin{equation} \dot y=\dot X\beta+\dot u \end{equation}\] (5)
donde \(\dot y = Wy\),\(\dot X = WX\), y \(\dot u = Wu\).
Si el vector de las perturbaciones en (4) cumple las hipoteis clásicas del modelo de regresión: \(E[u] = 0\) y \(E[uu']=\sigma^2 I_n\). entonces el vector de perturbaciones transformado al dominio de la frecuencia, \(\dot u\), tendrá las mims propiedades. Por otro lado, dado que la matriz W es ortogonal., \(WW^{T}= I\), entonces \(W^T\) sería la transpuesta de la completa conjugada de W. De forma que las observaciones del modelo (5) acaban conteniendo el mismo tipo de información que las observaciones del modelo inicialmente planteado.
Si aplicamos MCO a (5) , dadas las propiedades de \(\dot u\), obtendríamos el mejor estimador lineal insesgando (ELIO) de \(\dot \beta\). El estimador obtenido sería de hecho identico al estimador MCO de (4).
Estimar (5) manteniendo unicamente determinadas frecuencias, puede llevarse a cabo omitiendo las observaciones correspondientes a las restantes frecuencias, si bien, dado que las variables en (5) son complejas, Engle (1974) sugiere la transformada inversa de Fourier para recomponer el modelo estimado en términos de tiempo.
Definiendo una matriz de tamaño \(A\) de tamaño n x n de ceros excepto en las posiciones de la diagonal principal correspondientes a las frecuencias que queremos incluir en la regresión y premultiplicando \(\dot y\) y \(\dot X\) por \(A\) eleminamos determindas observaciones y las reemplazamos por ceros para realizar la regresión band spectrum. Devolver al dominio del tiempo estas observaciones requiere:
\[\begin{equation} y^* = W^{T}A\dot y = W^{T}AWy \\ x^* = W^{T}A\dot x = W^{T}AWx \end{equation}\] (6)
Al regresar \(y^*\) sobre \(x^*\) obtenemos un \(\beta\) identico al estimador que obtendríamos al estimar por MCO \(\dot y\) frente a \(\dot x\).
Cuando se realiza la regresión band spectrum de esta mnera, ocurre un problema asociado a los grados de libertad de la regresión de \(y^*\) sobre \(x^*\) que asumen los programas estadisticos convencionales, \(n - k\), en vez de los grados de libertad reales que serían unicamente \(n'- k\), donde \(n'\) es el numero de frecuencias incluidas en la regresión band spectrum.
Si la regresión espectral va a ser usada para obtener un estimador asintóticamente eficiente de \(\beta\) en presencia de autocorrelación en el termino de error, la matriz \(A\) ha de ser reemplazada por otra matriz diagonal, \(V\). En dicha diagonal principal ha de incluirse el estimador de \(\int_u^{1/2}(\lambda)\), donde \(\int_u (\lambda)\) es el la transformación del termino de error obtenido en (4) al dominio de la frecuencia \(\lambda\). Puede utilizarse un programa convencional para obtener \(\beta\) haciendo una transformación análoga a (6); ver Engle and Gardner [1976]. Sin embargo, si el procedimiento va a ser iterativo, lo que podría llevar a una mejora en las propiededes de las muestra pequeñas, la transformada inversa de fourier debería emplearse en cada iteración.
rbs <- function(a,b,A) {
a <- matrix(a, nrow=1)
n <- length(a)
unos <- rep(1,n)
lm1 <- lm(diag(A)%*%gdf(a) ~ 0 + diag(A)%*%gdf(b) + diag(A)%*%gdf(unos))
summary <- summary(lm1)
fitted <- gdt(lm1$fitted)
residuals <- gdt(lm1$residuals)
list(summary=summary,fitted=c(fitted),residuals=c(residuals))
}Función rdf (a)
Realiza la regresión en el dominio de la frecuencia de los vectores “a” y “b”,seleccionando las frecuencias más relevantes a partir del co-espectro.
Consideramos ahora el modelo de regresión siguiente:
\[\begin{equation} y_t=\beta_tx_t+u_t \end{equation}\] (7)
donde \(x_t\) es un vector n x 1 de observaciones de las variable independiente, \(\beta_t\) es un vector de n x 1 parametros, \(y_t\) es un vector de n x 1 observaciones de la variable depenendiente, y \(u_t\) es un vector de errores distribuidos con media cero y varianza constante.
Asumiendo que las series, \(y_t\),\(x_t\),\(\beta_t\) and \(ut\), pueden ser transformadas en el dominio de la frecuencia:
\[y_t=\eta^y+\sum_{j=1}^N[a^y_j\cos(\omega_j)+b^y_j\sin(\omega_j)\]
\[x_t=\eta^x+\sum_{j=1}^N[a^y_j\cos(\omega_j)+b^y_j\sin(\omega_j)]\]
\[ \beta_t=\eta^\beta+\sum_{j=1}^N[a^\beta_j\cos(\omega_j)+b^\beta_j\sin(\omega_j)]\]
Otenemos dichas series pre-multiplicando (7) por \(W\)
\(\dot y=\dot x\dot\beta+\dot u\) (8)
donde \(\dot y = Wy\),\(\dot x = Wx\), \(\dot \beta = W\beta\) y \(\dot u = Wu\)
El sistema (8) puede reescribirse como:
\[\begin{equation} \dot y=Wx_tI_nW^T\dot \beta + WI_nW^T\dot u \end{equation}\]
Si denominamos \(\dot e=WI_nW^T\dot u\), podrían buscarse los \(\dot \beta\) que minimizaran la suma cuadrática de los errores \(e_t=W^T\dot e\).
Una vez encontrada la solución a dicha optimización, se transformarían las series al dominio del tiempo para obtener el sistema (7).
El algoritmo de calculo se realiza en las siguentes fases:
- Calcula el co-espectro de la serie “x” e “y”
Sea \(x\) un vector n x 1 el modelo transformado en el dominio de la frecuencia esta dado por:
\(\hat x= Wx\)
Sea \(y\) un vector n x 1 el modelo transformado en el dominio de la frecuencia esta dado por:
\(\hat y= Wy\)
Denominando \(p_j\) el ordinal del cross-periodograma de \(\hat x\) y \(\hat y\) en la frecuencia \(\lambda_j=2\pi j/n\), y \(\hat x_j\) el j-th elemento de \(\hat x\) y \(\hat y_j\) el j-th elemento de \(\hat y\), entonces
\[ \left\lbrace \begin{array}{ll} p_j=\hat x_{2j}\hat y_{2j}+\hat x_{2j+1}\hat y_{2j+1} & \forall j = 1,...\frac{n-1}{2}\\ p_j=\hat x_{2j}\hat y_{2j}& \forall j = \frac{n}{2}-1 \end{array} \right . \]
\[p_0=\hat x_{1}\hat y_{1}\]
Ordena el co-espectro en base al valor absoluto de \(|p_j|\) y genera un índice en base a ese orden para cada coeficiente de fourier.
Calcula la matriz \(Wx_tI_nW^T\) y la ordena en base a el indice anterior.
Obtiene \(\dot e=WI_nW^T\dot u\), incluyendo el vector correspondiente al parámetro constante, \((1,0,...0)^n\), y calucula el modelo utilizando los dos primeros regresores de la matriz \(Wx_tI_nW^T\) reordenada y ampliadas, calcula el modelo para los 4 primeros, para los 6 primeros, hasta completar los \(n\) regresores de la matriz.
Realiza el test de durbin a los modelos estimados, y selecciona aquellos en donde los \(e_t=W^T\dot e\) están dentro de las bandas elegidas a los niveles de significación \(\alpha=0.1;0.05;0.025;0.01;0.005\).
De todos ellos elige aquel que tiene menos regresores. Si no encuentra modelo ofrece el aviso.
rdf <- function (y,x,significance) {
# Author: Francisco Parra Rodríguez
# http://rpubs.com/PacoParra/24432
# Leemos datos en forma matriz
a <- matrix(y, nrow=1)
b <- matrix(x, nrow=1)
n <- length(a)
# calculamos el cros espectro mediante la funcion cperiodograma
cperiodograma <- function(y,x) {
# Author: Francisco Parra Rodríguez
# http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/
cfx <- gdf(y)
n <- length(y)
cfy <- gdf(x)
if (n%%2==0) {
m1x <- c(0)
m2x <- c()
for(i in 1:n){
if(i%%2==0) m1x <-c(m1x,cfx[i]) else m2x <-c(m2x,cfx[i])}
m2x <- c(m2x,0)
m1y <- c(0)
m2y <- c()
for(i in 1:n){
if(i%%2==0) m1y <-c(m1y,cfy[i]) else m2y <-c(m2y,cfy[i])}
m2y <-c(m2y,0)
frecuencia <- seq(0:(n/2))
frecuencia <- frecuencia-1
omega <- pi*frecuencia/(n/2)
periodos <- n/frecuencia
densidad <- (m1x*m1y+m2x*m2y)/(4*pi)
tabla <- data.frame(omega,frecuencia, periodos,densidad)
tabla$densidad[(n/2+1)] <- 4*tabla$densidad[(n/2+1)]
data.frame(tabla[2:(n/2+1),])}
else {m1x <- c(0)
m2x <- c()
for(i in 1:(n-1)){
if(i%%2==0) m1x <-c(m1x,cfx[i]) else m2x <-c(m2x,cfx[i])}
m2x <-c(m2x,cfx[n])
m1y <- c(0)
m2y <- c()
for(i in 1:(n-1)){
if(i%%2==0) m1y <-c(m1y,cfy[i]) else m2y <-c(m2y,cfy[i])}
m2y <-c(m2y,cfy[n])
frecuencia <- seq(0:((n-1)/2))
frecuencia <- frecuencia-1
omega <- pi*frecuencia/(n/2)
periodos <- n/frecuencia
densidad <- (m1x*m1y+m2x*m2y)/(4*pi)
tabla <- data.frame(omega,frecuencia, periodos,densidad)
data.frame(tabla[2:((n+1)/2),])}
}
cper <- cperiodograma(a,b)
# Ordenamos de mayor a menor las densidades absolutas del periodograma, utilizando la funcion "sort.data.frame" function, Kevin Wright. Package taRifx
S1 <- data.frame(f1=cper$frecuencia,p=abs(cper$densidad))
S <- S1[order(-S1$p),]
id <- seq(2,n)
m1 <- cbind(S$f1*2,evens(id))
if (n%%2==0) {m2 <- cbind(S$f1[1:(n/2-1)]*2+1,odds(id))} else
{m2 <- cbind(S$f1*2+1,odds(id))}
m <- rbind(m1,m2)
colnames(m) <- c("f1","id")
M <- sort.data.frame (m,formula=~id)
M <- rbind(c(1,1),M)
# Obtenemos la funcion auxiliar (cdf) del predictor y se ordena segun el indice de las mayores densidades absolutas del co-espectro.
cx <- cdf(b)
id <- seq(1,n)
S1 <- data.frame(cx,c=id)
S2 <- merge(M,S1,by.x="id",by.y="c")
S3 <- sort.data.frame (S2,formula=~f1)
m <- n+2
X1 <- S3[,3:m]
X1 <- rbind(C=c(1,rep(0,(n-1))),S3[,3:m])
# Se realizan las regresiones en el dominio de la frecuencia utilizando un modelo con constante, pendiente y los arm?nicos correspondientes a las frecuencias mas altas de la densidad del coespectro. Se realiza un test de durbin para el residuo y se seleccionan aquellas que son significativas.
par <- evens(id)
i <- 1
D <- 1
resultado <- cbind(i,D)
for (i in par) {
X <- as.matrix(X1[1:i,])
cy <- gdf(a)
B1 <- solve(X%*%t(X))%*%(X%*%cy)
Y <- t(X)%*%B1
F <- gdt(Y)
res <- (t(a) - F)
T <- td(res,significance)
L <- as.numeric(c(T$min<T$s2,T$s2<T$max))
LT <- sum(L)
if (n%%2==0) {D=LT-n} else {D=LT-(n-1)}
resultado1 <- cbind(i,D)
resultado <- rbind(resultado,resultado1)
resultado}
resultado2 <-data.frame(resultado)
criterio <- resultado2[which(resultado2$D==0),]
sol <- as.numeric(is.na(criterio$i[1]))
if (sol==1) {
X <- as.matrix(X1[1:2,])
cy <- gdf(a)
B1 <- solve(X%*%t(X))%*%(X%*%cy)
Y <- t(X)%*%B1
F <- gdt(Y)
res <- (t(a) - F)
datos <- data.frame(cbind(t(a),t(b),F,res))
colnames(datos) <- c("Y","X","F","res")
list(datos=datos,Fregresores=t(X),Tregresores= t(MW(n))%*%t(X),Nregresores=criterio$i[1],Betas=B1) } else {
X <- as.matrix(X1[1:criterio$i[1],])
cy <- gdf(a)
B1 <- solve(X%*%t(X))%*%(X%*%cy)
Y <- t(X)%*%B1
F <- gdt(Y)
res <- (t(a) - F)
datos <- data.frame(cbind(t(a),t(b),F,res))
colnames(datos) <- c("Y","X","F","res")
list(datos=datos,Fregresores=t(X),Tregresores= t(MW(n))%*%t(X),Nregresores=criterio$i[1],Betas=B1)}
}Función descomponer(y,frequency,type)
En base al modelo de regresión en el dominio de la frecuencia descompone una serie \(y_t\) en los factores de tendencia \(TD\), estacionales \(ST\), e irregulares \(IR\).
La función se desarrolla en los siguientes pasos:
Se calcula el periodograma de la serie, y se ordena según el vector de frecuencias para crear diferentes indices de orden.
Se obtiene un modelo de tendencia, a partir de las frecuencias mayores que \(\frac{n}{2*frequency}\) si la serie es par ó mayeros que \(\frac{n-1}{2*frequency}\) si la serie es impar. Para ello, se realiza la regresión en domininio de la frecuencia entre la serie \(y_t\) y los regresores que se obtienen con la matriz auxiliar \(Wx_tI_nW^T\), donde \(x_t\) es el resultado de ajustar un modelo lineal del tipo \(y_t=a+bt+e_t\) a la serie de datos (tipo=1) ó un modelo cuadrático del tipo \(y_t=a+bt+ct^2+e_t\), en donde solo se consideran los regresores correspondientes a las diferentes frecuencias seleccionadas.Una vez obtenidos los parámetros del modelo, se calcula la serie en el dominio de la frecuencia que una vez convierten al dominio del tiempo da como resultado la serie de tendencia \(TD\).
Se obtiene la serie residual \(IRST=y_t-TD\), se y sobre esa serie se realiza una nueva selección de frecuencias, las correspondientes a los factores estacionales es decir:\(\frac{n}{2*frequency}\), \(\frac{2n}{2*frequency}\),\(\frac{3n}{2*frequency}\), etc….. Se realiza la regresión en el dominio de la frecuencia entre \(IRST\) y los regresores correspondientes a las frecuencias seleccionadas obtenidas a partir de a matriz auxiliar \(Wx_tI_nW^T\), donde \(x_t\) es el resultado de ajustar un modelo lineal del tipo \(IRST=a+bt+e_t\) a la serie de datos (tipo=1) ó un modelo cuadrático del tipo \(IRST=a+bt+ct^2+e_t\). Una vez obtenidos los parámetros del modelo, se calcula la serie en el dominio de la frecuencia que una vez convierten al dominio del tiempo da como resultado la serie de tendencia \(ST\).
Se obtiene la serie irregular a partir de \(IR=IRST-ST\).
Nueva versión de la función descomponer:
descomponer <- function (y,frequency,type) {
# Author: Francisco Parra Rodriguez
# http://rpubs.com/PacoParra/24432
# date:"y", frequency:"frequency".
# Use 7 for frequency when the data are sampled daily, and the natural time period is a week,
# or 4 and 12 when the data are sampled quarterly and monthly and the natural time period is a year.
n <- length(y)
y <- matrix(y,ncol=1)
f1 <- NULL
if(n%%2==0) {f2 <- n/(2*frequency)} else {
f2 <- (n-1)/(2*frequency)}
#Modelo para obtener serie con tendencia
c <- seq(from=2, to=(2+(n/frequency) ))
#Use the "sort.data.frame" function, Kevin Wright. Package taRifx
i <- seq(1:n)
i2 <- i*i
if (type==1)
{eq <- lm(y~i)
z <- eq$fitted} else {
if (type==2) eq <- lm(y~i+i2)
z <- eq$fitted}
cx <- cdf(z)
id <- seq(1,n)
S1 <- data.frame(cx)
S2 <- S1[1:(2+(n/frequency)),]
X <- as.matrix(S2)
cy <- gdf(y)
B <- solve(X%*%t(X))%*%(X%*%cy)
Y <- t(X)%*%B
BTD <- B
XTD <- t(MW(n))%*%t(X)
TD <- gdt(Y)
# Genero la serie residual
IRST <- y-TD
# Realizo la regresión dependiente de la frecienca utilizando como explicativa IRST.
# modelo para obtener serie con estacionalidad con trunc ó round.
frecuencia <- seq(0:(n/2))
frecuencia <- frecuencia-1
S <- data.frame(f1=frecuencia)
sel <- subset(S,f1==trunc(2*f2))
c <- seq(from=2,to=(n/f2))
for (i in c) {sel1 <- subset(S,f1==i*trunc(2*f2))
sel <- rbind(sel,sel1)}
m1 <- c(sel$f1 * 2)
m2 <- c(m1+1)
c <- c(m1,m2)
n3 <- length(c)
d <- rep(1,n3)
s <- data.frame(c,d)
S <- sort.data.frame (s,formula=~c)
#Use the "sort.data.frame" function, Kevin Wright. Package taRifx
# Se realiza el ejercicio con los datos del año completo
l <- frequency*trunc(n/frequency)
i <- seq(1:l)
i2 <- i*i
if (type==1)
{eq <- lm(y[1:l]~i)
z <- eq$fitted} else {
if (type==2) eq <- lm(y[1:l]~i+i2)
z <- eq$fitted}
cx <- cdf(z)
id <- seq(1,l)
S1 <- data.frame(cx,c=id)
S2 <- merge(S,S1,by.x="c",by.y="c")
S3 <- rbind(c(1,1,cx[1,]),S2)
m <- l+2
X1 <- S3[,3:m]
# matriz de regresores a l
X1 <- as.matrix(X1)
# la paso al dominio del tiempo
X2 <- data.frame(t(MW(l))%*%t(X1))
if (n==l) X3 <- X2 else
X3 <- rbind(X2,X2[1:(n-l),])
# la paso al dominio de la frecuencia
X4 <-MW(n)%*%as.matrix(X3)
cy <- gdf(IRST)
B1 <- solve(t(X4)%*%X4)%*%(t(X4)%*%cy)
Y <- X4%*%B1
BST <- B1
XST <- t(MW(n))%*%X4
ST <- gdt(Y)
TDST <- TD+ST
IR <- IRST-ST
data <- data.frame(y,TDST,TD,ST,IR)
regresoresTD <- data.frame(XTD)
regresoresST <- data.frame(XST)
list(datos=data,regresoresTD=regresoresTD,regresoresST=regresoresST,coeficientesTD=BTD,coeficientesST=BST)}Ejemplo: Regresión consumo energía electrica y PIB
Datos de energía y PIB españa:
celec <- c(12458,12822,13345,14288,15309,16207,17290,17805,19037,19915,20867,21543,21935,22253,21757,22409,20636,20663,19952)
PIB <- c(65.726893627466,67.4849070579256,69.9748367116452,72.9879275245349,76.2613328315868,80.2948751495255,83.5075398872297,85.9123891441976,88.6508975712911,91.4582554354157,94.863281682855,98.8229948578551,102.54758058591,103.691935100126,99.9861932591599,100,99.3823739745937,97.3065369287316,96.1097074148)Analisis PIB
periodograma(PIB)## omega frecuencia periodos densidad
## 2 0.3306940 1 19.000000 183.834066
## 3 0.6613879 2 9.500000 17.837461
## 4 0.9920819 3 6.333333 9.647461
## 5 1.3227759 4 4.750000 6.704018
## 6 1.6534698 5 3.800000 2.880418
## 7 1.9841638 6 3.166667 2.301889
## 8 2.3148577 7 2.714286 2.662076
## 9 2.6455517 8 2.375000 2.505850
## 10 2.9762457 9 2.111111 1.810210plot(ts(PIB), plot.type="single", lty=1:3)
gperiodograma (PIB)
gtd (PIB,3)
Periodograma del PIB y representación gráfica a través de la FFT:
densidad <- Mod(fft(PIB))^2/length(PIB)
plot(densidad[2:10],type="l")
# periodogramas acumulados
gtd(PIB,3)
cpgram(PIB)
Analisis Consumo de electricidad
periodograma(celec)## omega frecuencia periodos densidad
## 2 0.3306940 1 19.000000 13891050.15
## 3 0.6613879 2 9.500000 1211590.40
## 4 0.9920819 3 6.333333 571726.35
## 5 1.3227759 4 4.750000 237655.16
## 6 1.6534698 5 3.800000 204650.06
## 7 1.9841638 6 3.166667 221402.88
## 8 2.3148577 7 2.714286 196405.87
## 9 2.6455517 8 2.375000 192040.45
## 10 2.9762457 9 2.111111 38013.19plot(ts(celec), plot.type="single", lty=1:3)
gperiodograma (celec)
gtd (celec,3)
Regresión MCO entre el consumo energía electrica y PIB
lm1 <- lm(celec ~ PIB)
plot(PIB,celec,pch=19,col="blue")
lines(PIB,lm1$fitted,lwd=3,col="red")
summary(lm1)##
## Call:
## lm(formula = celec ~ PIB)
##
## Residuals:
## Min 1Q Median 3Q Max
## -818.00 -233.29 -40.81 190.04 789.55
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5167.470 708.616 -7.292 1.26e-06 ***
## PIB 267.869 7.961 33.649 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 428.1 on 17 degrees of freedom
## Multiple R-squared: 0.9852, Adjusted R-squared: 0.9843
## F-statistic: 1132 on 1 and 17 DF, p-value: < 2.2e-16plot(lm1$residuals,celec,pch=19,col="blue")
gperiodograma (lm1$residuals)
gtd (lm1$residuals,3)
Regresión consumo energía electrica y PIB en el dominio de la frecuencia
unos <- rep(1,19)
lm2 <- lm(gdf(celec) ~ 0 + gdf(PIB) + gdf(unos))
summary(lm2)##
## Call:
## lm(formula = gdf(celec) ~ 0 + gdf(PIB) + gdf(unos))
##
## Residuals:
## Min 1Q Median 3Q Max
## -888.3 -137.5 116.5 317.9 790.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## gdf(PIB) 267.869 7.961 33.649 < 2e-16 ***
## gdf(unos) -5167.470 708.616 -7.292 1.26e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 428.1 on 17 degrees of freedom
## Multiple R-squared: 0.9995, Adjusted R-squared: 0.9995
## F-statistic: 1.82e+04 on 2 and 17 DF, p-value: < 2.2e-16Regresión band spectrum del consumo de electricidad y el PIB utilizando el filtro \(A=(1,1,1,1,1,1,1,1,1,0,...,0)^{19}\).
A=c(rep(1,9),rep(0,10))
rbs(celec,PIB,A)## $summary
##
## Call:
## lm(formula = diag(A) %*% gdf(a) ~ 0 + diag(A) %*% gdf(b) + diag(A) %*%
## gdf(unos))
##
## Residuals:
## Min 1Q Median 3Q Max
## -866.9 0.0 0.0 104.1 796.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## diag(A) %*% gdf(b) 268.730 6.719 39.995 < 2e-16 ***
## diag(A) %*% gdf(unos) -5243.346 597.801 -8.771 1.02e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 351.7 on 17 degrees of freedom
## Multiple R-squared: 0.9997, Adjusted R-squared: 0.9996
## F-statistic: 2.694e+04 on 2 and 17 DF, p-value: < 2.2e-16
##
##
## $fitted
## [1] 14556.68 12359.29 12904.91 14630.84 15714.22 16119.88 16844.04
## [8] 18020.30 18864.25 19220.42 19951.16 21428.08 22615.07 22450.15
## [15] 21537.02 21370.51 21965.95 21437.88 18500.37
##
## $residuals
## [1] -107.668995 19.428378 -130.859102 -191.588820 -30.522729
## [6] 80.672535 -9.719923 -14.562077 332.213390 738.160229
## [11] 652.883983 65.495250 -381.067916 -215.794504 223.979788
## [16] 258.605027 -209.332279 -600.140323 -480.181913rbs1 <- rbs(celec,PIB,A)
plot(PIB,celec,pch=19,col="blue")
lines(PIB,rbs1$fitted,lwd=3,col="red")
gtd(rbs1$residuals,3)
Regresión band spectrum del consumo de electricidad y el PIB utilizando el filtro \(A=(1,..,1)^{19}\).
A=c(rep(1,19))
rbs(celec,PIB,A)## $summary
##
## Call:
## lm(formula = diag(A) %*% gdf(a) ~ 0 + diag(A) %*% gdf(b) + diag(A) %*%
## gdf(unos))
##
## Residuals:
## Min 1Q Median 3Q Max
## -888.3 -137.5 116.5 317.9 790.2
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## diag(A) %*% gdf(b) 267.869 7.961 33.649 < 2e-16 ***
## diag(A) %*% gdf(unos) -5167.470 708.616 -7.292 1.26e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 428.1 on 17 degrees of freedom
## Multiple R-squared: 0.9995, Adjusted R-squared: 0.9995
## F-statistic: 1.82e+04 on 2 and 17 DF, p-value: < 2.2e-16
##
##
## $fitted
## [1] 12438.74 12909.66 13576.63 14383.74 15260.59 16341.05 17201.62
## [8] 17845.81 18579.37 19331.38 20243.48 21304.16 22301.86 22608.40
## [15] 21615.75 21619.45 21454.00 20897.95 20577.36
##
## $residuals
## [1] 19.26218 -87.65540 -231.63076 -95.74486 48.41081 -134.05078
## [7] 88.37542 -40.80953 457.62852 583.62394 623.52242 238.83738
## [13] -366.86426 -355.40155 141.25240 789.55400 -818.00303 -234.95031
## [19] -625.35659rbs1 <- rbs(celec,PIB,A)
plot(PIB,celec,pch=19,col="blue")
lines(PIB,rbs1$fitted,lwd=3,col="red")
gtd(rbs1$residuals,3)
Realiza la regresión dependiente de la frecuencia entre el PIB y Celec.
reg1 <- rdf (celec,PIB,3)
reg1## $datos
## Y X F res
## 1 12458 65.72689 12438.74 19.26218
## 2 12822 67.48491 12909.66 -87.65540
## 3 13345 69.97484 13576.63 -231.63076
## 4 14288 72.98793 14383.74 -95.74486
## 5 15309 76.26133 15260.59 48.41081
## 6 16207 80.29488 16341.05 -134.05078
## 7 17290 83.50754 17201.62 88.37542
## 8 17805 85.91239 17845.81 -40.80953
## 9 19037 88.65090 18579.37 457.62852
## 10 19915 91.45826 19331.38 583.62394
## 11 20867 94.86328 20243.48 623.52242
## 12 21543 98.82299 21304.16 238.83738
## 13 21935 102.54758 22301.86 -366.86426
## 14 22253 103.69194 22608.40 -355.40155
## 15 21757 99.98619 21615.75 141.25240
## 16 22409 100.00000 21619.45 789.55400
## 17 20636 99.38237 21454.00 -818.00303
## 18 20663 97.30654 20897.95 -234.95031
## 19 19952 96.10971 20577.36 -625.35659
##
## $Fregresores
## C 2
## X1 1 88.15633993
## X2 0 -5.68444066
## X3 0 -9.44842664
## X4 0 -2.21612470
## X5 0 -2.62417085
## X6 0 -0.79654035
## X7 0 -2.39713113
## X8 0 -1.53918673
## X9 0 -1.43696240
## X10 0 -1.18967167
## X11 0 -0.69982515
## X12 0 -0.92147259
## X13 0 -0.82056671
## X14 0 -1.14883221
## X15 0 -0.66396512
## X16 0 -1.26963244
## X17 0 -0.21300835
## X18 0 -1.09411224
## X19 0 -0.01302396
##
## $Tregresores
## C 2
## [1,] 0.2294157 15.07878
## [2,] 0.2294157 15.48210
## [3,] 0.2294157 16.05333
## [4,] 0.2294157 16.74458
## [5,] 0.2294157 17.49555
## [6,] 0.2294157 18.42091
## [7,] 0.2294157 19.15794
## [8,] 0.2294157 19.70965
## [9,] 0.2294157 20.33791
## [10,] 0.2294157 20.98196
## [11,] 0.2294157 21.76313
## [12,] 0.2294157 22.67155
## [13,] 0.2294157 23.52603
## [14,] 0.2294157 23.78856
## [15,] 0.2294157 22.93841
## [16,] 0.2294157 22.94157
## [17,] 0.2294157 22.79988
## [18,] 0.2294157 22.32365
## [19,] 0.2294157 22.04908
##
## $Nregresores
## [1] 2
##
## $Betas
## [,1]
## C -22524.479
## 2 1167.615plot(reg1$datos$X,reg1$datos$Y,pch=19,col="blue")
lines(reg1$datos$X,reg1$datos$F,col="red")
gtd (reg1$datos$res,3)
reg2 <- rdf (celec,PIB,2)
reg2## $datos
## Y X F res
## 1 12458 65.72689 12438.74 19.26218
## 2 12822 67.48491 12909.66 -87.65540
## 3 13345 69.97484 13576.63 -231.63076
## 4 14288 72.98793 14383.74 -95.74486
## 5 15309 76.26133 15260.59 48.41081
## 6 16207 80.29488 16341.05 -134.05078
## 7 17290 83.50754 17201.62 88.37542
## 8 17805 85.91239 17845.81 -40.80953
## 9 19037 88.65090 18579.37 457.62852
## 10 19915 91.45826 19331.38 583.62394
## 11 20867 94.86328 20243.48 623.52242
## 12 21543 98.82299 21304.16 238.83738
## 13 21935 102.54758 22301.86 -366.86426
## 14 22253 103.69194 22608.40 -355.40155
## 15 21757 99.98619 21615.75 141.25240
## 16 22409 100.00000 21619.45 789.55400
## 17 20636 99.38237 21454.00 -818.00303
## 18 20663 97.30654 20897.95 -234.95031
## 19 19952 96.10971 20577.36 -625.35659
##
## $Fregresores
## C 2
## X1 1 88.15633993
## X2 0 -5.68444066
## X3 0 -9.44842664
## X4 0 -2.21612470
## X5 0 -2.62417085
## X6 0 -0.79654035
## X7 0 -2.39713113
## X8 0 -1.53918673
## X9 0 -1.43696240
## X10 0 -1.18967167
## X11 0 -0.69982515
## X12 0 -0.92147259
## X13 0 -0.82056671
## X14 0 -1.14883221
## X15 0 -0.66396512
## X16 0 -1.26963244
## X17 0 -0.21300835
## X18 0 -1.09411224
## X19 0 -0.01302396
##
## $Tregresores
## C 2
## [1,] 0.2294157 15.07878
## [2,] 0.2294157 15.48210
## [3,] 0.2294157 16.05333
## [4,] 0.2294157 16.74458
## [5,] 0.2294157 17.49555
## [6,] 0.2294157 18.42091
## [7,] 0.2294157 19.15794
## [8,] 0.2294157 19.70965
## [9,] 0.2294157 20.33791
## [10,] 0.2294157 20.98196
## [11,] 0.2294157 21.76313
## [12,] 0.2294157 22.67155
## [13,] 0.2294157 23.52603
## [14,] 0.2294157 23.78856
## [15,] 0.2294157 22.93841
## [16,] 0.2294157 22.94157
## [17,] 0.2294157 22.79988
## [18,] 0.2294157 22.32365
## [19,] 0.2294157 22.04908
##
## $Nregresores
## [1] 2
##
## $Betas
## [,1]
## C -22524.479
## 2 1167.615plot(reg2$datos$X,reg2$datos$Y,pch=19,col="blue")
lines(reg2$datos$X,reg2$datos$F,col="red")
gtd (reg2$datos$res,2)
reg3 <- rdf (celec,PIB,1)
reg3## $datos
## Y X F res
## 1 12458 65.72689 12438.74 19.26218
## 2 12822 67.48491 12909.66 -87.65540
## 3 13345 69.97484 13576.63 -231.63076
## 4 14288 72.98793 14383.74 -95.74486
## 5 15309 76.26133 15260.59 48.41081
## 6 16207 80.29488 16341.05 -134.05078
## 7 17290 83.50754 17201.62 88.37542
## 8 17805 85.91239 17845.81 -40.80953
## 9 19037 88.65090 18579.37 457.62852
## 10 19915 91.45826 19331.38 583.62394
## 11 20867 94.86328 20243.48 623.52242
## 12 21543 98.82299 21304.16 238.83738
## 13 21935 102.54758 22301.86 -366.86426
## 14 22253 103.69194 22608.40 -355.40155
## 15 21757 99.98619 21615.75 141.25240
## 16 22409 100.00000 21619.45 789.55400
## 17 20636 99.38237 21454.00 -818.00303
## 18 20663 97.30654 20897.95 -234.95031
## 19 19952 96.10971 20577.36 -625.35659
##
## $Fregresores
## C 2
## X1 1 88.15633993
## X2 0 -5.68444066
## X3 0 -9.44842664
## X4 0 -2.21612470
## X5 0 -2.62417085
## X6 0 -0.79654035
## X7 0 -2.39713113
## X8 0 -1.53918673
## X9 0 -1.43696240
## X10 0 -1.18967167
## X11 0 -0.69982515
## X12 0 -0.92147259
## X13 0 -0.82056671
## X14 0 -1.14883221
## X15 0 -0.66396512
## X16 0 -1.26963244
## X17 0 -0.21300835
## X18 0 -1.09411224
## X19 0 -0.01302396
##
## $Tregresores
## C 2
## [1,] 0.2294157 15.07878
## [2,] 0.2294157 15.48210
## [3,] 0.2294157 16.05333
## [4,] 0.2294157 16.74458
## [5,] 0.2294157 17.49555
## [6,] 0.2294157 18.42091
## [7,] 0.2294157 19.15794
## [8,] 0.2294157 19.70965
## [9,] 0.2294157 20.33791
## [10,] 0.2294157 20.98196
## [11,] 0.2294157 21.76313
## [12,] 0.2294157 22.67155
## [13,] 0.2294157 23.52603
## [14,] 0.2294157 23.78856
## [15,] 0.2294157 22.93841
## [16,] 0.2294157 22.94157
## [17,] 0.2294157 22.79988
## [18,] 0.2294157 22.32365
## [19,] 0.2294157 22.04908
##
## $Nregresores
## [1] 2
##
## $Betas
## [,1]
## C -22524.479
## 2 1167.615plot(reg3$datos$X,reg3$datos$Y,pch=19,col="blue")
lines(reg3$datos$X,reg3$datos$F,col="red")
gtd (reg3$datos$res,1)
Ejemplo: Regresión entre el empleo y PIB de canada
Leemos los datos del PIB y empleo de Canada.
data("Canada")
summary(Canada)## e prod rw U
## Min. :928.6 Min. :401.3 Min. :386.1 Min. : 6.700
## 1st Qu.:935.4 1st Qu.:404.8 1st Qu.:423.9 1st Qu.: 7.782
## Median :946.0 Median :406.5 Median :444.4 Median : 9.450
## Mean :944.3 Mean :407.8 Mean :440.8 Mean : 9.321
## 3rd Qu.:950.0 3rd Qu.:410.7 3rd Qu.:461.1 3rd Qu.:10.607
## Max. :961.8 Max. :418.0 Max. :470.0 Max. :12.770PIBC <- as.numeric(Canada[, "prod"])
E <- as.numeric(Canada[, "e"])Periodograma del PIB de Canada y representación gráfica por diferentes metodos metodos
gperiodograma(PIBC)
densidad <- Mod(fft(PIBC))^2/length(PIB)
plot(densidad[2:43],type="l")
# periodogramas acumulados
gtd(PIBC,3)
cpgram(PIBC)
Analisis del empleo de Canada
gperiodograma (E)
gtd (E,3)
Regresion dependiente de la frecuencia entre el PIBC y E con datos del mercado de trabajo de Canada
reg4 <- rdf (PIBC,E,3)
reg4## $datos
## Y X F res
## 1 405.3665 929.6105 404.9961 0.37032757
## 2 404.6398 929.8040 404.8198 -0.17995416
## 3 403.8149 930.3184 404.6978 -0.88288767
## 4 404.2158 931.4277 404.5063 -0.29048691
## 5 405.0467 932.6620 404.1896 0.85707704
## 6 404.4167 933.5509 403.8066 0.61015563
## 7 402.8191 933.5315 403.0031 -0.18398172
## 8 401.9773 933.0769 402.4956 -0.51825046
## 9 402.0897 932.1238 401.9092 0.18048301
## 10 401.3067 930.6359 401.5777 -0.27103857
## 11 401.6302 929.0971 401.3602 0.26999169
## 12 401.5638 928.5633 401.6122 -0.04842846
## 13 402.8157 929.0694 402.3424 0.47332306
## 14 403.1421 930.2655 403.0546 0.08753953
## 15 403.0786 931.6770 403.9432 -0.86459222
## 16 403.7188 932.1390 404.1755 -0.45674396
## 17 404.8668 932.2767 404.4476 0.41920054
## 18 405.6362 932.8328 404.8733 0.76292632
## 19 405.1363 933.7334 405.4818 -0.34551128
## 20 406.0246 934.1772 405.9949 0.02978268
## 21 406.4123 934.5928 406.1861 0.22620643
## 22 406.3009 935.6067 406.5890 -0.28808010
## 23 406.3354 936.5111 406.4411 -0.10574311
## 24 406.7737 937.4201 406.1879 0.58578703
## 25 405.1525 938.4159 405.7419 -0.58935904
## 26 404.9298 938.9992 405.1420 -0.21217378
## 27 404.5765 939.2354 404.7091 -0.13258853
## 28 404.1995 939.6795 404.4974 -0.29794976
## 29 405.9499 940.2497 404.8916 1.05821803
## 30 405.8221 941.4358 405.5990 0.22311498
## 31 406.4463 942.2981 406.4810 -0.03468387
## 32 407.0512 943.5322 407.4302 -0.37895371
## 33 407.9460 944.3490 408.0807 -0.13469579
## 34 408.1796 944.8215 408.5261 -0.34654753
## 35 408.5998 945.0671 408.5272 0.07264907
## 36 409.0906 945.8067 408.8043 0.28623094
## 37 408.7042 946.8697 408.9007 -0.19645881
## 38 408.9803 946.8766 408.6459 0.33442519
## 39 408.3287 947.2497 408.3568 -0.02812911
## 40 407.8857 947.6513 407.9396 -0.05390408
## 41 407.2605 948.1840 407.5486 -0.28809968
## 42 406.7752 948.3492 406.7285 0.04668511
## 43 406.1794 948.0322 405.9115 0.26791213
## 44 405.4398 947.1065 404.7368 0.70295039
## 45 403.2800 946.0796 403.8920 -0.61204814
## 46 403.3649 946.1838 403.6963 -0.33140603
## 47 403.3807 946.2258 403.7474 -0.36676305
## 48 404.0032 945.9978 404.0227 -0.01950711
## 49 404.4774 945.5183 404.1361 0.34134053
## 50 404.7868 945.3514 404.5999 0.18685349
## 51 405.2710 945.2918 404.8398 0.43122386
## 52 405.3830 945.4008 405.2455 0.13745316
## 53 405.1564 945.9058 405.7174 -0.56101542
## 54 406.4700 945.9035 406.0392 0.43085624
## 55 406.2293 946.3190 406.7634 -0.53409498
## 56 406.7265 946.5796 407.3792 -0.65270514
## 57 408.5785 946.7800 408.2582 0.32028221
## 58 409.6767 947.6283 409.1492 0.52754233
## 59 410.3858 948.6221 410.1035 0.28230103
## 60 410.5395 949.3992 410.6546 -0.11509232
## 61 410.4453 949.9481 410.8648 -0.41950262
## 62 410.6256 949.7945 410.7464 -0.12079706
## 63 410.8672 949.9534 410.5557 0.31150147
## 64 411.2359 950.2502 410.7552 0.48070424
## 65 410.6637 950.5380 410.9421 -0.27841924
## 66 410.8085 950.7871 411.4736 -0.66511726
## 67 412.1160 950.8695 411.9627 0.15323537
## 68 412.9994 950.9281 412.3893 0.61012754
## 69 412.9551 951.8457 413.0895 -0.13441613
## 70 412.8241 952.6005 413.2716 -0.44744275
## 71 413.0489 953.5976 413.4971 -0.44822178
## 72 413.6110 954.1434 413.1449 0.46610866
## 73 413.6048 954.5426 412.8570 0.74779766
## 74 412.9684 955.2631 412.7270 0.24139339
## 75 412.2659 956.0561 412.8285 -0.56259872
## 76 412.9106 956.7966 413.2696 -0.35905584
## 77 413.8294 957.3865 413.6845 0.14488431
## 78 414.2242 958.0634 414.4877 -0.26358148
## 79 415.1678 958.7166 415.1145 0.05330533
## 80 415.7016 959.4881 415.9309 -0.22931482
## 81 416.8674 960.3625 416.6522 0.21517829
## 82 417.6104 960.7834 417.1141 0.49627826
## 83 418.0030 961.0290 417.5492 0.45376867
## 84 417.2667 961.7657 417.9135 -0.64677954
##
## $Fregresores
## C 1 2 3 4 5
## X1 1 944.257255028 -0.82104745 -6.332682221 1.18961038 -4.710896e+00
## X2 0 -0.821047451 945.09843659 -3.331106449 -0.51496048 -5.763330e+00
## X3 0 -6.332682221 -3.33110645 943.416073463 3.19243553 -6.461760e-01
## X4 0 1.189610377 -0.51496048 3.192435533 944.35840562 -1.305300e+00
## X5 0 -4.710895918 -5.76332955 -0.646175964 -1.30529972 9.441561e+02
## X6 0 0.092783361 0.94233215 2.025806729 -0.93576216 3.710103e+00
## X7 0 -1.817896593 -4.63640617 0.740030976 -5.24566189 -2.253743e-01
## X8 0 0.143048535 -0.28958619 0.517667661 0.52201628 2.651326e+00
## X9 0 -1.845972568 -2.05322636 0.420801680 -4.01088676 1.160347e+00
## X10 0 -0.502320083 -0.21801470 0.625519406 -0.25268908 6.230375e-01
## X11 0 -1.085803966 -1.98508004 0.420315876 -1.94785647 3.839046e-01
## X12 0 -0.451367877 -0.67349076 0.105369884 -0.22247668 5.833060e-01
## X13 0 -0.961354541 -1.43018881 -0.036897112 -2.02729347 4.247779e-01
## X14 0 -0.450139687 -0.64279256 -0.042213432 -0.72720222 1.183438e-01
## X15 0 -0.936788446 -1.40177406 0.004461984 -1.41721485 1.681435e-02
## X16 0 -0.457678076 -0.69030511 0.012973963 -0.49493991 2.898870e-02
## X17 0 -1.021053349 -1.31184496 0.053711457 -1.33057193 -1.433907e-01
## X18 0 -0.526099158 -0.49940189 0.071202134 -0.44003785 1.866166e-01
## X19 0 -0.918440492 -1.37278536 -0.147852653 -1.13820229 -1.965558e-01
## X20 0 -0.248582850 -0.49374931 0.173642672 -0.49164898 2.943305e-01
## X21 0 -0.920358327 -1.12522833 -0.250267255 -1.14965704 -1.556056e-01
## X22 0 -0.172167811 -0.34379633 0.223128320 -0.52401464 3.095270e-01
## X23 0 -0.672872670 -1.07845491 -0.007752907 -0.98934395 -2.200019e-01
## X24 0 -0.237618583 -0.27374738 0.135884377 -0.33211979 2.980580e-01
## X25 0 -0.604807230 -0.81570128 0.030265328 -1.00352521 -1.942945e-02
## X26 0 -0.214969449 -0.32436688 0.074929697 -0.40356891 2.003975e-01
## X27 0 -0.480703142 -0.78039689 -0.011676542 -0.75118815 1.600869e-01
## X28 0 -0.221105460 -0.43383424 0.064513127 -0.35215697 1.264454e-01
## X29 0 -0.498840636 -0.61530378 0.129821527 -0.72888122 1.611355e-02
## X30 0 -0.398564812 -0.34048043 0.051515674 -0.32999832 8.245974e-02
## X31 0 -0.389467803 -0.65395152 0.027790092 -0.59735716 2.598561e-02
## X32 0 -0.260406585 -0.45981985 0.017946614 -0.29644066 6.873121e-02
## X33 0 -0.425986472 -0.53284403 -0.103835912 -0.63673599 -1.624968e-02
## X34 0 -0.251718657 -0.32423075 0.017215532 -0.46179014 7.191110e-02
## X35 0 -0.364087458 -0.58522031 -0.044039773 -0.47887954 -1.018656e-01
## X36 0 -0.198124941 -0.35795423 0.053964491 -0.36189239 9.454275e-02
## X37 0 -0.401640033 -0.46093293 0.001970290 -0.50789310 -6.378136e-03
## X38 0 -0.254505068 -0.31785262 0.077327218 -0.36991166 6.943969e-02
## X39 0 -0.287770143 -0.49067756 0.037661637 -0.44545773 1.392772e-02
## X40 0 -0.251386539 -0.37188195 0.015475202 -0.33385254 1.048637e-01
## X41 0 -0.292282833 -0.39149324 0.011957431 -0.46314104 5.366156e-02
## X42 0 -0.271415430 -0.37151417 0.027536525 -0.35583730 2.374342e-02
## X43 0 -0.265884902 -0.38581382 0.015999921 -0.38322502 -4.087222e-03
## X44 0 -0.274013845 -0.36779473 0.008268215 -0.35215651 7.196551e-02
## X45 0 -0.253340306 -0.36774982 -0.016044653 -0.34138483 -3.357740e-03
## X46 0 -0.248724863 -0.36815643 0.044428987 -0.39981371 4.277995e-02
## X47 0 -0.254191881 -0.31384831 -0.019357661 -0.33323808 1.597433e-02
## X48 0 -0.246637978 -0.38376906 0.034511737 -0.38056999 4.626851e-02
## X49 0 -0.190508230 -0.32496987 0.032018985 -0.31200878 -6.944105e-03
## X50 0 -0.294006546 -0.36121233 0.001839525 -0.37807986 3.710649e-02
## X51 0 -0.205384915 -0.26757980 0.012413556 -0.32237512 2.632978e-02
## X52 0 -0.264193397 -0.41009884 0.002594752 -0.35517003 1.780977e-02
## X53 0 -0.187906749 -0.28786338 -0.005689202 -0.25160955 6.371252e-03
## X54 0 -0.285960798 -0.36758358 0.015970243 -0.40312097 3.518576e-02
## X55 0 -0.201715381 -0.24977003 -0.006042304 -0.25527237 -1.266708e-02
## X56 0 -0.255648290 -0.39743176 0.032591008 -0.39025382 3.862861e-02
## X57 0 -0.165321415 -0.25267762 -0.006977875 -0.22711167 1.662794e-02
## X58 0 -0.276092593 -0.38421152 0.022658363 -0.38683293 6.378715e-02
## X59 0 -0.155624735 -0.21114142 0.022670239 -0.22148148 -1.757671e-02
## X60 0 -0.287708850 -0.37985506 0.031196137 -0.36692613 3.103046e-02
## X61 0 -0.133277651 -0.18889047 -0.010598831 -0.20276932 5.384850e-03
## X62 0 -0.261103583 -0.38959637 0.008372100 -0.39995146 4.007436e-02
## X63 0 -0.111506735 -0.18011096 -0.017285389 -0.18001226 9.497568e-03
## X64 0 -0.263263618 -0.38935263 0.008878219 -0.40583610 3.473403e-02
## X65 0 -0.121437713 -0.14881612 0.020096399 -0.15374904 -1.045655e-03
## X66 0 -0.289524182 -0.38855071 0.026361925 -0.37176424 2.056755e-02
## X67 0 -0.098951038 -0.14537694 0.016239734 -0.13712679 2.508015e-03
## X68 0 -0.286230070 -0.39186064 0.011689329 -0.38476426 5.568577e-02
## X69 0 -0.084156321 -0.12824857 -0.017588384 -0.11605309 1.245328e-02
## X70 0 -0.264650452 -0.40100400 0.029323842 -0.38905854 2.348262e-02
## X71 0 -0.082419830 -0.08969117 -0.003786449 -0.11645528 -2.039049e-02
## X72 0 -0.280875222 -0.37147015 0.011793289 -0.39659184 3.998213e-02
## X73 0 -0.042686146 -0.10476595 -0.002802103 -0.07903288 -8.198610e-03
## X74 0 -0.260687679 -0.39280539 0.010658286 -0.38893658 3.036963e-02
## X75 0 -0.065741600 -0.04970904 -0.004412161 -0.08618961 1.466432e-02
## X76 0 -0.274635485 -0.38613448 0.018576339 -0.39745699 1.364376e-02
## X77 0 -0.027613053 -0.07439632 0.017466424 -0.04672357 2.394381e-04
## X78 0 -0.285388933 -0.39304483 0.002985474 -0.38001546 4.785441e-02
## X79 0 -0.039470690 -0.03606528 0.004651599 -0.04511826 1.134741e-02
## X80 0 -0.281213839 -0.39748188 0.029278069 -0.38615938 1.952538e-02
## X81 0 -0.023390955 -0.02654192 -0.006119017 -0.01952538 -2.233846e-03
## X82 0 -0.276735336 -0.39081098 0.016539903 -0.39748188 2.654192e-02
## X83 0 0.001934752 -0.01653990 -0.006885445 -0.02927807 -6.119017e-03
## X84 0 -0.191962767 -0.27673534 -0.001934752 -0.28121384 2.339096e-02
## 8 9 6 7 72
## X1 0.14304853 -1.845973e+00 0.092783361 -1.817897e+00 -0.28087522
## X2 -0.28958619 -2.053226e+00 0.942332154 -4.636406e+00 -0.37147015
## X3 0.51766766 4.208017e-01 2.025806729 7.400310e-01 0.01179329
## X4 0.52201628 -4.010887e+00 -0.935762157 -5.245662e+00 -0.39659184
## X5 2.65132613 1.160347e+00 3.710103194 -2.253743e-01 0.03998213
## X6 -0.89886505 -5.140292e+00 943.938089741 -6.797803e-01 -0.40652496
## X7 3.81547308 -2.622714e-01 -0.679780315 9.445764e+02 0.04205896
## X8 943.93362776 -7.219937e-01 -0.898865046 3.815473e+00 -0.38500370
## X9 -0.72199375 9.445809e+02 -5.140292004 -2.622714e-01 0.06932953
## X10 -0.95257650 3.828447e+00 0.517554294 2.609113e+00 -0.38030955
## X11 -5.12731804 -2.085599e-01 -4.053100197 1.164809e+00 0.08021524
## X12 0.66540695 2.680315e+00 -0.306400539 6.360115e-01 -0.39540365
## X13 -3.98189806 1.016956e+00 -1.934882508 4.376160e-01 0.09424153
## X14 -0.05613328 8.096542e-01 -0.074624030 6.545081e-01 -0.39090838
## X15 -1.76123984 1.873488e-01 -1.956091334 2.769252e-01 0.10867523
## X16 -0.06687112 8.776364e-01 -0.476934964 2.919865e-01 -0.37961885
## X17 -1.73296301 2.691723e-01 -1.243572175 -2.334529e-01 0.13343980
## X18 -0.50720029 4.278709e-01 -0.487186998 2.521170e-01 -0.40400527
## X19 -1.10768780 -2.031876e-01 -1.107443609 -1.511436e-01 0.17054431
## X20 -0.47551046 3.270467e-01 -0.470303180 3.225010e-01 -0.38100956
## X21 -1.03251391 -1.628201e-01 -1.002317914 -1.662905e-01 0.15239551
## X22 -0.60012471 3.870141e-01 -0.479972441 3.692602e-01 -0.39222805
## X23 -0.93780479 -3.646894e-02 -1.074727344 -1.672821e-01 0.19171540
## X24 -0.50776253 4.207758e-01 -0.653836164 3.740402e-01 -0.37300816
## X25 -1.02321167 -1.394920e-01 -0.924830824 -9.018040e-02 0.16489332
## X26 -0.55000025 3.919868e-01 -0.359909881 3.495737e-01 -0.36301117
## X27 -0.90688421 -1.940163e-01 -0.952009537 8.360644e-03 0.23802042
## X28 -0.31587011 3.667892e-01 -0.299732996 2.183441e-01 -0.39615227
## X29 -0.93479401 -3.567913e-02 -0.733241538 5.625094e-02 0.23864615
## X30 -0.30170329 2.723086e-01 -0.308117201 1.436609e-01 -0.39664420
## X31 -0.67927705 5.822123e-02 -0.711665685 -2.792622e-02 0.25797797
## X32 -0.34577884 2.209881e-01 -0.331968614 1.364242e-01 -0.36391262
## X33 -0.63433847 9.735415e-03 -0.543392671 2.795590e-02 0.29254460
## X34 -0.34392605 1.518994e-01 -0.334102296 1.460584e-01 -0.36459037
## X35 -0.52791747 3.991334e-02 -0.559408770 2.141196e-02 0.28233139
## X36 -0.35010222 1.735949e-01 -0.473747572 8.738631e-02 -0.34353637
## X37 -0.53187224 3.741188e-02 -0.463404342 -8.990819e-02 0.37824392
## X38 -0.45770292 9.565452e-02 -0.377892310 1.220793e-01 -0.37321891
## X39 -0.45513613 -1.059528e-01 -0.480356571 9.621786e-03 0.36749202
## X40 -0.35853465 1.665083e-01 -0.353867007 7.770791e-02 -0.36490590
## X41 -0.43592758 -9.735875e-03 -0.437189513 -2.116932e-03 0.41811782
## X42 -0.38588599 1.122196e-01 -0.314494876 1.492927e-01 -0.48403270
## X43 -0.40267778 2.990205e-02 -0.418712053 3.430390e-02 0.41802964
## X44 -0.32690843 1.511323e-01 -0.387856282 5.825515e-02 -0.34315811
## X45 -0.41687253 4.671745e-02 -0.348713285 2.793176e-02 0.48560373
## X46 -0.38216708 6.084991e-02 -0.364570069 7.380504e-02 -0.35990038
## X47 -0.34611853 2.224256e-02 -0.339545310 9.055816e-03 0.48513752
## X48 -0.35852777 8.977528e-02 -0.394124511 4.537470e-02 -0.34242110
## X49 -0.32357507 3.013513e-03 -0.330643331 1.028513e-02 0.56237296
## X50 -0.38714664 7.796571e-02 -0.374527687 6.223875e-02 -0.29761606
## X51 -0.29805232 3.307254e-03 -0.296038541 -1.298641e-02 0.65553363
## X52 -0.39719793 8.489712e-02 -0.371101982 6.969750e-02 -0.36953167
## X53 -0.27338018 9.683831e-03 -0.289784108 1.935191e-02 0.82993026
## X54 -0.36050315 1.008936e-01 -0.377840266 4.046813e-02 -0.56392797
## X55 -0.25858797 8.753076e-03 -0.228951192 2.904149e-02 0.83744452
## X56 -0.36055488 4.884023e-02 -0.392522136 6.638190e-02 -0.50138440
## X57 -0.22057909 1.175610e-02 -0.224076234 -2.326591e-02 0.92866892
## X58 -0.41261853 7.526012e-02 -0.372968433 4.700071e-02 -0.49825908
## X59 -0.21519802 -3.169510e-03 -0.218739566 -6.574530e-04 0.86589368
## X60 -0.38920817 7.336263e-02 -0.406929332 7.266536e-02 -0.45926078
## X61 -0.19237764 1.558228e-02 -0.212603264 2.519693e-03 0.96378271
## X62 -0.38934095 8.435469e-02 -0.383165863 5.739239e-02 -0.53318591
## X63 -0.20091393 -1.506869e-02 -0.176407398 2.162458e-02 1.02522806
## X64 -0.37937941 8.671623e-02 -0.382363073 5.176369e-02 -0.08298467
## X65 -0.14708356 1.783814e-02 -0.168322926 -8.090816e-03 1.60651764
## X66 -0.37956097 6.355697e-02 -0.402049653 6.405787e-02 -0.21622014
## X67 -0.15652964 -1.089292e-02 -0.124425194 -4.832104e-03 1.56084233
## X68 -0.39763749 7.471615e-02 -0.368962140 3.236084e-02 0.68483640
## X69 -0.11376691 -9.244265e-03 -0.125333500 -2.940881e-04 3.68384005
## X70 -0.38642856 5.093718e-02 -0.380352103 6.634405e-02 -0.73257458
## X71 -0.10675716 1.717234e-02 -0.105394808 8.041124e-03 4.81779099
## X72 -0.38500370 6.932953e-02 -0.406524962 4.205896e-02 944.08923332
## X73 -0.10240933 1.269272e-02 -0.097878942 -2.924063e-03 0.42766329
## X74 -0.40040595 7.133703e-02 -0.401243436 4.296760e-02 -0.70230925
## X75 -0.06860087 -9.043080e-03 -0.076047408 -3.547011e-03 -4.00208971
## X76 -0.39435799 5.950751e-02 -0.382817561 5.964770e-02 0.66540695
## X77 -0.05950751 -1.043246e-02 -0.056911544 8.545304e-03 -2.68031484
## X78 -0.38281756 5.691154e-02 -0.390571542 3.018366e-02 -0.30640054
## X79 -0.05964770 8.545304e-03 -0.030183663 -6.646007e-03 -0.63601151
## X80 -0.39745699 4.672357e-02 -0.380015458 4.511826e-02 -0.22247668
## X81 -0.01364376 2.394381e-04 -0.047854407 1.134741e-02 -0.58330597
## X82 -0.38613448 7.439632e-02 -0.393044826 3.606528e-02 -0.67349076
## X83 -0.01857634 1.746642e-02 -0.002985474 4.651599e-03 -0.10536988
## X84 -0.27463548 2.761305e-02 -0.285388933 3.947069e-02 -0.45136788
## 73 14 15 12 13
## X1 -4.268615e-02 -0.45013969 -9.367884e-01 -0.45136788 -9.613545e-01
## X2 -1.047660e-01 -0.64279256 -1.401774e+00 -0.67349076 -1.430189e+00
## X3 -2.802103e-03 -0.04221343 4.461984e-03 0.10536988 -3.689711e-02
## X4 -7.903288e-02 -0.72720222 -1.417215e+00 -0.22247668 -2.027293e+00
## X5 -8.198610e-03 0.11834385 1.681435e-02 0.58330597 4.247779e-01
## X6 -9.787894e-02 -0.07462403 -1.956091e+00 -0.30640054 -1.934883e+00
## X7 -2.924063e-03 0.65450811 2.769252e-01 0.63601151 4.376160e-01
## X8 -1.024093e-01 -0.05613328 -1.761240e+00 0.66540695 -3.981898e+00
## X9 1.269272e-02 0.80965418 1.873488e-01 2.68031484 1.016956e+00
## X10 -7.747909e-02 0.67315985 -3.758770e+00 -0.70230925 -4.953675e+00
## X11 1.105332e-02 2.90344316 1.009203e+00 4.00208971 -4.588272e-01
## X12 -9.424153e-02 -0.73257458 -4.817791e+00 944.08923332 -4.276633e-01
## X13 -1.147811e-02 4.13797409 -4.285619e-01 -0.42766329 9.444253e+02
## X14 -1.114114e-01 944.10090986 -3.527336e-01 -0.73257458 4.137974e+00
## X15 4.544878e-04 -0.35273360 9.444136e+02 -4.81779099 -4.285619e-01
## X16 -1.003600e-01 -0.86239610 4.202487e+00 0.68483640 2.978373e+00
## X17 1.807757e-02 -4.75327787 -2.987403e-01 -3.68384005 9.975267e-01
## X18 -1.147243e-01 0.65704630 3.029889e+00 -0.21622014 1.010052e+00
## X19 -4.043702e-04 -3.63232437 1.025317e+00 -1.56084233 3.474356e-01
## X20 -1.133448e-01 -0.11238423 1.027998e+00 -0.08298467 1.004082e+00
## X21 7.383671e-03 -1.54289572 2.435997e-01 -1.60651764 2.852859e-01
## X22 -9.874273e-02 -0.03894490 1.021297e+00 -0.53318591 5.103306e-01
## X23 -2.356000e-02 -1.58930211 2.412461e-01 -1.02522806 -1.772020e-01
## X24 -1.045260e-01 -0.53515620 5.642951e-01 -0.45926078 3.957779e-01
## X25 2.420939e-02 -0.97126357 -1.752317e-01 -0.96378271 -1.790698e-01
## X26 -1.214612e-01 -0.49692241 4.731051e-01 -0.49825908 4.589252e-01
## X27 1.126109e-02 -0.88645549 -1.414082e-01 -0.86589368 -1.383346e-01
## X28 -1.196311e-01 -0.51021652 4.744004e-01 -0.50138440 5.153186e-01
## X29 8.638176e-03 -0.85041848 -1.263771e-01 -0.92866892 -1.458701e-01
## X30 -1.180401e-01 -0.51738432 5.428551e-01 -0.56392797 4.614265e-01
## X31 1.280482e-02 -0.90113240 -1.298702e-01 -0.83744452 -1.800886e-01
## X32 -1.208057e-01 -0.54788332 4.696947e-01 -0.36953167 4.716530e-01
## X33 8.398363e-03 -0.82917630 -1.961332e-01 -0.82993026 1.798243e-02
## X34 -1.246371e-01 -0.35017401 5.160820e-01 -0.29761606 2.960520e-01
## X35 4.665854e-03 -0.78550128 -1.375232e-03 -0.65553363 5.413401e-02
## X36 -1.897609e-01 -0.32963505 3.305638e-01 -0.34242110 2.929536e-01
## X37 6.334539e-02 -0.62102189 8.615300e-02 -0.56237296 6.377675e-03
## X38 -1.474054e-01 -0.35483465 2.947932e-01 -0.35990038 1.946794e-01
## X39 1.723498e-02 -0.56053343 1.879123e-02 -0.48513752 5.588767e-02
## X40 -1.843180e-01 -0.35421117 1.972741e-01 -0.34315811 2.198635e-01
## X41 -3.364623e-03 -0.48254277 5.019846e-02 -0.48560373 3.046777e-02
## X42 -1.327610e-01 -0.33711581 2.358337e-01 -0.48403270 1.327610e-01
## X43 -7.962306e-02 -0.46963349 2.442547e-02 -0.41802964 -7.962306e-02
## X44 -2.198635e-01 -0.47705483 1.653520e-01 -0.36490590 1.843180e-01
## X45 3.046777e-02 -0.38543863 -8.660094e-02 -0.41811782 -3.364623e-03
## X46 -1.946794e-01 -0.38757614 2.069764e-01 -0.37321891 1.474054e-01
## X47 5.588767e-02 -0.39545945 1.930562e-02 -0.36749202 1.723498e-02
## X48 -2.929536e-01 -0.36262008 1.786015e-01 -0.34353637 1.897609e-01
## X49 6.377675e-03 -0.33629588 6.636145e-03 -0.37824392 6.334539e-02
## X50 -2.960520e-01 -0.32625098 1.981330e-01 -0.36459037 1.246371e-01
## X51 5.413401e-02 -0.36987182 4.606000e-02 -0.28233139 4.665854e-03
## X52 -4.716530e-01 -0.38468677 1.335153e-01 -0.36391262 1.208057e-01
## X53 1.798243e-02 -0.27345317 2.476225e-02 -0.29254460 8.398363e-03
## X54 -4.614265e-01 -0.38015235 1.471677e-01 -0.39664420 1.180401e-01
## X55 -1.800886e-01 -0.26618268 2.463810e-02 -0.25797797 1.280482e-02
## X56 -5.153186e-01 -0.37905582 1.297294e-01 -0.39615227 1.196311e-01
## X57 -1.458701e-01 -0.24628864 -4.783562e-03 -0.23864615 8.638176e-03
## X58 -4.589252e-01 -0.39236582 1.489550e-01 -0.36301117 1.214612e-01
## X59 -1.383346e-01 -0.20932231 4.851726e-03 -0.23802042 1.126109e-02
## X60 -3.957779e-01 -0.36020906 1.332545e-01 -0.37300816 1.045260e-01
## X61 -1.790698e-01 -0.22622713 8.458988e-03 -0.16489332 2.420939e-02
## X62 -5.103306e-01 -0.36859600 1.151843e-01 -0.39222805 9.874273e-02
## X63 -1.772020e-01 -0.15423504 1.979723e-02 -0.19171540 -2.356000e-02
## X64 -1.004082e+00 -0.40969447 1.173191e-01 -0.38100956 1.133448e-01
## X65 2.852859e-01 -0.17313906 -6.093573e-03 -0.15239551 7.383671e-03
## X66 -1.010052e+00 -0.38566116 1.163302e-01 -0.40400527 1.147243e-01
## X67 3.474356e-01 -0.14941004 1.203527e-02 -0.17054431 -4.043702e-04
## X68 -2.978373e+00 -0.39788625 1.440024e-01 -0.37961885 1.003600e-01
## X69 9.975267e-01 -0.14126624 -6.523387e-03 -0.13343980 1.807757e-02
## X70 -4.137974e+00 -0.37273341 1.168999e-01 -0.39090838 1.114114e-01
## X71 -4.285619e-01 -0.11689989 1.119213e-02 -0.10867523 4.544878e-04
## X72 4.276633e-01 -0.39090838 1.086752e-01 -0.39540365 9.424153e-02
## X73 9.444253e+02 -0.11141138 4.544878e-04 -0.09424153 -1.147811e-02
## X74 4.953675e+00 -0.40228909 1.107814e-01 -0.38030955 7.747909e-02
## X75 -4.588272e-01 -0.07770163 -4.592666e-03 -0.08021524 1.105332e-02
## X76 3.981898e+00 -0.38642856 1.067572e-01 -0.38500370 1.024093e-01
## X77 1.016956e+00 -0.05093718 1.717234e-02 -0.06932953 1.269272e-02
## X78 1.934883e+00 -0.38035210 1.053948e-01 -0.40652496 9.787894e-02
## X79 4.376160e-01 -0.06634405 8.041124e-03 -0.04205896 -2.924063e-03
## X80 2.027293e+00 -0.38905854 1.164553e-01 -0.39659184 7.903288e-02
## X81 4.247779e-01 -0.02348262 -2.039049e-02 -0.03998213 -8.198610e-03
## X82 1.430189e+00 -0.40100400 8.969117e-02 -0.37147015 1.047660e-01
## X83 -3.689711e-02 -0.02932384 -3.786449e-03 -0.01179329 -2.802103e-03
## X84 9.613545e-01 -0.26465045 8.241983e-02 -0.28087522 4.268615e-02
## 10 11 18 19
## X1 -0.50232008 -1.085803966 -0.52609916 -9.184405e-01
## X2 -0.21801470 -1.985080036 -0.49940189 -1.372785e+00
## X3 0.62551941 0.420315876 0.07120213 -1.478527e-01
## X4 -0.25268908 -1.947856471 -0.44003785 -1.138202e+00
## X5 0.62303755 0.383904569 0.18661663 -1.965558e-01
## X6 0.51755429 -4.053100197 -0.48718700 -1.107444e+00
## X7 2.60911270 1.164808836 0.25211702 -1.511436e-01
## X8 -0.95257650 -5.127318041 -0.50720029 -1.107688e+00
## X9 3.82844704 -0.208559938 0.42787090 -2.031876e-01
## X10 944.08148041 -0.650791614 -0.05519458 -1.658033e+00
## X11 -0.65079161 944.433029647 0.95256612 2.574958e-01
## X12 -0.70230925 4.002089714 -0.21622014 -1.560842e+00
## X13 -4.95367537 -0.458827193 1.01005168 3.474356e-01
## X14 0.67315985 2.903443156 0.65704630 -3.632324e+00
## X15 -3.75876974 1.009203276 3.02988853 1.025317e+00
## X16 -0.08639861 0.945538557 -0.75856019 -4.735331e+00
## X17 -1.62535546 0.217614098 4.22043383 -4.025763e-01
## X18 -0.05519458 0.952566124 944.11715954 -2.840024e-01
## X19 -1.65803332 0.257495759 -0.28400239 9.443974e+02
## X20 -0.63702182 0.492384023 -0.76053048 4.274398e+00
## X21 -1.04317467 -0.073366055 -4.68136676 -4.006060e-01
## X22 -0.50330055 0.378562392 0.66342444 3.124431e+00
## X23 -0.98099824 -0.135030025 -3.53778162 1.018939e+00
## X24 -0.49628879 0.404960752 -0.12631195 1.097438e+00
## X25 -0.91985817 -0.140304856 -1.47345603 2.575274e-01
## X26 -0.46372276 0.437991356 -0.09260646 1.126161e+00
## X27 -1.00599614 -0.183531782 -1.48443837 2.949076e-01
## X28 -0.55197054 0.445951280 -0.53106897 5.880385e-01
## X29 -0.85291972 -0.192046023 -0.94752015 -1.793189e-01
## X30 -0.35353175 0.444116440 -0.49356467 5.450707e-01
## X31 -0.85746679 0.001982508 -0.81448998 -1.447659e-01
## X32 -0.31366072 0.287783810 -0.52619085 5.171804e-01
## X33 -0.66380185 0.070178664 -0.80763853 -1.104028e-01
## X34 -0.36177876 0.248524646 -0.51044021 5.891236e-01
## X35 -0.60680194 0.025735336 -0.85486388 -1.368143e-01
## X36 -0.32788139 0.160167649 -0.57421310 5.068012e-01
## X37 -0.51964925 0.023868683 -0.79206981 -1.698035e-01
## X38 -0.33074456 0.218023935 -0.35654526 5.338917e-01
## X39 -0.48744326 0.018054217 -0.76769151 4.996021e-03
## X40 -0.48972190 0.130166258 -0.31696797 3.657495e-01
## X41 -0.42062439 -0.073933859 -0.58583613 7.348592e-02
## X42 -0.37094820 0.168347787 -0.37146259 3.334218e-01
## X43 -0.43408806 0.002677681 -0.52190482 3.541917e-02
## X44 -0.38019679 0.114814397 -0.33663447 2.610613e-01
## X45 -0.40008302 0.024212850 -0.41875562 3.262176e-02
## X46 -0.32086613 0.167102498 -0.34250066 2.668642e-01
## X47 -0.40090228 0.040675150 -0.43860303 2.981032e-02
## X48 -0.37518920 0.093440914 -0.48655239 2.054264e-01
## X49 -0.31352753 0.015264685 -0.34536427 -7.710337e-02
## X50 -0.38119801 0.112433643 -0.38653049 2.417104e-01
## X51 -0.30091670 0.025683752 -0.36072543 1.825996e-02
## X52 -0.37654780 0.109161849 -0.36512810 1.991691e-01
## X53 -0.26685619 -0.007291577 -0.31572833 9.144160e-03
## X54 -0.37991254 0.093269218 -0.33870426 2.538187e-01
## X55 -0.26500808 -0.007601558 -0.31418605 5.851328e-02
## X56 -0.38059955 0.109771853 -0.36429629 1.569979e-01
## X57 -0.24970975 0.028849475 -0.24997055 4.371766e-03
## X58 -0.37679461 0.075202156 -0.37195374 1.871498e-01
## X59 -0.19421717 0.027995837 -0.22620055 1.643949e-02
## X60 -0.39503015 0.086949445 -0.39372014 1.600990e-01
## X61 -0.20350869 -0.020757893 -0.21591901 9.880759e-03
## X62 -0.38542172 0.102686473 -0.39260526 1.625987e-01
## X63 -0.16305380 0.011795831 -0.19567855 5.091165e-03
## X64 -0.38653885 0.096147983 -0.37155647 1.811089e-01
## X65 -0.18912065 -0.017870794 -0.17837273 1.980639e-02
## X66 -0.37496725 0.097374516 -0.36636215 1.347097e-01
## X67 -0.13642527 0.013425974 -0.13470966 1.756338e-02
## X68 -0.39702739 0.082133313 -0.40357545 1.438610e-01
## X69 -0.13795330 0.006573505 -0.14659714 -1.221259e-02
## X70 -0.40228909 0.077701628 -0.38566116 1.494100e-01
## X71 -0.11078143 -0.004592666 -0.11633023 1.203527e-02
## X72 -0.38030955 0.080215245 -0.40400527 1.705443e-01
## X73 -0.07747909 0.011053318 -0.11472432 -4.043702e-04
## X74 -0.37811826 0.085869430 -0.37496725 1.364253e-01
## X75 -0.08586943 0.005807277 -0.09737452 1.342597e-02
## X76 -0.40040595 0.068600874 -0.37956097 1.565296e-01
## X77 -0.07133703 -0.009043080 -0.06355697 -1.089292e-02
## X78 -0.40124344 0.076047408 -0.40204965 1.244252e-01
## X79 -0.04296760 -0.003547011 -0.06405787 -4.832104e-03
## X80 -0.38893658 0.086189613 -0.37176424 1.371268e-01
## X81 -0.03036963 0.014664321 -0.02056755 2.508015e-03
## X82 -0.39280539 0.049709041 -0.38855071 1.453769e-01
## X83 -0.01065829 -0.004412161 -0.02636193 1.623973e-02
## X84 -0.26068768 0.065741600 -0.28952418 9.895104e-02
##
## $Tregresores
## C 1 2 3 4
## [1,] 0.1091089 101.4288 1.434420e+02 4.371130e-13 143.44202
## [2,] 0.1091089 101.4499 1.430707e+02 1.072167e+01 141.86941
## [3,] 0.1091089 101.5061 1.419479e+02 2.139520e+01 137.17366
## [4,] 0.1091089 101.6271 1.401190e+02 3.198125e+01 129.48942
## [5,] 0.1091089 101.7618 1.375192e+02 4.241906e+01 118.90639
## [6,] 0.1091089 101.8588 1.340924e+02 5.262739e+01 105.59615
## [7,] 0.1091089 101.8566 1.297819e+02 6.249967e+01 89.81186
## [8,] 0.1091089 101.8070 1.246876e+02 7.198844e+01 71.98844
## [9,] 0.1091089 101.7030 1.188378e+02 8.102222e+01 52.54693
## [10,] 0.1091089 101.5407 1.122712e+02 8.953329e+01 31.95406
## [11,] 0.1091089 101.3728 1.050924e+02 9.751146e+01 10.71351
## [12,] 0.1091089 101.3146 9.745544e+01 1.050320e+02 -10.70736
## [13,] 0.1091089 101.3698 8.938257e+01 1.120822e+02 -31.90027
## [14,] 0.1091089 101.5003 8.086070e+01 1.186009e+02 -52.44218
## [15,] 0.1091089 101.6543 7.188044e+01 1.245006e+02 -71.88044
## [16,] 0.1091089 101.7047 6.240644e+01 1.295883e+02 -89.67789
## [17,] 0.1091089 101.7197 5.255555e+01 1.339094e+02 -105.45202
## [18,] 0.1091089 101.7804 4.242683e+01 1.375444e+02 -118.92817
## [19,] 0.1091089 101.8787 3.206041e+01 1.404659e+02 -129.80997
## [20,] 0.1091089 101.9271 2.148395e+01 1.425367e+02 -137.74264
## [21,] 0.1091089 101.9724 1.077689e+01 1.438076e+02 -142.60009
## [22,] 0.1091089 102.0831 -7.872626e-13 1.443672e+02 -144.36725
## [23,] 0.1091089 102.1817 -1.079901e+01 1.441027e+02 -142.89278
## [24,] 0.1091089 102.2809 -2.155853e+01 1.430315e+02 -138.22080
## [25,] 0.1091089 102.3896 -3.222119e+01 1.411703e+02 -130.46094
## [26,] 0.1091089 102.4532 -4.270729e+01 1.384536e+02 -119.71433
## [27,] 0.1091089 102.4790 -5.294784e+01 1.349089e+02 -106.23913
## [28,] 0.1091089 102.5274 -6.291127e+01 1.306366e+02 -90.40334
## [29,] 0.1091089 102.5897 -7.254184e+01 1.256461e+02 -72.54184
## [30,] 0.1091089 102.7191 -8.183165e+01 1.200250e+02 -53.07189
## [31,] 0.1091089 102.8132 -9.065526e+01 1.136781e+02 -32.35449
## [32,] 0.1091089 102.9478 -9.902647e+01 1.067252e+02 -10.87997
## [33,] 0.1091089 103.0369 -1.068175e+02 9.911219e+01 10.88939
## [34,] 0.1091089 103.0885 -1.139825e+02 9.089803e+01 32.44113
## [35,] 0.1091089 103.1153 -1.204879e+02 8.214729e+01 53.27659
## [36,] 0.1091089 103.1960 -1.263887e+02 7.297057e+01 72.97057
## [37,] 0.1091089 103.3119 -1.316362e+02 6.339265e+01 91.09508
## [38,] 0.1091089 103.3127 -1.360065e+02 5.337860e+01 107.10345
## [39,] 0.1091089 103.3534 -1.396702e+02 4.308254e+01 120.76620
## [40,] 0.1091089 103.3972 -1.425596e+02 3.253829e+01 131.74486
## [41,] 0.1091089 103.4554 -1.446738e+02 2.180607e+01 139.80791
## [42,] 0.1091089 103.4734 -1.459243e+02 1.093551e+01 144.69904
## [43,] 0.1091089 103.4388 -1.462845e+02 1.030013e-12 146.28454
## [44,] 0.1091089 103.3378 -1.457331e+02 -1.092118e+01 144.50942
## [45,] 0.1091089 103.2257 -1.443527e+02 -2.175767e+01 139.49762
## [46,] 0.1091089 103.2371 -1.423388e+02 -3.248791e+01 131.54085
## [47,] 0.1091089 103.2417 -1.395192e+02 -4.303597e+01 120.63566
## [48,] 0.1091089 103.2168 -1.358802e+02 -5.332906e+01 107.00404
## [49,] 0.1091089 103.1645 -1.314483e+02 -6.330218e+01 90.96507
## [50,] 0.1091089 103.1463 -1.263279e+02 -7.293544e+01 72.93544
## [51,] 0.1091089 103.1398 -1.205166e+02 -8.216682e+01 53.28926
## [52,] 0.1091089 103.1517 -1.140524e+02 -9.095376e+01 32.46102
## [53,] 0.1091089 103.2068 -1.069936e+02 -9.927559e+01 10.90734
## [54,] 0.1091089 103.2065 -9.927534e+01 -1.069934e+02 -10.90731
## [55,] 0.1091089 103.2519 -9.104210e+01 -1.141632e+02 -32.49255
## [56,] 0.1091089 103.2803 -8.227876e+01 -1.206808e+02 -53.36186
## [57,] 0.1091089 103.3022 -7.304567e+01 -1.265188e+02 -73.04567
## [58,] 0.1091089 103.3947 -6.344344e+01 -1.317417e+02 -91.16806
## [59,] 0.1091089 103.5032 -5.347700e+01 -1.362572e+02 -107.30088
## [60,] 0.1091089 103.5879 -4.318030e+01 -1.399871e+02 -121.04024
## [61,] 0.1091089 103.6478 -3.261716e+01 -1.429051e+02 -132.06418
## [62,] 0.1091089 103.6311 -2.184311e+01 -1.449196e+02 -140.04538
## [63,] 0.1091089 103.6484 -1.095401e+01 -1.461711e+02 -144.94380
## [64,] 0.1091089 103.6808 3.152409e-13 -1.466268e+02 -146.62680
## [65,] 0.1091089 103.7122 1.096075e+01 -1.462611e+02 -145.03301
## [66,] 0.1091089 103.7394 2.186594e+01 -1.450710e+02 -140.19174
## [67,] 0.1091089 103.7484 3.264880e+01 -1.430437e+02 -132.19227
## [68,] 0.1091089 103.7548 4.324984e+01 -1.402125e+02 -121.23517
## [69,] 0.1091089 103.8549 5.365873e+01 -1.367202e+02 -107.66552
## [70,] 0.1091089 103.9372 6.377633e+01 -1.324329e+02 -91.64642
## [71,] 0.1091089 104.0460 7.357165e+01 -1.274298e+02 -73.57165
## [72,] 0.1091089 104.1056 8.293622e+01 -1.216451e+02 -53.78825
## [73,] 0.1091089 104.1491 9.183326e+01 -1.151553e+02 -32.77491
## [74,] 0.1091089 104.2278 1.002577e+02 -1.080521e+02 -11.01524
## [75,] 0.1091089 104.3143 1.081418e+02 -1.003409e+02 11.02438
## [76,] 0.1091089 104.3951 1.154272e+02 -9.205011e+01 32.85230
## [77,] 0.1091089 104.4594 1.220586e+02 -8.321811e+01 53.97108
## [78,] 0.1091089 104.5333 1.280266e+02 -7.391620e+01 73.91620
## [79,] 0.1091089 104.6046 1.332832e+02 -6.418580e+01 92.23483
## [80,] 0.1091089 104.6887 1.378179e+02 -5.408956e+01 108.52997
## [81,] 0.1091089 104.7841 1.416036e+02 -4.367893e+01 122.43797
## [82,] 0.1091089 104.8301 1.445351e+02 -3.298919e+01 133.57052
## [83,] 0.1091089 104.8569 1.466337e+02 -2.210148e+01 141.70189
## [84,] 0.1091089 104.9372 1.479887e+02 -1.109022e+01 146.74612
## 5 8 9 6 7
## [1,] -8.075246e-13 143.44202 1.208007e-12 1.434420e+02 4.130273e-13
## [2,] 2.138337e+01 137.09782 4.228908e+01 1.398747e+02 3.192549e+01
## [3,] 4.231247e+01 118.60760 8.086529e+01 1.293352e+02 6.228455e+01
## [4,] 6.235882e+01 89.60946 1.123667e+02 1.123667e+02 8.960946e+01
## [5,] 8.106901e+01 52.57728 1.339647e+02 8.972821e+01 1.125156e+02
## [6,] 9.797891e+01 10.76487 1.436472e+02 6.250097e+01 1.297846e+02
## [7,] 1.126205e+02 -32.05348 1.404355e+02 3.205348e+01 1.404355e+02
## [8,] 1.246876e+02 -71.98844 1.246876e+02 -3.969741e-13 1.439769e+02
## [9,] 1.338874e+02 -105.43472 9.782912e+01 -3.200515e+01 1.402237e+02
## [10,] 1.399999e+02 -129.37935 6.230581e+01 -6.230581e+01 1.293793e+02
## [11,] 1.429619e+02 -141.76154 2.136711e+01 -8.938524e+01 1.120855e+02
## [12,] 1.428798e+02 -141.68011 -2.135484e+01 -1.120212e+02 8.933389e+01
## [13,] 1.397642e+02 -129.16156 -6.220093e+01 -1.291616e+02 6.220093e+01
## [14,] 1.336205e+02 -105.22453 -9.763409e+01 -1.399442e+02 3.194134e+01
## [15,] 1.245006e+02 -71.88044 -1.245006e+02 -1.437609e+02 1.240067e-14
## [16,] 1.124525e+02 -32.00567 -1.402260e+02 -1.402260e+02 -3.200567e+01
## [17,] 9.784517e+01 10.75018 -1.434512e+02 -1.296074e+02 -6.241566e+01
## [18,] 8.108385e+01 52.58690 -1.339892e+02 -1.125362e+02 -8.974464e+01
## [19,] 6.251319e+01 89.83128 -1.126449e+02 -8.983128e+01 -1.126449e+02
## [20,] 4.248798e+01 119.09957 -8.120071e+01 -6.254290e+01 -1.298717e+02
## [21,] 2.149351e+01 137.80392 -4.250688e+01 -3.208992e+01 -1.405951e+02
## [22,] 1.217822e-12 144.36725 7.362297e-14 7.262940e-13 -1.443672e+02
## [23,] -2.153762e+01 138.08677 4.259413e+01 3.215579e+01 -1.408837e+02
## [24,] -4.263547e+01 119.51301 8.148259e+01 6.276001e+01 -1.303225e+02
## [25,] -6.282668e+01 90.28177 1.132098e+02 9.028177e+01 -1.132098e+02
## [26,] -8.161985e+01 52.93452 1.348750e+02 1.132801e+02 -9.033788e+01
## [27,] -9.857550e+01 10.83042 1.445219e+02 1.305749e+02 -6.288154e+01
## [28,] -1.133622e+02 -32.26458 1.413604e+02 1.413604e+02 -3.226458e+01
## [29,] -1.256461e+02 -72.54184 1.256461e+02 1.450837e+02 9.506562e-13
## [30,] -1.352250e+02 -106.48803 9.880645e+01 1.416246e+02 3.232488e+01
## [31,] -1.417543e+02 -131.00065 6.308659e+01 1.310007e+02 6.308659e+01
## [32,] -1.451831e+02 -143.96406 2.169909e+01 1.138270e+02 9.077399e+01
## [33,] -1.453088e+02 -144.08868 -2.171787e+01 9.085257e+01 1.139255e+02
## [34,] -1.421339e+02 -131.35146 -6.325553e+01 6.325553e+01 1.313515e+02
## [35,] -1.357465e+02 -106.89877 -9.918757e+01 3.244957e+01 1.421708e+02
## [36,] -1.263887e+02 -72.97057 -1.263887e+02 -1.005623e-12 1.459411e+02
## [37,] -1.142296e+02 -32.51146 -1.424420e+02 -3.251146e+01 1.424420e+02
## [38,] -9.937748e+01 10.91853 -1.456977e+02 -6.339312e+01 1.316372e+02
## [39,] -8.233700e+01 53.39963 -1.360600e+02 -9.113164e+01 1.142755e+02
## [40,] -6.344498e+01 91.17027 -1.143239e+02 -1.143239e+02 9.117027e+01
## [41,] -4.312503e+01 120.88531 -8.241821e+01 -1.318189e+02 6.348065e+01
## [42,] -2.180987e+01 139.83228 -4.313255e+01 -1.426646e+02 3.256226e+01
## [43,] 9.507586e-15 146.28454 5.545091e-13 -1.462845e+02 3.488434e-13
## [44,] 2.178129e+01 139.64904 4.307602e+01 -1.424776e+02 -3.251959e+01
## [45,] 4.302932e+01 120.61702 8.223529e+01 -1.315264e+02 -6.333976e+01
## [46,] 6.334674e+01 91.02909 1.141469e+02 -1.141469e+02 -9.102909e+01
## [47,] 8.224800e+01 53.34191 1.359130e+02 -9.103313e+01 -1.141519e+02
## [48,] 9.928524e+01 10.90840 1.455625e+02 -6.333428e+01 -1.315150e+02
## [49,] 1.140666e+02 -32.46506 1.422387e+02 -3.246506e+01 -1.422387e+02
## [50,] 1.263279e+02 -72.93544 1.263279e+02 -1.125315e-12 -1.458709e+02
## [51,] 1.357788e+02 -106.92418 9.921114e+01 3.245728e+01 -1.422046e+02
## [52,] 1.422210e+02 -131.43199 6.329431e+01 6.329431e+01 -1.314320e+02
## [53,] 1.455483e+02 -144.32622 2.175368e+01 9.100235e+01 -1.141133e+02
## [54,] 1.455480e+02 -144.32587 -2.175362e+01 1.141131e+02 -9.100212e+01
## [55,] 1.423592e+02 -131.55965 -6.335579e+01 1.315597e+02 -6.335579e+01
## [56,] 1.359638e+02 -107.06985 -9.934631e+01 1.423984e+02 -3.250150e+01
## [57,] 1.265188e+02 -73.04567 -1.265188e+02 1.460913e+02 -8.359433e-13
## [58,] 1.143211e+02 -32.53750 -1.425561e+02 1.425561e+02 3.253750e+01
## [59,] 9.956067e+01 10.93866 -1.459663e+02 1.318798e+02 6.350998e+01
## [60,] 8.252384e+01 53.52081 -1.363688e+02 1.145348e+02 9.133843e+01
## [61,] 6.359876e+01 91.39125 -1.146010e+02 9.139125e+01 1.146010e+02
## [62,] 4.319828e+01 121.09064 -8.255820e+01 6.358847e+01 1.320428e+02
## [63,] 2.184676e+01 140.06881 -4.320550e+01 3.261734e+01 1.429059e+02
## [64,] -9.732666e-15 146.62680 -1.470699e-13 -1.873571e-13 1.466268e+02
## [65,] -2.186021e+01 140.15501 4.323210e+01 -3.263741e+01 1.429938e+02
## [66,] -4.324343e+01 121.21719 8.264448e+01 -6.365493e+01 1.321808e+02
## [67,] -6.366044e+01 91.47989 1.147122e+02 -9.147989e+01 1.147122e+02
## [68,] -8.265674e+01 53.60700 1.365884e+02 -1.147192e+02 9.148553e+01
## [69,] -9.989900e+01 10.97583 1.464623e+02 -1.323280e+02 6.372580e+01
## [70,] -1.149210e+02 -32.70823 1.433041e+02 -1.433041e+02 3.270823e+01
## [71,] -1.274298e+02 -73.57165 1.274298e+02 -1.471433e+02 -5.143099e-13
## [72,] -1.370502e+02 -107.92541 1.001401e+02 -1.435362e+02 -3.276121e+01
## [73,] -1.435963e+02 -132.70291 6.390635e+01 -1.327029e+02 -6.390635e+01
## [74,] -1.469881e+02 -145.75396 2.196888e+01 -1.152422e+02 -9.190259e+01
## [75,] -1.471101e+02 -145.87495 -2.198711e+01 -9.197887e+01 -1.153379e+02
## [76,] -1.439354e+02 -133.01627 -6.405726e+01 -6.405726e+01 -1.330163e+02
## [77,] -1.375161e+02 -108.29224 -1.004805e+02 -3.287256e+01 -1.440241e+02
## [78,] -1.280266e+02 -73.91620 -1.280266e+02 3.744782e-13 -1.478324e+02
## [79,] -1.156588e+02 -32.91823 -1.442242e+02 3.291823e+01 -1.442242e+02
## [80,] -1.007011e+02 11.06396 -1.476383e+02 6.423746e+01 -1.333905e+02
## [81,] -8.347679e+01 54.13885 -1.379435e+02 9.239318e+01 -1.158574e+02
## [82,] -6.432417e+01 92.43367 -1.159082e+02 1.159082e+02 -9.243367e+01
## [83,] -4.370924e+01 122.52295 -8.353473e+01 1.336047e+02 -6.434062e+01
## [84,] -2.211842e+01 141.81051 -4.374275e+01 1.446829e+02 -3.302292e+01
## 72 73 14 15 12
## [1,] 143.44202 6.429440e-13 1.434420e+02 -5.902622e-13 143.44202
## [2,] -129.26369 6.225011e+01 1.242503e+02 7.173593e+01 129.26369
## [3,] 89.50274 -1.122329e+02 7.177562e+01 1.243190e+02 89.50274
## [4,] -31.98125 1.401190e+02 4.008946e-13 1.437224e+02 31.98125
## [5,] -32.02363 -1.403047e+02 -7.195644e+01 1.246322e+02 -32.02363
## [6,] 89.81373 1.126229e+02 -1.247510e+02 7.202502e+01 -89.81373
## [7,] -129.78190 -6.249967e+01 -1.440470e+02 -4.657906e-14 -129.78190
## [8,] 143.97689 6.451228e-13 -1.246876e+02 -7.198844e+01 -143.97689
## [9,] -129.58619 6.240542e+01 -7.191491e+01 -1.245603e+02 -129.58619
## [10,] 89.53329 -1.122712e+02 -1.262272e-12 -1.436002e+02 -89.53329
## [11,] -31.90122 1.397684e+02 7.168139e+01 -1.241558e+02 -31.90122
## [12,] -31.88290 -1.396881e+02 1.240845e+02 -7.164022e+01 31.88290
## [13,] 89.38257 1.120822e+02 1.433585e+02 6.528684e-13 89.38257
## [14,] -129.32785 -6.228101e+01 1.243120e+02 7.177154e+01 129.32785
## [15,] 143.76089 2.689238e-13 7.188044e+01 1.245006e+02 143.76089
## [16,] -129.58830 6.240644e+01 -4.310441e-14 1.438322e+02 129.58830
## [17,] 89.69114 -1.124691e+02 -7.192671e+01 1.245807e+02 89.69114
## [18,] -32.02949 1.403304e+02 -1.246550e+02 7.196961e+01 32.02949
## [19,] -32.06041 -1.404659e+02 -1.440782e+02 2.918048e-13 -32.06041
## [20,] 89.87398 1.126984e+02 -1.248347e+02 -7.207334e+01 -89.87398
## [21,] -129.92945 -6.257072e+01 -7.210540e+01 -1.248902e+02 -129.92945
## [22,] 144.36725 -2.339795e-13 -9.305716e-13 -1.443672e+02 -144.36725
## [23,] -130.19613 6.269915e+01 7.225340e+01 -1.251466e+02 -130.19613
## [24,] 90.18597 -1.130896e+02 1.252680e+02 -7.232353e+01 -90.18597
## [25,] -32.22119 1.411703e+02 1.448007e+02 -4.779545e-13 -32.22119
## [26,] -32.24122 -1.412580e+02 1.254790e+02 7.244536e+01 32.24122
## [27,] 90.36061 1.133086e+02 7.246358e+01 1.255106e+02 90.36061
## [28,] -130.63661 -6.291127e+01 1.273287e-13 1.449957e+02 130.63661
## [29,] 145.08367 7.083917e-13 -7.254184e+01 1.256461e+02 145.08367
## [30,] -130.88077 6.302886e+01 -1.258047e+02 7.263335e+01 130.88077
## [31,] 90.65526 -1.136781e+02 -1.453998e+02 1.167020e-12 90.65526
## [32,] -32.39686 1.419399e+02 -1.260848e+02 -7.279509e+01 32.39686
## [33,] -32.42491 -1.420628e+02 -7.285810e+01 -1.261939e+02 -32.42491
## [34,] 90.89803 1.139825e+02 5.404913e-13 -1.457891e+02 -90.89803
## [35,] -131.38561 -6.327197e+01 7.291351e+01 -1.262899e+02 -131.38561
## [36,] 145.94115 2.299216e-12 1.263887e+02 -7.297057e+01 -145.94115
## [37,] -131.63620 6.339265e+01 1.461052e+02 -4.274948e-13 -131.63620
## [38,] 91.09575 -1.142305e+02 1.265317e+02 7.305312e+01 -91.09575
## [39,] -32.52451 1.424992e+02 7.308190e+01 1.265816e+02 -32.52451
## [40,] -32.53829 -1.425596e+02 -8.638472e-13 1.462258e+02 32.53829
## [41,] 91.22152 1.143882e+02 -7.315398e+01 1.267064e+02 91.22152
## [42,] -131.84190 -6.349171e+01 -1.267285e+02 7.316673e+01 131.84190
## [43,] 146.28454 -2.469136e-13 -1.462845e+02 -4.902502e-13 146.28454
## [44,] -131.66912 6.340851e+01 -1.265624e+02 -7.307085e+01 131.66912
## [45,] 91.01906 -1.141343e+02 -7.299162e+01 -1.264252e+02 91.01906
## [46,] -32.48791 1.423388e+02 1.617623e-12 -1.459993e+02 32.48791
## [47,] -32.48935 -1.423451e+02 7.300291e+01 -1.264447e+02 -32.48935
## [48,] 91.01120 1.141244e+02 1.264143e+02 -7.298531e+01 -91.01120
## [49,] -131.44833 -6.330218e+01 1.458966e+02 -1.706794e-13 -131.44833
## [50,] 145.87089 1.643519e-12 1.263279e+02 7.293544e+01 -145.87089
## [51,] -131.41684 6.328702e+01 7.293084e+01 1.263199e+02 -131.41684
## [52,] 90.95376 -1.140524e+02 1.650086e-12 1.458785e+02 -90.95376
## [53,] -32.47836 1.422970e+02 -7.297822e+01 1.264020e+02 -32.47836
## [54,] -32.47828 -1.422967e+02 -1.264017e+02 7.297804e+01 32.47828
## [55,] 91.04210 1.141632e+02 -1.460202e+02 -1.672967e-14 91.04210
## [56,] -131.59588 -6.337324e+01 -1.264920e+02 -7.303020e+01 131.59588
## [57,] 146.09133 -1.258466e-12 -7.304567e+01 -1.265188e+02 146.09133
## [58,] -131.74167 6.344344e+01 -1.254760e-13 -1.462222e+02 131.74167
## [59,] 91.26367 -1.144410e+02 7.318778e+01 -1.267650e+02 91.26367
## [60,] -32.59831 1.428225e+02 1.268688e+02 -7.324774e+01 32.59831
## [61,] -32.61716 -1.429051e+02 1.465802e+02 5.585671e-13 -32.61716
## [62,] 91.37647 1.145825e+02 1.269216e+02 7.327824e+01 -91.37647
## [63,] -132.06491 -6.359911e+01 7.329049e+01 1.269429e+02 -132.06491
## [64,] 146.62680 -2.518000e-12 -9.291179e-14 1.466268e+02 -146.62680
## [65,] -132.14619 6.363825e+01 -7.333560e+01 1.270210e+02 -132.14619
## [66,] 91.47196 -1.147022e+02 -1.270543e+02 7.335482e+01 -91.47196
## [67,] -32.64880 1.430437e+02 -1.467224e+02 -1.003659e-12 -32.64880
## [68,] -32.65081 -1.430525e+02 -1.270731e+02 -7.336570e+01 32.65081
## [69,] 91.57381 1.148299e+02 -7.343649e+01 -1.271957e+02 91.57381
## [70,] -132.43291 -6.377633e+01 -8.810244e-13 -1.469894e+02 132.43291
## [71,] 147.14330 2.563588e-12 7.357165e+01 -1.274298e+02 147.14330
## [72,] -132.64741 6.387963e+01 1.275028e+02 -7.361376e+01 132.64741
## [73,] 91.83326 -1.151553e+02 1.472891e+02 -8.270589e-13 91.83326
## [74,] -32.79965 1.437047e+02 1.276524e+02 7.370015e+01 32.79965
## [75,] -32.82688 -1.438240e+02 7.376133e+01 1.277584e+02 -32.82688
## [76,] 92.05011 1.154272e+02 5.264539e-14 1.476369e+02 -92.05011
## [77,] -133.09828 -6.409675e+01 -7.386397e+01 1.279361e+02 -133.09828
## [78,] 147.83239 -7.542661e-12 -1.280266e+02 7.391620e+01 -147.83239
## [79,] -133.28319 6.418580e+01 -1.479332e+02 -3.225285e-13 -133.28319
## [80,] 92.30906 -1.157519e+02 -1.282170e+02 -7.402612e+01 -92.30906
## [81,] -32.97474 1.444718e+02 -7.409357e+01 -1.283338e+02 -32.97474
## [82,] -32.98919 -1.445351e+02 -1.113849e-12 -1.482521e+02 32.98919
## [83,] 92.45730 1.159378e+02 7.414500e+01 -1.284229e+02 92.45730
## [84,] -133.70709 -6.438994e+01 1.285213e+02 -7.420184e+01 133.70709
## 13 10 11 18
## [1,] -3.069290e-13 1.434420e+02 7.129653e-13 1.434420e+02
## [2,] 6.225011e+01 1.335542e+02 5.241616e+01 1.121708e+02
## [3,] 1.122329e+02 1.052305e+02 9.763964e+01 3.194316e+01
## [4,] 1.401190e+02 6.235882e+01 1.294894e+02 -6.235882e+01
## [5,] 1.403047e+02 1.075462e+01 1.435105e+02 -1.296610e+02
## [6,] 1.126229e+02 -4.245949e+01 1.376503e+02 -1.404384e+02
## [7,] 6.249967e+01 -8.981186e+01 1.126205e+02 -8.981186e+01
## [8,] 7.151224e-13 -1.246876e+02 7.198844e+01 -2.363040e-13
## [9,] -6.240542e+01 -1.422234e+02 2.143672e+01 8.967642e+01
## [10,] -1.122712e+02 -1.399999e+02 -3.195406e+01 1.399999e+02
## [11,] -1.397684e+02 -1.184519e+02 -8.075913e+01 1.291654e+02
## [12,] -1.396881e+02 -8.071274e+01 -1.183838e+02 6.216705e+01
## [13,] -1.120822e+02 -3.190027e+01 -1.397642e+02 -3.190027e+01
## [14,] -6.228101e+01 2.139399e+01 -1.419398e+02 -1.122265e+02
## [15,] 4.068768e-13 7.188044e+01 -1.245006e+02 -1.437609e+02
## [16,] 6.240644e+01 1.124525e+02 -8.967789e+01 -1.124525e+02
## [17,] 1.124691e+02 1.374624e+02 -4.240154e+01 -3.201040e+01
## [18,] 1.403304e+02 1.435367e+02 1.075659e+01 6.245289e+01
## [19,] 1.404659e+02 1.298100e+02 6.251319e+01 1.298100e+02
## [20,] 1.126984e+02 9.804464e+01 1.056670e+02 1.405326e+02
## [21,] 6.257072e+01 5.268612e+01 1.342421e+02 8.991397e+01
## [22,] -1.848062e-13 -4.087009e-14 1.443672e+02 1.185253e-12
## [23,] -6.269915e+01 -5.279426e+01 1.345176e+02 -9.009851e+01
## [24,] -1.130896e+02 -9.838499e+01 1.060338e+02 -1.410205e+02
## [25,] -1.411703e+02 -1.304609e+02 6.282668e+01 -1.304609e+02
## [26,] -1.412580e+02 -1.444856e+02 1.082770e+01 -6.286573e+01
## [27,] -1.133086e+02 -1.384885e+02 -4.271803e+01 3.224933e+01
## [28,] -6.291127e+01 -1.133622e+02 -9.040334e+01 1.133622e+02
## [29,] 4.797248e-13 -7.254184e+01 -1.256461e+02 1.450837e+02
## [30,] 6.302886e+01 -2.165088e+01 -1.436442e+02 1.135741e+02
## [31,] 1.136781e+02 3.235449e+01 -1.417543e+02 3.235449e+01
## [32,] 1.419399e+02 8.201387e+01 -1.202923e+02 -6.316921e+01
## [33,] 1.420628e+02 1.203964e+02 -8.208486e+01 -1.312858e+02
## [34,] 1.139825e+02 1.421339e+02 -3.244113e+01 -1.421339e+02
## [35,] 6.327197e+01 1.441983e+02 2.173439e+01 -9.092166e+01
## [36,] 1.361488e-12 1.263887e+02 7.297057e+01 6.992740e-13
## [37,] -6.339265e+01 9.109508e+01 1.142296e+02 9.109508e+01
## [38,] -1.142305e+02 4.306557e+01 1.396151e+02 1.424430e+02
## [39,] -1.424992e+02 -1.092283e+01 1.457551e+02 1.316890e+02
## [40,] -1.425596e+02 -6.344498e+01 1.317449e+02 6.344498e+01
## [41,] -1.143882e+02 -1.072513e+02 9.951469e+01 -3.255658e+01
## [42,] -6.349171e+01 -1.362180e+02 5.346162e+01 -1.144081e+02
## [43,] 2.460905e-13 -1.462845e+02 4.268304e-13 -1.462845e+02
## [44,] 6.340851e+01 -1.360395e+02 -5.339156e+01 -1.142582e+02
## [45,] 1.141343e+02 -1.070133e+02 -9.929382e+01 -3.248433e+01
## [46,] 1.423388e+02 -6.334674e+01 -1.315409e+02 6.334674e+01
## [47,] 1.423451e+02 -1.091103e+01 -1.455975e+02 1.315467e+02
## [48,] 1.141244e+02 4.302560e+01 -1.394856e+02 1.423108e+02
## [49,] 6.330218e+01 9.096507e+01 -1.140666e+02 9.096507e+01
## [50,] -3.072594e-13 1.263279e+02 -7.293544e+01 1.427539e-13
## [51,] -6.328702e+01 1.442325e+02 -2.173956e+01 -9.094328e+01
## [52,] -1.140524e+02 1.422210e+02 3.246102e+01 -1.422210e+02
## [53,] -1.422970e+02 1.205949e+02 8.222019e+01 -1.315022e+02
## [54,] -1.422967e+02 8.221998e+01 1.205946e+02 -6.332797e+01
## [55,] -1.141632e+02 3.249255e+01 1.423592e+02 3.249255e+01
## [56,] -6.337324e+01 -2.176917e+01 1.444290e+02 1.141946e+02
## [57,] -1.125169e-12 -7.304567e+01 1.265188e+02 1.460913e+02
## [58,] 6.344344e+01 -1.143211e+02 9.116806e+01 1.143211e+02
## [59,] 1.144410e+02 -1.398725e+02 4.314495e+01 3.257163e+01
## [60,] 1.428225e+02 -1.460858e+02 -1.094762e+01 -6.356200e+01
## [61,] 1.429051e+02 -1.320642e+02 -6.359876e+01 -1.320642e+02
## [62,] 1.145825e+02 -9.968372e+01 -1.074335e+02 -1.428820e+02
## [63,] 6.359911e+01 -5.355205e+01 -1.364484e+02 -9.139175e+01
## [64,] 4.979446e-13 2.592371e-14 -1.466268e+02 -1.007278e-12
## [65,] -6.363825e+01 5.358501e+01 -1.365324e+02 9.144800e+01
## [66,] -1.147022e+02 9.978790e+01 -1.075458e+02 1.430313e+02
## [67,] -1.430437e+02 1.321923e+02 -6.366044e+01 1.321923e+02
## [68,] -1.430525e+02 1.463211e+02 -1.096525e+01 6.366437e+01
## [69,] -1.148299e+02 1.403478e+02 4.329157e+01 -3.268231e+01
## [70,] -6.377633e+01 1.149210e+02 9.164642e+01 -1.149210e+02
## [71,] 4.638998e-14 7.357165e+01 1.274298e+02 -1.471433e+02
## [72,] 6.387963e+01 2.194312e+01 1.455831e+02 -1.151071e+02
## [73,] 1.151553e+02 -3.277491e+01 1.435963e+02 -3.277491e+01
## [74,] 1.437047e+02 -8.303355e+01 1.217878e+02 6.395459e+01
## [75,] 1.438240e+02 -1.218889e+02 8.310247e+01 1.329133e+02
## [76,] 1.154272e+02 -1.439354e+02 3.285230e+01 1.439354e+02
## [77,] 6.409675e+01 -1.460779e+02 -2.201771e+01 9.210686e+01
## [78,] -3.431595e-13 -1.280266e+02 -7.391620e+01 4.344164e-13
## [79,] -6.418580e+01 -9.223483e+01 -1.156588e+02 -9.223483e+01
## [80,] -1.157519e+02 -4.363916e+01 -1.414747e+02 -1.443403e+02
## [81,] -1.444718e+02 1.107404e+01 -1.477728e+02 -1.335120e+02
## [82,] -1.445351e+02 6.432417e+01 -1.335705e+02 -6.432417e+01
## [83,] -1.159378e+02 1.087043e+02 -1.008628e+02 3.299763e+01
## [84,] -6.438994e+01 1.381451e+02 -5.421795e+01 1.160267e+02
## 19
## [1,] 2.835995e-13
## [2,] 8.945325e+01
## [3,] 1.399521e+02
## [4,] 1.294894e+02
## [5,] 6.244145e+01
## [6,] -3.205415e+01
## [7,] -1.126205e+02
## [8,] -1.439769e+02
## [9,] -1.124507e+02
## [10,] -3.195406e+01
## [11,] 6.220278e+01
## [12,] 1.290912e+02
## [13,] 1.397642e+02
## [14,] 8.949765e+01
## [15,] 3.989170e-13
## [16,] -8.967789e+01
## [17,] -1.402467e+02
## [18,] -1.296848e+02
## [19,] -6.251319e+01
## [20,] 3.207565e+01
## [21,] 1.127485e+02
## [22,] 1.443672e+02
## [23,] 1.129800e+02
## [24,] 3.218700e+01
## [25,] -6.282668e+01
## [26,] -1.305420e+02
## [27,] -1.412935e+02
## [28,] -9.040334e+01
## [29,] 2.175378e-13
## [30,] 9.057231e+01
## [31,] 1.417543e+02
## [32,] 1.311722e+02
## [33,] 6.322389e+01
## [34,] -3.244113e+01
## [35,] -1.140122e+02
## [36,] -1.459411e+02
## [37,] -1.142296e+02
## [38,] -3.251170e+01
## [39,] 6.341810e+01
## [40,] 1.317449e+02
## [41,] 1.426397e+02
## [42,] 9.123742e+01
## [43,] 1.720967e-13
## [44,] -9.111786e+01
## [45,] -1.423231e+02
## [46,] -1.315409e+02
## [47,] -6.334955e+01
## [48,] 3.248152e+01
## [49,] 1.140666e+02
## [50,] 1.458709e+02
## [51,] 1.140393e+02
## [52,] 3.246102e+01
## [53,] -6.332812e+01
## [54,] -1.315019e+02
## [55,] -1.423592e+02
## [56,] -9.106717e+01
## [57,] 1.668804e-14
## [58,] 9.116806e+01
## [59,] 1.427056e+02
## [60,] 1.319879e+02
## [61,] 6.359876e+01
## [62,] -3.261188e+01
## [63,] -1.146016e+02
## [64,] -1.466268e+02
## [65,] -1.146722e+02
## [66,] -3.264597e+01
## [67,] 6.366044e+01
## [68,] 1.322004e+02
## [69,] 1.431906e+02
## [70,] 9.164642e+01
## [71,] -3.377576e-13
## [72,] -9.179486e+01
## [73,] -1.435963e+02
## [74,] -1.328031e+02
## [75,] -6.400768e+01
## [76,] 3.285230e+01
## [77,] 1.154984e+02
## [78,] 1.478324e+02
## [79,] 1.156588e+02
## [80,] 3.294472e+01
## [81,] -6.429599e+01
## [82,] -1.335705e+02
## [83,] -1.445721e+02
## [84,] -9.252818e+01
##
## $Nregresores
## [1] 20
##
## $Betas
## [,1]
## C 2.501209e+02
## 1 3.693508e+00
## 2 1.386760e-02
## 3 1.799185e-03
## 4 -5.953325e-03
## 5 -5.820870e-03
## 8 3.911076e-03
## 9 -5.933446e-03
## 6 2.574805e-03
## 7 2.648074e-03
## 72 3.772846e-04
## 73 1.128145e-04
## 14 1.491245e-03
## 15 -1.689340e-03
## 12 6.656558e-04
## 13 -4.256071e-04
## 10 5.329224e-03
## 11 2.937598e-03
## 18 -8.085076e-04
## 19 2.258851e-03Regresion dependiente de la frecuencia entre el PIBC y empleo con datos del mercado de trabajo de Canada
reg5 <- rdf (E,PIBC,4)
reg5## $datos
## Y X F res
## 1 929.6105 405.3665 931.7636 -2.153094777
## 2 929.8040 404.6398 930.7738 -0.969818214
## 3 930.3184 403.8149 929.5617 0.756677040
## 4 931.4277 404.2158 931.6228 -0.195107190
## 5 932.6620 405.0467 934.7974 -2.135347526
## 6 933.5509 404.4167 934.4661 -0.915132065
## 7 933.5315 402.8191 932.3376 1.193909516
## 8 933.0769 401.9773 930.8736 2.203262084
## 9 932.1238 402.0897 931.7271 0.396695094
## 10 930.6359 401.3067 929.7421 0.893823968
## 11 929.0971 401.6302 930.1002 -1.003101101
## 12 928.5633 401.5638 929.3738 -0.810503313
## 13 929.0694 402.8157 931.0588 -1.989395049
## 14 930.2655 403.1421 931.1853 -0.919783073
## 15 931.6770 403.0786 929.8379 1.839098684
## 16 932.1390 403.7188 930.7300 1.408991152
## 17 932.2767 404.8668 932.3535 -0.076767512
## 18 932.8328 405.6362 933.6135 -0.780683828
## 19 933.7334 405.1363 932.3819 1.351491371
## 20 934.1772 406.0246 934.1391 0.038143470
## 21 934.5928 406.4123 935.6584 -1.065583304
## 22 935.6067 406.3009 935.7812 -0.174448203
## 23 936.5111 406.3354 937.1611 -0.649990641
## 24 937.4201 406.7737 939.1433 -1.723172017
## 25 938.4159 405.1525 937.0363 1.379608960
## 26 938.9992 404.9298 937.9482 1.050997386
## 27 939.2354 404.5765 938.0848 1.150566215
## 28 939.6795 404.1995 938.3615 1.318013669
## 29 940.2497 405.9499 942.2151 -1.965440531
## 30 941.4358 405.8221 942.1550 -0.719167365
## 31 942.2981 406.4463 942.8315 -0.533400980
## 32 943.5322 407.0512 943.4625 0.069730378
## 33 944.3490 407.9460 944.6470 -0.298066834
## 34 944.8215 408.1796 944.2002 0.621316773
## 35 945.0671 408.5998 944.9913 0.075868255
## 36 945.8067 409.0906 945.7322 0.074561033
## 37 946.8697 408.7042 945.7234 1.146264263
## 38 946.8766 408.9803 947.1466 -0.269977510
## 39 947.2497 408.3287 947.2235 0.026239799
## 40 947.6513 407.8857 948.0178 -0.366495221
## 41 948.1840 407.2605 948.1775 0.006482568
## 42 948.3492 406.7752 949.0606 -0.711367655
## 43 948.0322 406.1794 948.8036 -0.771411385
## 44 947.1065 405.4398 948.5275 -1.420989144
## 45 946.0796 403.2800 944.2414 1.838113878
## 46 946.1838 403.3649 944.8062 1.377563454
## 47 946.2258 403.3807 944.9164 1.309400950
## 48 945.9978 404.0032 945.8010 0.196782599
## 49 945.5183 404.4774 946.6685 -1.150262922
## 50 945.3514 404.7868 946.3548 -1.003355554
## 51 945.2918 405.2710 946.9114 -1.619566883
## 52 945.4008 405.3830 946.0107 -0.609907574
## 53 945.9058 405.1564 944.5228 1.382979806
## 54 945.9035 406.4700 946.3429 -0.439406342
## 55 946.3190 406.2293 944.4210 1.898023449
## 56 946.5796 406.7265 944.6716 1.907983043
## 57 946.7800 408.5785 947.3354 -0.555357544
## 58 947.6283 409.6767 949.1629 -1.534572363
## 59 948.6221 410.3858 949.8444 -1.222310725
## 60 949.3992 410.5395 949.8093 -0.410161010
## 61 949.9481 410.4453 949.4349 0.513222968
## 62 949.7945 410.6256 949.4690 0.325493795
## 63 949.9534 410.8672 950.1949 -0.241502827
## 64 950.2502 411.2359 950.4887 -0.238492409
## 65 950.5380 410.6637 949.2746 1.263437253
## 66 950.7871 410.8085 948.9946 1.792503069
## 67 950.8695 412.1160 951.4451 -0.575575508
## 68 950.9281 412.9994 953.0067 -2.078537355
## 69 951.8457 412.9551 952.3764 -0.530647333
## 70 952.6005 412.8241 952.3269 0.273560215
## 71 953.5976 413.0489 952.6946 0.902998712
## 72 954.1434 413.6110 954.7529 -0.609511069
## 73 954.5426 413.6048 955.3023 -0.759687139
## 74 955.2631 412.9684 954.8611 0.402077365
## 75 956.0561 412.2659 954.2151 1.840936628
## 76 956.7966 412.9106 955.9376 0.858986106
## 77 957.3865 413.8294 958.3763 -0.989836727
## 78 958.0634 414.2242 958.5083 -0.444907632
## 79 958.7166 415.1678 959.9833 -1.266723686
## 80 959.4881 415.7016 959.6417 -0.153546694
## 81 960.3625 416.8674 960.7214 -0.358930865
## 82 960.7834 417.6104 960.8974 -0.113976788
## 83 961.0290 418.0030 960.2399 0.789142112
## 84 961.7657 417.2667 958.1156 3.650076178
##
## $Fregresores
## C 1 2 3 4
## X1 1 407.820910977 1.101647001 -2.372322e+00 -1.332132e-01
## X2 0 1.101647001 407.726715019 -1.770789e+00 9.942845e-01
## X3 0 -2.372322091 -1.770789239 4.079151e+02 1.352597e+00
## X4 0 -0.133213202 0.994284539 1.352597e+00 4.081443e+02
## X5 0 -2.504274157 -2.002372720 5.636796e-01 -9.588785e-01
## X6 0 0.304483679 0.229214643 8.119107e-01 1.022470e+00
## X7 0 -0.459460566 -2.729667773 -4.176066e-01 -1.776054e+00
## X8 0 0.457371658 0.458790398 2.263185e-01 -1.754348e-01
## X9 0 -1.356059028 -0.423456819 -2.818545e-02 -2.080014e+00
## X10 0 0.344343923 0.242171715 6.496536e-01 1.948338e-01
## X11 0 -0.139397810 -1.268103487 4.046495e-01 -7.182042e-01
## X12 0 -0.114889135 0.223019254 -2.947474e-01 1.696598e-01
## X13 0 -0.437310122 -0.491885700 2.639566e-01 -1.316347e+00
## X14 0 -0.028947069 -0.234989661 -4.824345e-02 3.396932e-02
## X15 0 -0.556233618 -0.666693355 7.251189e-02 -1.980937e-01
## X16 0 -0.217436431 -0.229987276 2.937920e-01 -1.733080e-01
## X17 0 -0.505536663 -0.492841125 1.890499e-01 -5.833212e-01
## X18 0 -0.296304057 -0.245819865 8.337215e-02 -1.645524e-01
## X19 0 -0.140748986 -0.631564650 -6.168169e-02 -6.065592e-01
## X20 0 -0.130205356 -0.353602353 -1.137181e-01 -2.067007e-01
## X21 0 -0.387630631 -0.312767196 -6.543486e-02 -5.116175e-01
## X22 0 -0.203765186 -0.145019002 1.199471e-01 -3.327174e-01
## X23 0 -0.301570624 -0.428245362 -3.911918e-02 -2.843265e-01
## X24 0 -0.074882484 -0.267282497 2.844071e-02 -1.265830e-01
## X25 0 -0.217999768 -0.398044556 -2.088499e-02 -4.682630e-01
## X26 0 -0.174229346 -0.087463802 -4.001763e-02 -1.912143e-01
## X27 0 -0.261349385 -0.348315856 -1.843602e-02 -3.455260e-01
## X28 0 -0.048810011 -0.170329271 5.251851e-02 -9.687923e-02
## X29 0 -0.274593239 -0.317085334 -7.606823e-02 -2.970466e-01
## X30 0 -0.066652619 -0.078443207 5.126926e-02 -2.775376e-01
## X31 0 -0.187076995 -0.337064222 9.415428e-03 -3.414972e-01
## X32 0 -0.062125436 -0.201469323 -2.441183e-02 -1.063564e-01
## X33 0 -0.202087555 -0.288978656 1.072083e-01 -2.464175e-01
## X34 0 -0.218268029 -0.115771789 9.064668e-02 -8.133376e-02
## X35 0 -0.221600539 -0.195148282 2.791315e-02 -1.891347e-01
## X36 0 -0.101600598 -0.188542043 9.984393e-02 -3.748884e-02
## X37 0 -0.073893792 -0.213546557 -1.201356e-01 -2.347506e-01
## X38 0 -0.048370686 -0.065401990 -3.960230e-02 -1.806714e-01
## X39 0 -0.080399897 -0.144103902 -7.828295e-02 -2.141852e-01
## X40 0 0.009108216 -0.060535859 -6.386325e-04 -1.149145e-01
## X41 0 -0.129899900 -0.114341258 -7.870620e-03 -6.895546e-02
## X42 0 -0.037239947 -0.036631583 7.514844e-02 -1.423532e-01
## X43 0 -0.081303060 -0.108557763 4.951255e-02 -9.825609e-02
## X44 0 -0.060913098 -0.134482614 1.608517e-02 -5.547114e-02
## X45 0 -0.023623961 -0.098894719 8.181738e-02 -1.117372e-01
## X46 0 -0.152947190 -0.104983683 -3.179458e-03 -9.969282e-02
## X47 0 -0.058555192 -0.036588783 1.883955e-02 -1.368533e-01
## X48 0 -0.087556250 -0.181510191 -3.795858e-02 -1.164487e-01
## X49 0 -0.028120393 -0.120768128 -3.478980e-02 -4.475588e-02
## X50 0 -0.103746984 -0.135288273 -8.167094e-03 -1.670569e-01
## X51 0 -0.112236732 -0.047935335 1.146504e-02 -2.230761e-02
## X52 0 -0.103770261 -0.132267056 9.846051e-02 -1.603479e-01
## X53 0 -0.039670408 -0.060266194 -1.445333e-02 -5.269803e-02
## X54 0 -0.083306881 -0.171812964 -4.762692e-03 -1.434749e-01
## X55 0 0.027007463 -0.060865122 2.505965e-02 -1.432642e-01
## X56 0 -0.139209964 -0.129021600 -8.299799e-02 -1.062467e-01
## X57 0 -0.046405872 -0.044803665 1.120788e-02 -3.783239e-02
## X58 0 -0.099157215 -0.131306328 2.303273e-02 -1.567347e-01
## X59 0 -0.090369414 -0.042595086 -6.556629e-02 -2.817290e-02
## X60 0 -0.046485226 -0.167942580 1.663076e-02 -1.728131e-01
## X61 0 -0.013832676 -0.111170890 2.771310e-02 -5.037161e-02
## X62 0 -0.138349459 -0.107246797 -7.776522e-03 -1.024701e-01
## X63 0 -0.066849966 -0.027338881 4.150676e-02 -1.226558e-01
## X64 0 -0.105184648 -0.130183177 -1.148491e-02 -1.155256e-01
## X65 0 -0.024830340 -0.106025041 -6.547250e-02 -3.451017e-03
## X66 0 -0.045757356 -0.157032385 2.388786e-02 -1.770188e-01
## X67 0 -0.083092086 -0.011227539 8.278829e-03 -5.837383e-02
## X68 0 -0.116892680 -0.111546313 4.765121e-02 -1.275784e-01
## X69 0 0.008952201 -0.069858744 4.683564e-02 -2.158890e-02
## X70 0 -0.111992952 -0.135857239 -1.036136e-02 -1.167382e-01
## X71 0 -0.015703097 0.002298968 -2.945397e-02 -3.431219e-02
## X72 0 -0.075238471 -0.163573834 3.554655e-02 -1.860626e-01
## X73 0 -0.005700970 0.013339021 5.191882e-03 -9.404575e-03
## X74 0 -0.119335382 -0.156608614 -1.170354e-02 -1.212562e-01
## X75 0 0.034567321 -0.019765932 5.020535e-02 -3.947051e-02
## X76 0 -0.146239555 -0.126448068 -5.280954e-02 -1.196106e-01
## X77 0 -0.022252279 -0.003923961 -4.231765e-02 -9.219608e-04
## X78 0 -0.059489191 -0.169815898 1.884397e-02 -1.197631e-01
## X79 0 -0.040116640 -0.012625504 -3.699806e-02 1.320891e-02
## X80 0 -0.093916392 -0.077445495 1.713288e-02 -1.826664e-01
## X81 0 0.004397121 -0.039600621 -6.684925e-03 -1.573474e-02
## X82 0 -0.050035279 -0.145668288 -3.109234e-03 -7.744550e-02
## X83 0 -0.015887095 0.003109234 1.285045e-02 -1.713288e-02
## X84 0 -0.079259371 -0.050035279 1.588709e-02 -9.391639e-02
## 5 8 9 6 7
## X1 -2.504274e+00 4.573717e-01 -1.356059e+00 0.304483679 -4.594606e-01
## X2 -2.002373e+00 4.587904e-01 -4.234568e-01 0.229214643 -2.729668e+00
## X3 5.636796e-01 2.263185e-01 -2.818545e-02 0.811910704 -4.176066e-01
## X4 -9.588785e-01 -1.754348e-01 -2.080014e+00 1.022469988 -1.776054e+00
## X5 4.074975e+02 1.461564e+00 -1.295707e-02 1.578915901 5.354941e-01
## X6 1.578916e+00 7.585134e-01 -2.070802e+00 407.739672091 -3.092250e-01
## X7 5.354941e-01 1.284168e+00 7.994507e-01 -0.309224953 4.079021e+02
## X8 1.461564e+00 4.076672e+02 -3.574684e-01 0.758513396 1.284168e+00
## X9 -1.295707e-02 -3.574684e-01 4.079747e+02 -2.070801601 7.994507e-01
## X10 -6.842888e-02 5.694635e-01 1.577960e+00 -0.247946733 1.413321e+00
## X11 2.357711e-01 -1.777010e+00 9.885007e-01 -2.128257641 5.955482e-02
## X12 6.014101e-01 -1.862650e-01 1.496693e+00 0.005783867 2.253631e-01
## X13 4.771614e-01 -2.044885e+00 -2.126868e-03 -0.424412244 4.248211e-01
## X14 -9.554254e-04 7.121873e-02 1.116450e-01 0.231341511 6.847823e-01
## X15 4.530065e-01 -5.381303e-01 3.593862e-01 -1.232974782 4.154797e-01
## X16 3.512871e-02 2.704607e-01 8.047294e-01 0.099404178 -1.146735e-01
## X17 1.083020e-02 -1.113028e+00 3.763605e-01 -0.311811770 3.875717e-01
## X18 1.800739e-01 1.202892e-01 -8.623279e-02 -0.134188798 1.550758e-01
## X19 1.236151e-01 -2.833711e-01 3.666867e-01 -0.463374067 -2.828897e-02
## X20 2.033193e-01 -1.157528e-01 1.150582e-01 -0.143667421 2.085146e-01
## X21 -1.008009e-01 -5.033917e-01 -4.672500e-02 -0.578118485 1.027301e-01
## X22 -8.527736e-02 -6.759919e-02 2.610332e-01 -0.188264665 1.633017e-01
## X23 -8.631986e-02 -5.256000e-01 2.666185e-02 -0.551635144 -1.192369e-01
## X24 7.992951e-02 -1.976801e-01 2.145709e-01 -0.256649127 -3.275885e-02
## X25 -5.755520e-02 -5.003659e-01 -1.098215e-01 -0.231807974 -1.623881e-01
## X26 8.095922e-02 -3.638574e-01 -5.717068e-02 -0.135998407 1.311988e-01
## X27 -9.695323e-02 -2.562198e-01 -5.517980e-02 -0.416993728 -4.813977e-02
## X28 1.125163e-02 -1.639116e-01 2.218454e-01 -0.298422549 5.654739e-02
## X29 -9.020595e-03 -3.263470e-01 -2.022662e-02 -0.369937878 1.025506e-02
## X30 2.810668e-02 -1.782870e-01 1.563913e-01 -0.124792384 1.018983e-01
## X31 3.114005e-02 -2.700939e-01 -1.098805e-01 -0.206399916 1.889256e-02
## X32 1.419159e-01 -4.650943e-02 6.229601e-02 -0.157401992 1.279506e-01
## X33 3.732858e-02 -2.460022e-01 -5.939039e-02 -0.241653235 -8.899551e-02
## X34 7.543210e-02 -1.495314e-01 1.273120e-01 -0.028073408 1.023136e-01
## X35 -1.292728e-02 -2.422919e-01 -9.686613e-02 -0.286019842 -4.095437e-02
## X36 5.104438e-02 -7.758595e-02 1.774621e-01 -0.073463138 7.479347e-02
## X37 -5.036980e-02 -2.108714e-01 8.558175e-03 -0.189773357 -2.079790e-02
## X38 9.920530e-02 -1.552805e-01 9.087864e-02 -0.087001382 1.261928e-01
## X39 -1.280062e-01 -1.736882e-01 6.101948e-02 -0.159602143 -8.572525e-04
## X40 3.554614e-02 -1.058409e-01 1.230134e-01 -0.262488799 1.152905e-01
## X41 -2.877041e-02 -1.627816e-01 1.798230e-02 -0.198100017 -4.618881e-02
## X42 1.544654e-02 -2.276990e-01 7.733189e-02 -0.133754090 3.236668e-02
## X43 7.394676e-02 -2.360586e-01 -8.097861e-02 -0.072134922 -9.930854e-03
## X44 7.196898e-02 -1.452191e-01 2.419959e-02 -0.107563435 -2.251204e-02
## X45 6.835210e-02 -8.030202e-02 1.534183e-03 -0.136214667 3.915696e-02
## X46 -2.187341e-02 -9.311010e-02 7.594847e-02 -0.066936173 6.380189e-02
## X47 4.702758e-02 -3.775415e-02 2.470362e-02 -0.119904315 7.981714e-02
## X48 -1.134655e-02 -9.199583e-02 5.903919e-02 -0.085239480 7.658711e-02
## X49 3.030459e-02 -1.246670e-01 1.048768e-01 -0.038392785 3.257424e-02
## X50 6.050193e-02 -9.644736e-02 -6.410880e-03 -0.141508374 -1.610924e-02
## X51 -4.924313e-02 -1.213908e-01 4.378212e-02 -0.049518570 5.536424e-02
## X52 -1.292979e-02 -7.594208e-02 6.923484e-03 -0.178264734 -2.249605e-02
## X53 3.652469e-02 -2.648584e-02 -1.020205e-02 -0.105305599 -3.803526e-02
## X54 1.546253e-02 -2.059778e-01 -5.865291e-03 -0.094781637 1.010294e-02
## X55 -3.245456e-03 -8.867484e-02 -1.032215e-02 -0.029665300 -2.904160e-02
## X56 1.827004e-02 -1.362884e-01 2.326419e-03 -0.171188036 3.209329e-02
## X57 -4.050664e-02 -3.744182e-02 1.246516e-02 -0.126633418 2.446764e-02
## X58 -6.636722e-02 -1.057155e-01 2.060838e-02 -0.147753433 1.049351e-02
## X59 3.892098e-02 -1.381183e-01 -4.100486e-02 -0.045608916 1.000123e-03
## X60 1.525621e-02 -1.560323e-01 3.438138e-02 -0.091262197 -7.785214e-02
## X61 -2.405953e-02 -2.172105e-02 9.278952e-03 -0.039657817 -2.655152e-02
## X62 5.145848e-03 -1.380978e-01 -3.020093e-02 -0.181091916 3.914407e-02
## X63 -3.775940e-02 7.993394e-03 2.028412e-02 -0.026483745 -1.578070e-02
## X64 1.611134e-02 -1.516379e-01 2.878271e-02 -0.149305715 5.279706e-02
## X65 4.978559e-02 -3.684510e-02 -4.523468e-02 -0.075004592 9.076237e-03
## X66 3.616630e-02 -1.544976e-01 8.834361e-02 -0.086071652 5.749985e-03
## X67 -1.863686e-02 -3.945804e-02 1.426812e-02 -0.013812374 2.033161e-02
## X68 1.352651e-02 -1.362770e-01 -5.953558e-03 -0.182210698 7.171285e-02
## X69 -2.117515e-02 -2.551592e-02 7.053696e-02 -0.022827277 -1.344498e-02
## X70 8.319776e-02 -1.398931e-01 1.890332e-02 -0.177783759 1.822964e-03
## X71 5.202752e-02 -7.563681e-02 -5.576263e-02 -0.033292439 2.903020e-02
## X72 -2.206490e-02 -1.407857e-01 2.066694e-02 -0.074420547 3.038823e-02
## X73 2.075137e-02 -1.444847e-02 -7.967861e-03 -0.087121725 9.709874e-03
## X74 -1.726298e-02 -6.773562e-02 4.752110e-02 -0.149064524 -3.220929e-03
## X75 -3.712577e-02 -6.998885e-02 3.024949e-03 0.009439396 -1.624669e-02
## X76 7.140428e-03 -1.619150e-01 -6.330162e-03 -0.114571261 -1.301062e-04
## X77 1.320728e-02 6.330162e-03 -3.396236e-03 -0.022337639 -4.381069e-02
## X78 -3.567666e-02 -1.145713e-01 2.233764e-02 -0.132461004 4.031195e-03
## X79 -4.900257e-02 1.301062e-04 -4.381069e-02 -0.004031195 2.605774e-02
## X80 1.573474e-02 -1.196106e-01 9.219608e-04 -0.119763143 -1.320891e-02
## X81 -2.414761e-02 -7.140428e-03 1.320728e-02 0.035676660 -4.900257e-02
## X82 3.960062e-02 -1.264481e-01 3.923961e-03 -0.169815898 1.262550e-02
## X83 -6.684925e-03 5.280954e-02 -4.231765e-02 -0.018843971 -3.699806e-02
## X84 -4.397121e-03 -1.462396e-01 2.225228e-02 -0.059489191 4.011664e-02
## 72 73 14 15 12
## X1 -0.075238471 -0.005700970 -2.894707e-02 -0.556233618 -0.114889135
## X2 -0.163573834 0.013339021 -2.349897e-01 -0.666693355 0.223019254
## X3 0.035546554 0.005191882 -4.824345e-02 0.072511889 -0.294747426
## X4 -0.186062588 -0.009404575 3.396932e-02 -0.198093699 0.169659826
## X5 -0.022064900 0.020751374 -9.554254e-04 0.453006531 0.601410132
## X6 -0.074420547 -0.087121725 2.313415e-01 -1.232974782 0.005783867
## X7 0.030388229 0.009709874 6.847823e-01 0.415479691 0.225363120
## X8 -0.140785695 -0.014448468 7.121873e-02 -0.538130316 -0.186265048
## X9 0.020666935 -0.007967861 1.116450e-01 0.359386220 1.496692991
## X10 -0.133208126 -0.058503937 -1.471459e-01 -1.924938353 0.634898319
## X11 0.036036192 -0.062447555 1.616640e+00 -0.041246046 1.464242405
## X12 -0.112129390 -0.009781179 6.557833e-01 -1.862286960 407.767961065
## X13 0.009781179 0.046389352 1.492683e+00 0.902180817 -0.154149115
## X14 -0.105495024 -0.052666953 4.077864e+02 -0.194166742 0.655783312
## X15 0.075134698 -0.034734454 -1.941667e-01 407.855424867 -1.862286960
## X16 -0.164845227 -0.035923141 7.318515e-01 1.545201627 -0.128709848
## X17 0.029704673 -0.032027392 -1.809768e+00 0.826112583 -1.964955980
## X18 -0.100972071 0.047463909 -1.381253e-01 1.627891758 0.168171956
## X19 0.009269588 -0.016841651 -1.913687e+00 -0.050266641 -0.457171094
## X20 -0.176783636 -0.012316477 6.096367e-02 0.168192438 0.279481284
## X21 0.043785952 0.030030326 -4.815829e-01 0.369641278 -1.101776015
## X22 -0.157743053 -0.103806142 2.515681e-01 0.906627733 0.089149119
## X23 0.054920567 0.011022662 -1.011129e+00 0.395253073 -0.255264381
## X24 -0.115113251 -0.015852926 2.092847e-01 0.041717824 -0.153081358
## X25 0.023915315 -0.008709985 -1.554204e-01 0.277691163 -0.361475754
## X26 -0.187340971 -0.030301007 -7.479840e-02 0.217371852 -0.054671909
## X27 0.052508540 -0.028959019 -4.010781e-01 -0.087679368 -0.450167876
## X28 -0.125727671 -0.023034825 -4.680129e-02 0.335826618 -0.147310294
## X29 0.010374500 0.039583542 -4.508065e-01 0.005863951 -0.449321503
## X30 -0.058687956 0.001265032 -1.968228e-01 0.340763740 -0.235851227
## X31 0.116244922 0.006022717 -3.741731e-01 -0.110678711 -0.157014507
## X32 -0.067936297 -0.074295399 -3.176686e-01 0.058119789 -0.135141155
## X33 0.109410802 0.080817259 -1.409293e-01 -0.101368613 -0.290800910
## X34 -0.132031080 -0.009581249 -1.539807e-01 0.254212127 -0.252233740
## X35 0.104121377 0.063624601 -2.939804e-01 -0.030157472 -0.254647407
## X36 -0.104712491 -0.042469622 -2.174439e-01 0.133879279 -0.114861530
## X37 0.062031981 -0.038972453 -2.926060e-01 -0.070723549 -0.174033235
## X38 -0.224453543 -0.092794419 -1.263266e-01 0.126097900 -0.196558948
## X39 0.220596069 -0.084224064 -1.822003e-01 0.020426743 -0.264165276
## X40 -0.142365626 -0.110083574 -1.821056e-01 0.203899082 -0.107890544
## X41 0.175711387 0.054506992 -1.657048e-01 -0.064291892 -0.222217956
## X42 -0.106037380 -0.151380572 -1.329502e-01 0.161352835 -0.106037380
## X43 0.113186251 0.011776342 -2.269806e-01 0.063922420 -0.113186251
## X44 -0.107890544 -0.166115527 -1.172453e-01 0.068382586 -0.142365626
## X45 0.222217956 0.038862765 -1.961842e-01 0.022984220 -0.175711387
## X46 -0.196558948 -0.105438568 -7.679934e-02 0.133116301 -0.224453543
## X47 0.264165276 -0.049838557 -1.526787e-01 -0.011059298 -0.220596069
## X48 -0.114861530 -0.134264994 -2.521666e-01 0.109425180 -0.104712491
## X49 0.174033235 0.008961706 -2.039653e-01 -0.056510963 -0.062031981
## X50 -0.252233740 -0.171837860 -1.462192e-01 0.034693100 -0.132031080
## X51 0.254647407 -0.035933750 -6.980850e-02 0.002534306 -0.104121377
## X52 -0.135141155 -0.257391585 -6.655858e-02 -0.001903665 -0.067936297
## X53 0.290800910 -0.048997025 -1.156063e-01 -0.001847903 -0.109410802
## X54 -0.235851227 -0.042034617 -7.621513e-02 0.098183263 -0.058687956
## X55 0.157014507 -0.183185988 -8.552294e-02 0.089096088 -0.116244922
## X56 -0.147310294 -0.265615302 -1.055236e-01 0.046386179 -0.125727671
## X57 0.449321503 -0.160191257 -6.859371e-02 0.052858357 -0.010374500
## X58 -0.054671909 -0.336465250 -9.627370e-02 0.012673468 -0.187340971
## X59 0.450167876 0.013734571 -2.073586e-02 0.010129568 -0.052508540
## X60 -0.153081358 -0.256974151 -1.925329e-01 0.065847561 -0.115113251
## X61 0.361475754 -0.009396415 -1.696199e-02 -0.023767137 -0.023915315
## X62 0.089149119 0.058126107 -1.653186e-01 0.004149383 -0.157743053
## X63 0.255264381 0.397826727 -3.561886e-02 0.041495363 -0.054920567
## X64 0.279481284 -0.815981054 -1.154254e-01 0.050996606 -0.176783636
## X65 1.101776015 0.367339918 -1.077301e-01 -0.031294985 -0.043785952
## X66 0.168171956 -0.192604271 -1.397856e-01 0.031160448 -0.100972071
## X67 0.457171094 0.262432993 -2.494198e-02 -0.006967738 -0.009269588
## X68 -0.128709848 -1.576622497 -9.428715e-02 -0.030331033 -0.164845227
## X69 1.964955980 -0.059682069 7.863288e-03 -0.023526576 -0.029704673
## X70 0.655783312 -1.492683116 -1.776957e-01 0.032813907 -0.105495024
## X71 1.862286960 0.902180817 -3.281391e-02 -0.019176938 -0.075134698
## X72 407.767961065 0.154149115 -1.054950e-01 0.075134698 -0.112129390
## X73 0.154149115 407.873860890 -5.266695e-02 -0.034734454 -0.009781179
## X74 0.634898319 1.890727672 -9.927894e-02 0.006671945 -0.133208126
## X75 -1.464242405 0.923065810 -1.289041e-02 0.033538899 -0.036036192
## X76 -0.186265048 2.044885486 -1.398931e-01 0.075636812 -0.140785695
## X77 -1.496692991 -0.002126868 -1.890332e-02 -0.055762630 -0.020666935
## X78 0.005783867 0.424412244 -1.777838e-01 0.033292439 -0.074420547
## X79 -0.225363120 0.424821082 -1.822964e-03 0.029030203 -0.030388229
## X80 0.169659826 1.316346937 -1.167382e-01 0.034312190 -0.186062588
## X81 -0.601410132 0.477161376 -8.319776e-02 0.052027521 0.022064900
## X82 0.223019254 0.491885700 -1.358572e-01 -0.002298968 -0.163573834
## X83 0.294747426 0.263956592 1.036136e-02 -0.029453974 -0.035546554
## X84 -0.114889135 0.437310122 -1.119930e-01 0.015703097 -0.075238471
## 13 10 11
## X1 -0.437310122 0.344343923 -1.393978e-01
## X2 -0.491885700 0.242171715 -1.268103e+00
## X3 0.263956592 0.649653582 4.046495e-01
## X4 -1.316346937 0.194833806 -7.182042e-01
## X5 0.477161376 -0.068428881 2.357711e-01
## X6 -0.424412244 -0.247946733 -2.128258e+00
## X7 0.424821082 1.413320836 5.955482e-02
## X8 -2.044885486 0.569463457 -1.777010e+00
## X9 -0.002126868 1.577960476 9.885007e-01
## X10 -1.890727672 407.728841887 -2.740962e-01
## X11 0.923065810 -0.274096248 4.079130e+02
## X12 -0.154149115 0.634898319 1.464242e+00
## X13 407.873860890 -1.890727672 9.230658e-01
## X14 1.492683116 -0.147145870 1.616640e+00
## X15 0.902180817 -1.924938353 -4.124605e-02
## X16 1.576622497 0.092103722 1.400858e-01
## X17 -0.059682069 -0.509689604 3.385012e-01
## X18 0.192604271 0.288896712 7.647118e-01
## X19 0.262432993 -1.153045276 3.579245e-01
## X20 0.815981054 0.196357404 -3.371427e-02
## X21 0.367339918 -0.230852548 2.906184e-01
## X22 -0.058126107 -0.125168203 1.663275e-01
## X23 0.397826727 -0.452122433 -3.730957e-02
## X24 0.256974151 -0.174807472 2.366213e-01
## X25 -0.009396415 -0.550011807 1.338701e-01
## X26 0.336465250 -0.225593247 3.052176e-01
## X27 0.013734571 -0.409719204 -8.190830e-02
## X28 0.265615302 -0.243721848 4.267325e-02
## X29 -0.160191257 -0.156375875 -1.753154e-01
## X30 0.042034617 -0.085628608 1.822431e-01
## X31 -0.183185988 -0.365949348 -9.850957e-02
## X32 0.257391585 -0.170416365 1.557527e-01
## X33 -0.048997025 -0.270732579 -1.177511e-01
## X34 0.171837860 -0.096021977 1.374445e-01
## X35 -0.035933750 -0.170853777 -9.877848e-03
## X36 0.134264994 -0.231348747 1.433971e-01
## X37 0.008961706 -0.226206696 -1.504876e-02
## X38 0.105438568 -0.096425507 1.742826e-01
## X39 -0.049838557 -0.214050862 2.739773e-02
## X40 0.166115527 -0.120490714 5.292006e-02
## X41 0.038862765 -0.211646766 2.622968e-02
## X42 0.151380572 -0.117305972 1.148463e-01
## X43 0.011776342 -0.170948695 2.944734e-02
## X44 0.110083574 -0.213245664 1.757924e-01
## X45 0.054506992 -0.137598084 -9.543194e-02
## X46 0.092794419 -0.170278781 1.943689e-02
## X47 -0.084224064 -0.085064708 2.659384e-02
## X48 0.042469622 -0.104317979 -7.049513e-03
## X49 -0.038972453 -0.120752138 3.591150e-02
## X50 0.009581249 -0.026429537 8.207192e-02
## X51 0.063624601 -0.101634280 3.931050e-02
## X52 0.074295399 -0.124160460 1.021988e-02
## X53 0.080817259 -0.104760009 7.149522e-02
## X54 -0.001265032 -0.117448843 -8.530388e-04
## X55 0.006022717 -0.034262364 3.130471e-02
## X56 0.023034825 -0.140505332 -1.735020e-02
## X57 0.039583542 -0.100159751 -7.579466e-02
## X58 0.030301007 -0.144567225 2.621428e-02
## X59 -0.028959019 -0.013553958 2.074399e-02
## X60 0.015852926 -0.152551172 6.825959e-02
## X61 -0.008709985 -0.090467121 5.830780e-03
## X62 0.103806142 -0.126578288 2.402002e-02
## X63 0.011022662 -0.032082409 -2.017502e-02
## X64 0.012316477 -0.143289719 5.345627e-03
## X65 0.030030326 0.043539948 2.547600e-02
## X66 -0.047463909 -0.201843290 1.707917e-02
## X67 -0.016841651 -0.048548644 4.970672e-03
## X68 0.035923141 -0.112179949 3.553408e-02
## X69 -0.032027392 -0.092267574 -2.804953e-02
## X70 0.052666953 -0.099278936 1.289041e-02
## X71 -0.034734454 -0.006671945 3.353890e-02
## X72 0.009781179 -0.133208126 3.603619e-02
## X73 0.046389352 -0.058503937 -6.244756e-02
## X74 0.058503937 -0.153636149 1.755770e-02
## X75 -0.062447555 -0.017557702 4.882593e-03
## X76 0.014448468 -0.067735622 6.998885e-02
## X77 -0.007967861 -0.047521105 3.024949e-03
## X78 0.087121725 -0.149064524 -9.439396e-03
## X79 0.009709874 0.003220929 -1.624669e-02
## X80 0.009404575 -0.121256186 3.947051e-02
## X81 0.020751374 0.017262982 -3.712577e-02
## X82 -0.013339021 -0.156608614 1.976593e-02
## X83 0.005191882 0.011703543 5.020535e-02
## X84 0.005700970 -0.119335382 -3.456732e-02
##
## $Tregresores
## C 1 2 3 4
## [1,] 0.1091089 44.22911 6.254940e+01 1.796827e-13 62.549404
## [2,] 0.1091089 44.14983 6.226269e+01 4.665944e+00 61.739909
## [3,] 0.1091089 44.05982 6.161404e+01 9.286822e+00 59.541731
## [4,] 0.1091089 44.10356 6.080806e+01 1.387904e+01 56.195093
## [5,] 0.1091089 44.19422 5.972336e+01 1.842222e+01 51.639977
## [6,] 0.1091089 44.12548 5.808918e+01 2.279832e+01 45.744532
## [7,] 0.1091089 43.95117 5.600093e+01 2.696863e+01 38.753845
## [8,] 0.1091089 43.85932 5.371648e+01 3.101322e+01 31.013225
## [9,] 0.1091089 43.87159 5.126299e+01 3.495051e+01 22.667142
## [10,] 0.1091089 43.78615 4.841332e+01 3.860834e+01 13.779156
## [11,] 0.1091089 43.82144 4.542934e+01 4.215226e+01 4.631239
## [12,] 0.1091089 43.81420 4.214529e+01 4.542182e+01 -4.630473
## [13,] 0.1091089 43.95080 3.875351e+01 4.859537e+01 -13.830969
## [14,] 0.1091089 43.98641 3.504199e+01 5.139716e+01 -22.726469
## [15,] 0.1091089 43.97948 3.109819e+01 5.386365e+01 -31.098191
## [16,] 0.1091089 44.04933 2.702886e+01 5.612600e+01 -38.840398
## [17,] 0.1091089 44.17459 2.282370e+01 5.815383e+01 -45.795439
## [18,] 0.1091089 44.25854 1.844903e+01 5.981028e+01 -51.715130
## [19,] 0.1091089 44.20399 1.391065e+01 6.094653e+01 -56.323065
## [20,] 0.1091089 44.30092 9.337641e+00 6.195120e+01 -59.867556
## [21,] 0.1091089 44.34321 4.686382e+00 6.253542e+01 -62.010347
## [22,] 0.1091089 44.33107 -3.496882e-13 6.269359e+01 -62.693595
## [23,] 0.1091089 44.33482 -4.685495e+00 6.252359e+01 -61.998611
## [24,] 0.1091089 44.38265 -9.354868e+00 6.206549e+01 -59.978002
## [25,] 0.1091089 44.20577 -1.391121e+01 6.094898e+01 -56.325326
## [26,] 0.1091089 44.18147 -1.841690e+01 5.970613e+01 -51.625075
## [27,] 0.1091089 44.14292 -2.280733e+01 5.811214e+01 -45.762608
## [28,] 0.1091089 44.10178 -2.706104e+01 5.619283e+01 -38.886645
## [29,] 0.1091089 44.29276 -3.131971e+01 5.424733e+01 -31.319711
## [30,] 0.1091089 44.27882 -3.527494e+01 5.173883e+01 -22.877548
## [31,] 0.1091089 44.34693 -3.910280e+01 4.903336e+01 -13.955628
## [32,] 0.1091089 44.41293 -4.272122e+01 4.604253e+01 -4.693750
## [33,] 0.1091089 44.51056 -4.614374e+01 4.281513e+01 4.704068
## [34,] 0.1091089 44.53604 -4.924247e+01 3.926956e+01 14.015142
## [35,] 0.1091089 44.58189 -5.209297e+01 3.551638e+01 23.034138
## [36,] 0.1091089 44.63544 -5.466703e+01 3.156202e+01 31.562022
## [37,] 0.1091089 44.59329 -5.681909e+01 2.736263e+01 39.320029
## [38,] 0.1091089 44.62341 -5.874467e+01 2.305559e+01 46.260724
## [39,] 0.1091089 44.55231 -6.020728e+01 1.857149e+01 52.058401
## [40,] 0.1091089 44.50398 -6.136014e+01 1.400505e+01 56.705295
## [41,] 0.1091089 44.43577 -6.213977e+01 9.366064e+00 60.049786
## [42,] 0.1091089 44.38281 -6.259126e+01 4.690566e+00 62.065716
## [43,] 0.1091089 44.31781 -6.267484e+01 4.473936e-13 62.674844
## [44,] 0.1091089 44.23711 -6.238579e+01 -4.675168e+00 61.861967
## [45,] 0.1091089 44.00145 -6.153242e+01 -9.274520e+00 59.462859
## [46,] 0.1091089 44.01071 -6.068005e+01 -1.384982e+01 56.076797
## [47,] 0.1091089 44.01244 -5.947771e+01 -1.834644e+01 51.427572
## [48,] 0.1091089 44.08036 -5.802978e+01 -2.277501e+01 45.697753
## [49,] 0.1091089 44.13210 -5.623146e+01 -2.707965e+01 38.913381
## [50,] 0.1091089 44.16586 -5.409191e+01 -3.122998e+01 31.229978
## [51,] 0.1091089 44.21869 -5.166857e+01 -3.522704e+01 22.846482
## [52,] 0.1091089 44.23091 -4.890509e+01 -3.900051e+01 13.919119
## [53,] 0.1091089 44.20619 -4.582820e+01 -4.252235e+01 4.671901
## [54,] 0.1091089 44.34952 -4.266022e+01 -4.597679e+01 -4.687048
## [55,] 0.1091089 44.32325 -3.908193e+01 -4.900719e+01 -13.948178
## [56,] 0.1091089 44.37750 -3.535355e+01 -5.185413e+01 -22.928532
## [57,] 0.1091089 44.57957 -3.152252e+01 -5.459860e+01 -31.522516
## [58,] 0.1091089 44.69939 -2.742774e+01 -5.695429e+01 -39.413589
## [59,] 0.1091089 44.77676 -2.313482e+01 -5.894655e+01 -46.419702
## [60,] 0.1091089 44.79353 -1.867204e+01 -6.053327e+01 -52.340263
## [61,] 0.1091089 44.78325 -1.409294e+01 -6.174519e+01 -57.061132
## [62,] 0.1091089 44.80293 -9.443453e+00 -6.265322e+01 -60.545959
## [63,] 0.1091089 44.82929 -4.737753e+00 -6.322092e+01 -62.690086
## [64,] 0.1091089 44.86952 1.530234e-13 -6.345508e+01 -63.455080
## [65,] 0.1091089 44.80708 4.735405e+00 -6.318959e+01 -62.659023
## [66,] 0.1091089 44.82288 9.447659e+00 -6.268112e+01 -60.572928
## [67,] 0.1091089 44.96554 1.415030e+01 -6.199652e+01 -57.293397
## [68,] 0.1091089 45.06193 1.878392e+01 -6.089597e+01 -52.653877
## [69,] 0.1091089 45.05709 2.327966e+01 -5.931560e+01 -46.710321
## [70,] 0.1091089 45.04281 2.763846e+01 -5.739185e+01 -39.716392
## [71,] 0.1091089 45.06733 3.186741e+01 -5.519598e+01 -31.867413
## [72,] 0.1091089 45.12866 3.595197e+01 -5.273185e+01 -23.316636
## [73,] 0.1091089 45.12798 3.979150e+01 -4.989696e+01 -14.201420
## [74,] 0.1091089 45.05855 4.334224e+01 -4.671183e+01 -4.761981
## [75,] 0.1091089 44.98190 4.663237e+01 -4.326851e+01 4.753881
## [76,] 0.1091089 45.05224 4.981321e+01 -3.972471e+01 14.177585
## [77,] 0.1091089 45.15249 5.275970e+01 -3.597095e+01 23.328948
## [78,] 0.1091089 45.19556 5.535303e+01 -3.195809e+01 31.958087
## [79,] 0.1091089 45.29852 5.771767e+01 -2.779536e+01 39.941865
## [80,] 0.1091089 45.35676 5.971010e+01 -2.343449e+01 47.020987
## [81,] 0.1091089 45.48396 6.146630e+01 -1.895984e+01 53.147014
## [82,] 0.1091089 45.56503 6.282307e+01 -1.433896e+01 58.057248
## [83,] 0.1091089 45.60786 6.377886e+01 -9.613116e+00 61.633739
## [84,] 0.1091089 45.52753 6.420561e+01 -4.811545e+00 63.666512
## 5 8 9 6 7
## [1,] -3.312882e-13 62.549404 5.365170e-13 6.254940e+01 2.005123e-13
## [2,] 9.305794e+00 59.663369 1.840371e+01 6.087185e+01 1.389360e+01
## [3,] 1.836619e+01 51.482929 3.510047e+01 5.613936e+01 2.703529e+01
## [4,] 2.706213e+01 38.888211 4.876427e+01 4.876427e+01 3.888821e+01
## [5,] 3.520754e+01 22.833838 5.817967e+01 3.896815e+01 4.886452e+01
## [6,] 4.244472e+01 4.663371 6.222837e+01 2.707559e+01 5.622303e+01
## [7,] 4.859578e+01 -13.831087 6.059795e+01 1.383109e+01 6.059795e+01
## [8,] 5.371648e+01 -31.013225 5.371648e+01 -1.635705e-13 6.202645e+01
## [9,] 5.775494e+01 -45.481318 4.220050e+01 -1.380604e+01 6.048822e+01
## [10,] 6.037043e+01 -55.790665 2.686737e+01 -2.686737e+01 5.579066e+01
## [11,] 6.179959e+01 -61.280695 9.236579e+00 -3.863946e+01 4.845235e+01
## [12,] 6.178937e+01 -61.270561 -9.235051e+00 -4.844434e+01 3.863307e+01
## [13,] 6.059744e+01 -56.000451 -2.696840e+01 -5.600045e+01 2.696840e+01
## [14,] 5.790610e+01 -45.600355 -4.231095e+01 -6.064654e+01 1.384218e+01
## [15,] 5.386365e+01 -31.098191 -5.386365e+01 -6.219638e+01 -1.130693e-14
## [16,] 4.870432e+01 -13.861977 -6.073329e+01 -6.073329e+01 -1.386198e+01
## [17,] 4.249196e+01 4.668561 -6.229762e+01 -5.628560e+01 -2.710572e+01
## [18,] 3.525878e+01 22.867068 -5.826434e+01 -4.893563e+01 -3.902486e+01
## [19,] 2.712376e+01 38.976770 -4.887532e+01 -3.897677e+01 -4.887532e+01
## [20,] 1.846670e+01 51.764654 -3.529254e+01 -2.718323e+01 -5.644657e+01
## [21,] 9.346556e+00 59.924711 -1.848433e+01 -1.395446e+01 -6.113848e+01
## [22,] 5.372072e-13 62.693595 2.192474e-14 3.022834e-13 -6.269359e+01
## [23,] -9.344787e+00 59.913370 1.848083e+01 1.395182e+01 -6.112691e+01
## [24,] -1.850076e+01 51.860152 3.535765e+01 2.723338e+01 -5.655070e+01
## [25,] -2.712485e+01 38.978335 4.887729e+01 3.897833e+01 -4.887729e+01
## [26,] -3.519738e+01 22.827249 5.816288e+01 4.885042e+01 -3.895691e+01
## [27,] -4.246149e+01 4.665214 6.225296e+01 5.624525e+01 -2.708628e+01
## [28,] -4.876231e+01 -13.878483 6.080561e+01 6.080561e+01 -1.387848e+01
## [29,] -5.424733e+01 -31.319711 5.424733e+01 6.263942e+01 4.116698e-13
## [30,] -5.829104e+01 -45.903494 4.259222e+01 6.104970e+01 1.393420e+01
## [31,] -6.114360e+01 -56.505184 2.721146e+01 5.650518e+01 2.721146e+01
## [32,] -6.263374e+01 -62.107842 9.361251e+00 4.910634e+01 3.916100e+01
## [33,] -6.277142e+01 -62.244367 -9.381829e+00 3.924709e+01 4.921429e+01
## [34,] -6.140435e+01 -56.746152 -2.732751e+01 2.732751e+01 5.674615e+01
## [35,] -5.869003e+01 -46.217689 -4.288375e+01 1.402957e+01 6.146757e+01
## [36,] -5.466703e+01 -31.562022 -5.466703e+01 -4.411116e-13 6.312404e+01
## [37,] -4.930576e+01 -14.033156 -6.148327e+01 -1.403316e+01 6.148327e+01
## [38,] -4.292368e+01 4.715994 -6.293057e+01 -2.738111e+01 5.685747e+01
## [39,] -3.549282e+01 23.018854 -5.865108e+01 -3.928390e+01 4.926045e+01
## [40,] -2.730783e+01 39.241282 -4.920701e+01 -4.920701e+01 3.924128e+01
## [41,] -1.852291e+01 51.922220 -3.539997e+01 -5.661838e+01 2.726598e+01
## [42,] -9.354901e+00 59.978217 -1.850083e+01 -6.119307e+01 1.396692e+01
## [43,] -6.299540e-15 62.674844 2.136403e-13 -6.267484e+01 1.574357e-13
## [44,] 9.324191e+00 59.781321 1.844010e+01 -6.099219e+01 -1.392107e+01
## [45,] 1.834186e+01 51.414732 3.505397e+01 -5.606500e+01 -2.699948e+01
## [46,] 2.700516e+01 38.806347 4.866162e+01 -4.866162e+01 -3.880635e+01
## [47,] 3.506272e+01 22.739918 5.794037e+01 -3.880787e+01 -4.866353e+01
## [48,] 4.240132e+01 4.658603 6.216473e+01 -2.704790e+01 -5.616554e+01
## [49,] 4.879584e+01 -13.888025 6.084741e+01 -1.388802e+01 -6.084741e+01
## [50,] 5.409191e+01 -31.229978 5.409191e+01 -4.767029e-13 -6.245996e+01
## [51,] 5.821189e+01 -45.841159 4.253438e+01 1.391527e+01 -6.096680e+01
## [52,] 6.098365e+01 -56.357363 2.714028e+01 2.714028e+01 -5.635736e+01
## [53,] 6.234218e+01 -61.818729 9.317674e+00 3.897871e+01 -4.887775e+01
## [54,] 6.254431e+01 -62.019162 -9.347885e+00 4.903623e+01 -3.910509e+01
## [55,] 6.111096e+01 -56.475020 -2.719694e+01 5.647502e+01 -2.719694e+01
## [56,] 5.842095e+01 -46.005792 -4.268714e+01 6.118575e+01 -1.396525e+01
## [57,] 5.459860e+01 -31.522516 -5.459860e+01 6.304503e+01 -3.738797e-13
## [58,] 4.942308e+01 -14.066547 -6.162957e+01 6.162957e+01 1.406655e+01
## [59,] 4.307119e+01 4.732201 -6.314683e+01 5.705286e+01 2.747521e+01
## [60,] 3.568499e+01 23.143486 -5.896864e+01 4.952717e+01 3.949660e+01
## [61,] 2.747919e+01 39.487528 -4.951579e+01 3.948753e+01 4.951579e+01
## [62,] 1.867596e+01 52.351238 -3.569247e+01 2.749127e+01 5.708620e+01
## [63,] 9.449010e+00 60.581588 -1.868694e+01 1.410742e+01 6.180867e+01
## [64,] -7.960212e-15 63.455080 -4.957276e-14 -7.378126e-14 6.345508e+01
## [65,] -9.444328e+00 60.551570 1.867769e+01 -1.410043e+01 6.177804e+01
## [66,] -1.868427e+01 52.374556 3.570837e+01 -2.750351e+01 5.711163e+01
## [67,] -2.759105e+01 39.648261 4.971735e+01 -3.964826e+01 4.971735e+01
## [68,] -3.589881e+01 23.282158 5.932197e+01 -4.982393e+01 3.973325e+01
## [69,] -4.334084e+01 4.761828 6.354217e+01 -5.741005e+01 2.764722e+01
## [70,] -4.980278e+01 -14.174616 6.210305e+01 -6.210305e+01 1.417462e+01
## [71,] -5.519598e+01 -31.867413 5.519598e+01 -6.373483e+01 -2.123119e-13
## [72,] -5.940982e+01 -46.784518 4.340969e+01 -6.222143e+01 -1.420163e+01
## [73,] -6.222049e+01 -57.500377 2.769072e+01 -5.750038e+01 -2.769072e+01
## [74,] -6.354422e+01 -63.010679 9.497332e+00 -4.982018e+01 -3.973027e+01
## [75,] -6.343613e+01 -62.903491 -9.481176e+00 -3.966268e+01 -4.973543e+01
## [76,] -6.211606e+01 -57.403869 -2.764425e+01 -2.764425e+01 -5.740387e+01
## [77,] -5.944119e+01 -46.809222 -4.343261e+01 -1.420913e+01 -6.225428e+01
## [78,] -5.535303e+01 -31.958087 -5.535303e+01 1.558805e-13 -6.391617e+01
## [79,] -5.008551e+01 -14.255087 -6.245562e+01 1.425509e+01 -6.245562e+01
## [80,] -4.362910e+01 4.793498 -6.396479e+01 2.783110e+01 -5.779188e+01
## [81,] -3.623502e+01 23.500210 -5.987756e+01 4.010538e+01 -5.029056e+01
## [82,] -2.795890e+01 40.176862 -5.038019e+01 5.038019e+01 -4.017686e+01
## [83,] -1.901149e+01 53.291790 -3.633373e+01 5.811183e+01 -2.798518e+01
## [84,] -9.596183e+00 61.525173 -1.897800e+01 6.277136e+01 -1.432715e+01
## 72 73 14 15 12
## [1,] 62.54940 2.673348e-13 6.254940e+01 -2.499743e-13 62.54940
## [2,] -56.25405 2.709052e+01 5.407227e+01 3.121864e+01 56.25405
## [3,] 38.84964 -4.871591e+01 3.115499e+01 5.396203e+01 38.84964
## [4,] -13.87904 6.080806e+01 1.950592e-13 6.237185e+01 13.87904
## [5,] -13.90757 -6.093306e+01 -3.125003e+01 5.412664e+01 -13.90757
## [6,] 38.90755 4.878852e+01 -5.404246e+01 3.120143e+01 -38.90755
## [7,] -56.00093 -2.696863e+01 -6.215634e+01 -2.420395e-14 -56.00093
## [8,] 62.02645 2.792558e-13 -5.371648e+01 -3.101322e+01 -62.02645
## [9,] -55.89952 2.691979e+01 -3.102190e+01 -5.373150e+01 -55.89952
## [10,] 38.60834 -4.841332e+01 -5.641113e-13 -6.192297e+01 -38.60834
## [11,] -13.79026 6.041909e+01 3.098644e+01 -5.367009e+01 -13.79026
## [12,] -13.78798 -6.040910e+01 5.366121e+01 -3.098132e+01 13.78798
## [13,] 38.75351 4.859537e+01 6.215581e+01 2.941933e-13 38.75351
## [14,] -56.04583 -2.699025e+01 5.387213e+01 3.110309e+01 56.04583
## [15,] 62.19638 1.182665e-13 3.109819e+01 5.386365e+01 62.19638
## [16,] -56.12600 2.702886e+01 -1.670886e-14 6.229516e+01 56.12600
## [17,] 38.95084 -4.884281e+01 -3.123615e+01 5.410260e+01 38.95084
## [18,] -13.92781 6.102173e+01 -5.420542e+01 3.129551e+01 13.92781
## [19,] -13.91065 -6.094653e+01 -6.251389e+01 1.141832e-13 -13.91065
## [20,] 39.06224 4.898249e+01 -5.425732e+01 -3.132548e+01 -39.06224
## [21,] -56.50046 -2.720919e+01 -3.135539e+01 -5.430912e+01 -56.50046
## [22,] 62.69359 -9.033052e-14 -3.916624e-13 -6.269359e+01 -62.69359
## [23,] -56.48976 2.720404e+01 3.134945e+01 -5.429885e+01 -56.48976
## [24,] 39.13430 -4.907286e+01 5.435742e+01 -3.138327e+01 -39.13430
## [25,] -13.91121 6.094898e+01 6.251640e+01 -2.027699e-13 -13.91121
## [26,] -13.90356 -6.091547e+01 5.411102e+01 3.124101e+01 13.90356
## [27,] 38.92292 4.880780e+01 3.121376e+01 5.406382e+01 38.92292
## [28,] -56.19283 -2.706104e+01 3.890985e-14 6.236934e+01 56.19283
## [29,] 62.63942 3.102865e-13 -3.131971e+01 5.424733e+01 62.63942
## [30,] -56.41841 2.716967e+01 -5.423026e+01 3.130985e+01 56.41841
## [31,] 39.10280 -4.903336e+01 -6.271602e+01 4.998868e-13 39.10280
## [32,] -13.97640 6.123461e+01 -5.439451e+01 -3.140469e+01 13.97640
## [33,] -14.00712 -6.136921e+01 -3.147372e+01 -5.451408e+01 -14.00712
## [34,] 39.26956 4.924247e+01 2.449221e-13 -6.298348e+01 -39.26956
## [35,] -56.80457 -2.735564e+01 3.152416e+01 -5.460145e+01 -56.80457
## [36,] 63.12404 9.839143e-13 5.466703e+01 -3.156202e+01 -63.12404
## [37,] -56.81909 2.736263e+01 6.306443e+01 -1.973502e-13 -56.81909
## [38,] 39.34659 -4.933906e+01 5.465229e+01 3.155351e+01 -39.34659
## [39,] -14.02026 6.142678e+01 3.150324e+01 5.456522e+01 -14.02026
## [40,] -14.00505 -6.136014e+01 -4.085031e-13 6.293813e+01 14.00505
## [41,] 39.18114 4.913159e+01 -3.142083e+01 5.442248e+01 39.18114
## [42,] -56.55090 -2.723348e+01 -5.435762e+01 3.138338e+01 56.55090
## [43,] 62.67484 -1.137770e-13 -6.267484e+01 -1.962237e-13 62.67484
## [44,] -56.36526 2.714408e+01 -5.417917e+01 -3.128036e+01 56.36526
## [45,] 38.79818 -4.865138e+01 -3.111373e+01 -5.389055e+01 38.79818
## [46,] -13.84982 6.068005e+01 7.243806e-13 -6.224055e+01 13.84982
## [47,] -13.85037 -6.068243e+01 3.112150e+01 -5.390401e+01 -13.85037
## [48,] 38.86776 4.873863e+01 5.398720e+01 -3.116952e+01 -38.86776
## [49,] -56.23146 -2.707965e+01 6.241222e+01 -8.350460e-14 -56.23146
## [50,] 62.45996 6.984066e-13 5.409191e+01 3.122998e+01 -62.45996
## [51,] -56.34179 2.713278e+01 3.126734e+01 5.415662e+01 -56.34179
## [52,] 39.00051 -4.890509e+01 7.022265e-13 6.255195e+01 -39.00051
## [53,] -13.91134 6.094956e+01 -3.125850e+01 5.414130e+01 -13.91134
## [54,] -13.95644 -6.114718e+01 -5.431684e+01 3.135984e+01 13.95644
## [55,] 39.08193 4.900719e+01 -6.268254e+01 -5.574317e-15 39.08193
## [56,] -56.54414 -2.723022e+01 -5.435111e+01 -3.137963e+01 56.54414
## [57,] 63.04503 -5.396725e-13 -3.152252e+01 -5.459860e+01 63.04503
## [58,] -56.95429 2.742774e+01 -3.526346e-14 -6.321449e+01 56.95429
## [59,] 39.48180 -4.950862e+01 3.166195e+01 -5.484010e+01 39.48180
## [60,] -14.09617 6.175937e+01 5.486065e+01 -3.167381e+01 14.09617
## [61,] -14.09294 -6.174519e+01 6.333308e+01 2.515689e-13 -14.09294
## [62,] 39.50488 4.953755e+01 5.487215e+01 3.168045e+01 -39.50488
## [63,] -57.11980 -2.750744e+01 3.169910e+01 5.490444e+01 -57.11980
## [64,] 63.45508 -1.080122e-12 -3.754635e-14 6.345508e+01 -63.45508
## [65,] -57.09149 2.749381e+01 -3.168339e+01 5.487724e+01 -57.09149
## [66,] 39.52248 -4.955962e+01 -5.489660e+01 3.169456e+01 -39.52248
## [67,] -14.15030 6.199652e+01 -6.359087e+01 -4.325891e-13 -14.15030
## [68,] -14.18063 -6.212942e+01 -5.518937e+01 -3.186360e+01 14.18063
## [69,] 39.72899 4.981857e+01 -3.186017e+01 -5.518344e+01 39.72899
## [70,] -57.39185 -2.763846e+01 -3.917144e-13 -6.370015e+01 57.39185
## [71,] 63.73483 1.123095e-12 3.186741e+01 -5.519598e+01 63.73483
## [72,] -57.50124 2.769114e+01 5.527110e+01 -3.191078e+01 57.50124
## [73,] 39.79150 -4.989696e+01 6.382060e+01 -3.615563e-13 39.79150
## [74,] -14.17957 6.212475e+01 5.518522e+01 3.186120e+01 14.17957
## [75,] -14.15545 -6.201907e+01 3.180700e+01 5.509135e+01 -14.15545
## [76,] 39.72471 4.981321e+01 4.530057e-14 6.371349e+01 -39.72471
## [77,] -57.53161 -2.770576e+01 -3.192763e+01 5.530028e+01 -57.53161
## [78,] 63.91617 -3.243843e-12 -5.535303e+01 3.195809e+01 -63.91617
## [79,] -57.71767 2.779536e+01 -6.406178e+01 -1.351850e-13 -57.71767
## [80,] 39.99322 -5.014991e+01 -5.555046e+01 -3.207207e+01 -39.99322
## [81,] -14.31344 6.271130e+01 -3.216202e+01 -5.570625e+01 -14.31344
## [82,] -14.33896 -6.282307e+01 -5.224484e-13 -6.443868e+01 14.33896
## [83,] 40.21463 5.042755e+01 3.224963e+01 -5.585800e+01 40.21463
## [84,] -58.00946 -2.793589e+01 5.575961e+01 -3.219282e+01 58.00946
## 13 10 11
## [1,] -1.215226e-13 6.254940e+01 3.050737e-13
## [2,] 2.709052e+01 5.812123e+01 2.281090e+01
## [3,] 4.871591e+01 4.567645e+01 4.238156e+01
## [4,] 6.080806e+01 2.706213e+01 5.619509e+01
## [5,] 6.093306e+01 4.670636e+00 6.232530e+01
## [6,] 4.878852e+01 -1.839357e+01 5.963047e+01
## [7,] 2.696863e+01 -3.875384e+01 4.859578e+01
## [8,] 2.970332e-13 -5.371648e+01 3.101322e+01
## [9,] -2.691979e+01 -6.135081e+01 9.247147e+00
## [10,] -4.841332e+01 -6.037043e+01 -1.377916e+01
## [11,] -6.041909e+01 -5.120440e+01 -3.491057e+01
## [12,] -6.040910e+01 -3.490479e+01 -5.119593e+01
## [13,] -4.859537e+01 -1.383097e+01 -6.059744e+01
## [14,] -2.699025e+01 9.271350e+00 -6.151139e+01
## [15,] 1.885669e-13 3.109819e+01 -5.386365e+01
## [16,] 2.702886e+01 4.870432e+01 -3.884040e+01
## [17,] 4.884281e+01 5.969683e+01 -1.841403e+01
## [18,] 6.102173e+01 6.241601e+01 4.677433e+00
## [19,] 6.094653e+01 5.632307e+01 2.712376e+01
## [20,] 4.898249e+01 4.261348e+01 4.592641e+01
## [21,] 2.720919e+01 2.291082e+01 5.837581e+01
## [22,] -6.232157e-14 -2.048188e-14 6.269359e+01
## [23,] -2.720404e+01 -2.290648e+01 5.836477e+01
## [24,] -4.907286e+01 -4.269209e+01 4.601113e+01
## [25,] -6.094898e+01 -5.632533e+01 2.712485e+01
## [26,] -6.091547e+01 -6.230732e+01 4.669288e+00
## [27,] -4.880780e+01 -5.965404e+01 -1.840083e+01
## [28,] -2.706104e+01 -4.876231e+01 -3.888664e+01
## [29,] 1.929890e-13 -3.131971e+01 -5.424733e+01
## [30,] 2.716967e+01 -9.332983e+00 -6.192030e+01
## [31,] 4.903336e+01 1.395563e+01 -6.114360e+01
## [32,] 6.123461e+01 3.538178e+01 -5.189554e+01
## [33,] 6.136921e+01 5.200961e+01 -3.545955e+01
## [34,] 4.924247e+01 6.140435e+01 -1.401514e+01
## [35,] 2.735564e+01 6.234412e+01 9.396864e+00
## [36,] 5.951783e-13 5.466703e+01 3.156202e+01
## [37,] -2.736263e+01 3.932003e+01 4.930576e+01
## [38,] -4.933906e+01 1.860112e+01 6.030336e+01
## [39,] -6.142678e+01 -4.708481e+00 6.283031e+01
## [40,] -6.136014e+01 -2.730783e+01 5.670530e+01
## [41,] -4.913159e+01 -4.606620e+01 4.274319e+01
## [42,] -2.723348e+01 -5.842794e+01 2.293128e+01
## [43,] 9.656794e-14 -6.267484e+01 1.727923e-13
## [44,] 2.714408e+01 -5.823613e+01 -2.285600e+01
## [45,] 4.865138e+01 -4.561595e+01 -4.232542e+01
## [46,] 6.068005e+01 -2.700516e+01 -5.607680e+01
## [47,] 6.068243e+01 -4.651424e+00 -6.206895e+01
## [48,] 4.873863e+01 1.837476e+01 -5.956950e+01
## [49,] 2.707965e+01 3.891338e+01 -4.879584e+01
## [50,] -1.278127e-13 5.409191e+01 -3.122998e+01
## [51,] -2.713278e+01 6.183621e+01 -9.320309e+00
## [52,] -4.890509e+01 6.098365e+01 1.391912e+01
## [53,] -6.094956e+01 5.165396e+01 3.521708e+01
## [54,] -6.114718e+01 3.533126e+01 5.182144e+01
## [55,] -4.900719e+01 1.394818e+01 6.111096e+01
## [56,] -2.723022e+01 -9.353782e+00 6.205829e+01
## [57,] -4.973634e-13 -3.152252e+01 5.459860e+01
## [58,] 2.742774e+01 -4.942308e+01 3.941359e+01
## [59,] 4.950862e+01 -6.051059e+01 1.866505e+01
## [60,] 6.175937e+01 -6.317049e+01 -4.733974e+00
## [61,] 6.174519e+01 -5.706113e+01 -2.747919e+01
## [62,] 4.953755e+01 -4.309636e+01 -4.644683e+01
## [63,] 2.750744e+01 -2.316196e+01 -5.901571e+01
## [64,] 2.253224e-13 8.291978e-15 -6.345508e+01
## [65,] -2.749381e+01 2.315048e+01 -5.898647e+01
## [66,] -4.955962e+01 4.311556e+01 -4.646752e+01
## [67,] -6.199652e+01 5.729340e+01 -2.759105e+01
## [68,] -6.212942e+01 6.354900e+01 -4.762339e+00
## [69,] -4.981857e+01 6.088943e+01 1.878190e+01
## [70,] -2.763846e+01 4.980278e+01 3.971639e+01
## [71,] 3.418609e-14 3.186741e+01 5.519598e+01
## [72,] 2.769114e+01 9.512111e+00 6.310873e+01
## [73,] 4.989696e+01 -1.420142e+01 6.222049e+01
## [74,] 6.212475e+01 -3.589611e+01 5.264992e+01
## [75,] 6.201907e+01 -5.256036e+01 3.583505e+01
## [76,] 4.981321e+01 -6.211606e+01 1.417758e+01
## [77,] 2.770576e+01 -6.314205e+01 -9.517133e+00
## [78,] -1.563680e-13 -5.535303e+01 -3.195809e+01
## [79,] -2.779536e+01 -3.994187e+01 -5.008551e+01
## [80,] -5.014991e+01 -1.890682e+01 -6.129440e+01
## [81,] -6.271130e+01 4.806941e+00 -6.414417e+01
## [82,] -6.282307e+01 2.795890e+01 -5.805725e+01
## [83,] -5.042755e+01 4.728130e+01 -4.387064e+01
## [84,] -2.793589e+01 5.993491e+01 -2.352272e+01
##
## $Nregresores
## [1] 18
##
## $Betas
## [,1]
## C 5.123715e+02
## 1 1.996464e+01
## 2 -7.257998e-02
## 3 -2.654528e-02
## 4 3.362878e-02
## 5 1.663995e-02
## 8 -1.903189e-02
## 9 2.508835e-02
## 6 -1.278271e-02
## 7 -1.862982e-02
## 72 -2.682056e-03
## 73 -6.815002e-04
## 14 -8.551309e-03
## 15 5.852293e-03
## 12 -4.443794e-03
## 13 -3.542513e-04
## 10 -2.801267e-02
## 11 -1.791192e-02plot(reg5$datos$X,reg5$datos$Y,pch=19,col="blue")
lines(reg5$datos$X,reg5$datos$F,col="red")
gtd (reg5$datos$res,4)
plot(ts(E, frequency=4))
lines(ts(reg5$datos$F,frequency=4),col="red")
reg6 <- lm(E~PIBC)
reg6##
## Call:
## lm(formula = E ~ PIBC)
##
## Coefficients:
## (Intercept) PIBC
## 171.507 1.895plot(PIBC,E,pch=19,col="blue")
lines(PIBC,reg6$fitted,col="red")
gtd (reg6$resid,4)
plot(ts(E, frequency=4))
lines(ts(reg6$fitted,frequency=4),col="red")
Se comprueba que el resultado es el mismo realizando la estimación MCO con los regresores seleccionados de la matriz auxiliar \(WX_tIW^T\), una vez convertidos estos en series de tiempo:
regresores1 <- data.frame(reg5$Tregresores)
eq5 <- lm(E~0+.,data=regresores1)
plot(PIBC,E,pch=19,col="blue")
lines(PIBC,eq5$fitted,col="red")
lines(PIBC,reg5$datos$F,col="green")
summary(eq5)##
## Call:
## lm(formula = E ~ 0 + ., data = regresores1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1531 -0.7737 -0.1848 0.8961 3.6501
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## C 5.124e+02 4.510e+02 1.136 0.260019
## X1 1.996e+01 1.106e+00 18.052 < 2e-16 ***
## X2 -7.258e-02 4.337e-03 -16.736 < 2e-16 ***
## X3 -2.655e-02 7.170e-03 -3.702 0.000438 ***
## X4 3.363e-02 3.226e-03 10.423 1.39e-15 ***
## X5 1.664e-02 7.498e-03 2.219 0.029919 *
## X8 -1.903e-02 3.448e-03 -5.520 6.13e-07 ***
## X9 2.509e-02 4.873e-03 5.148 2.57e-06 ***
## X6 -1.278e-02 3.316e-03 -3.855 0.000265 ***
## X7 -1.863e-02 3.431e-03 -5.430 8.72e-07 ***
## X72 -2.682e-03 3.212e-03 -0.835 0.406767
## X73 -6.815e-04 3.205e-03 -0.213 0.832269
## X14 -8.551e-03 3.206e-03 -2.667 0.009618 **
## X15 5.852e-03 3.536e-03 1.655 0.102678
## X12 -4.444e-03 3.219e-03 -1.381 0.172069
## X13 -3.543e-04 3.409e-03 -0.104 0.917552
## X10 -2.801e-02 3.346e-03 -8.372 5.73e-12 ***
## X11 -1.791e-02 3.223e-03 -5.557 5.32e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.307 on 66 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 2.435e+06 on 18 and 66 DF, p-value: < 2.2e-16data.frame(E,eq5$fitted,reg5$datos$F)## E eq5.fitted reg5.datos.F
## 1 929.6105 931.7636 931.7636
## 2 929.8040 930.7738 930.7738
## 3 930.3184 929.5617 929.5617
## 4 931.4277 931.6228 931.6228
## 5 932.6620 934.7974 934.7974
## 6 933.5509 934.4661 934.4661
## 7 933.5315 932.3376 932.3376
## 8 933.0769 930.8736 930.8736
## 9 932.1238 931.7271 931.7271
## 10 930.6359 929.7421 929.7421
## 11 929.0971 930.1002 930.1002
## 12 928.5633 929.3738 929.3738
## 13 929.0694 931.0588 931.0588
## 14 930.2655 931.1853 931.1853
## 15 931.6770 929.8379 929.8379
## 16 932.1390 930.7300 930.7300
## 17 932.2767 932.3535 932.3535
## 18 932.8328 933.6135 933.6135
## 19 933.7334 932.3819 932.3819
## 20 934.1772 934.1391 934.1391
## 21 934.5928 935.6584 935.6584
## 22 935.6067 935.7812 935.7812
## 23 936.5111 937.1611 937.1611
## 24 937.4201 939.1433 939.1433
## 25 938.4159 937.0363 937.0363
## 26 938.9992 937.9482 937.9482
## 27 939.2354 938.0848 938.0848
## 28 939.6795 938.3615 938.3615
## 29 940.2497 942.2151 942.2151
## 30 941.4358 942.1550 942.1550
## 31 942.2981 942.8315 942.8315
## 32 943.5322 943.4625 943.4625
## 33 944.3490 944.6470 944.6470
## 34 944.8215 944.2002 944.2002
## 35 945.0671 944.9913 944.9913
## 36 945.8067 945.7322 945.7322
## 37 946.8697 945.7234 945.7234
## 38 946.8766 947.1466 947.1466
## 39 947.2497 947.2235 947.2235
## 40 947.6513 948.0178 948.0178
## 41 948.1840 948.1775 948.1775
## 42 948.3492 949.0606 949.0606
## 43 948.0322 948.8036 948.8036
## 44 947.1065 948.5275 948.5275
## 45 946.0796 944.2414 944.2414
## 46 946.1838 944.8062 944.8062
## 47 946.2258 944.9164 944.9164
## 48 945.9978 945.8010 945.8010
## 49 945.5183 946.6685 946.6685
## 50 945.3514 946.3548 946.3548
## 51 945.2918 946.9114 946.9114
## 52 945.4008 946.0107 946.0107
## 53 945.9058 944.5228 944.5228
## 54 945.9035 946.3429 946.3429
## 55 946.3190 944.4210 944.4210
## 56 946.5796 944.6716 944.6716
## 57 946.7800 947.3354 947.3354
## 58 947.6283 949.1629 949.1629
## 59 948.6221 949.8444 949.8444
## 60 949.3992 949.8093 949.8093
## 61 949.9481 949.4349 949.4349
## 62 949.7945 949.4690 949.4690
## 63 949.9534 950.1949 950.1949
## 64 950.2502 950.4887 950.4887
## 65 950.5380 949.2746 949.2746
## 66 950.7871 948.9946 948.9946
## 67 950.8695 951.4451 951.4451
## 68 950.9281 953.0067 953.0067
## 69 951.8457 952.3764 952.3764
## 70 952.6005 952.3269 952.3269
## 71 953.5976 952.6946 952.6946
## 72 954.1434 954.7529 954.7529
## 73 954.5426 955.3023 955.3023
## 74 955.2631 954.8611 954.8611
## 75 956.0561 954.2151 954.2151
## 76 956.7966 955.9376 955.9376
## 77 957.3865 958.3763 958.3763
## 78 958.0634 958.5083 958.5083
## 79 958.7166 959.9833 959.9833
## 80 959.4881 959.6417 959.6417
## 81 960.3625 960.7214 960.7214
## 82 960.7834 960.8974 960.8974
## 83 961.0290 960.2399 960.2399
## 84 961.7657 958.1156 958.1156Inferencia en la estimación en el dominio de la frecuencia entre el PIB y el empleo de Canada.
La inferencia en la estimación de un modelo en el dominio de la frecuencia, cuando se utilizan como variables auxiliares las frecuencias relevantes para acercar el regresor a la serie observada, presenta el problema del desfase que existe entre la serie en \(X_t\) en las frecuencias elegidas y la serie \(x_{t+m}\) para esas mismas frecuencias.
En el ejercicio siguiente se realiza la regresion dependiente de la frecuencia entre el PIBC y empleo con datos del mercado de trabajo de Canada, con los 80 primeros datos:
reg6 <- rdf (E[1:80],PIBC[1:80],4)
plot(reg6$datos$X,reg6$datos$Y,pch=19,col="blue")
lines(reg6$datos$X,reg6$datos$F,col="red")
gtd (reg6$datos$res,4)
plot(ts(E, frequency=4))
lines(ts(reg6$datos$F,frequency=4),col="red")
Realizamos ahora esa misma estimación en dominio del tiempo realizando la transformación en el dominio del tiempo de los regresores seleccionados, y comprobamos que los resultados son los mismos.
regresores2 <- data.frame(reg6$Tregresores)
eq6 <- lm(E[1:80]~X1+X2+X3+X4+X5+X8+X9+X6+X7+X34+X35+X12+X13+X22+X23+X14+X15+X10+X11+X16+X17,data=regresores2)
plot(PIBC[1:80],E[1:80],pch=19,col="blue")
lines(PIBC[1:80],eq6$fitted,col="red")
lines(PIBC[1:80],reg6$datos$F,col="green")
summary(eq6)##
## Call:
## lm(formula = E[1:80] ~ X1 + X2 + X3 + X4 + X5 + X8 + X9 + X6 +
## X7 + X34 + X35 + X12 + X13 + X22 + X23 + X14 + X15 + X10 +
## X11 + X16 + X17, data = regresores2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4517 -0.5675 -0.0340 0.6326 2.5639
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.622195 55.316667 0.716 0.476693
## X1 19.845578 1.214719 16.338 < 2e-16 ***
## X2 -0.065941 0.003700 -17.821 < 2e-16 ***
## X3 -0.035659 0.006582 -5.417 1.22e-06 ***
## X4 0.027535 0.002816 9.778 7.10e-14 ***
## X5 0.029274 0.007836 3.736 0.000430 ***
## X8 -0.025839 0.003441 -7.508 4.10e-10 ***
## X9 0.016738 0.004072 4.110 0.000126 ***
## X6 0.005184 0.002851 1.818 0.074174 .
## X7 -0.018402 0.003031 -6.072 1.04e-07 ***
## X34 -0.004402 0.002816 -1.563 0.123531
## X35 -0.005713 0.002825 -2.022 0.047796 *
## X12 -0.004364 0.002849 -1.532 0.131063
## X13 -0.007552 0.002929 -2.578 0.012500 *
## X22 -0.002420 0.002820 -0.858 0.394265
## X23 0.003076 0.002991 1.028 0.307991
## X14 -0.013600 0.002819 -4.824 1.06e-05 ***
## X15 -0.008523 0.002889 -2.950 0.004575 **
## X10 -0.011295 0.002818 -4.008 0.000177 ***
## X11 -0.027320 0.002820 -9.689 9.89e-14 ***
## X16 -0.013892 0.002839 -4.893 8.27e-06 ***
## X17 -0.003379 0.002977 -1.135 0.260990
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.147 on 58 degrees of freedom
## Multiple R-squared: 0.9868, Adjusted R-squared: 0.982
## F-statistic: 206.6 on 21 and 58 DF, p-value: < 2.2e-16data.frame(E[1:80],eq6$fitted,reg6$datos$F)## E.1.80. eq6.fitted reg6.datos.F
## 1 929.6105 932.0622 932.0622
## 2 929.8040 929.8432 929.8432
## 3 930.3184 929.0454 929.0454
## 4 931.4277 931.5471 931.5471
## 5 932.6620 934.6540 934.6540
## 6 933.5509 934.3330 934.3330
## 7 933.5315 932.1978 932.1978
## 8 933.0769 931.7487 931.7487
## 9 932.1238 932.4680 932.4680
## 10 930.6359 929.9689 929.9689
## 11 929.0971 929.5350 929.5350
## 12 928.5633 928.6755 928.6755
## 13 929.0694 930.9842 930.9842
## 14 930.2655 930.8712 930.8712
## 15 931.6770 929.6508 929.6508
## 16 932.1390 930.5025 930.5025
## 17 932.2767 933.1493 933.1493
## 18 932.8328 934.7914 934.7914
## 19 933.7334 932.8161 932.8161
## 20 934.1772 933.6959 933.6959
## 21 934.5928 934.4473 934.4473
## 22 935.6067 935.3418 935.3418
## 23 936.5111 936.9801 936.9801
## 24 937.4201 939.2983 939.2983
## 25 938.4159 937.1056 937.1056
## 26 938.9992 938.3677 938.3677
## 27 939.2354 939.1288 939.1288
## 28 939.6795 938.7276 938.7276
## 29 940.2497 942.0001 942.0001
## 30 941.4358 941.0487 941.0487
## 31 942.2981 942.3268 942.3268
## 32 943.5322 943.5806 943.5806
## 33 944.3490 944.7906 944.7906
## 34 944.8215 944.1970 944.1970
## 35 945.0671 944.7069 944.7069
## 36 945.8067 946.3668 946.3668
## 37 946.8697 946.3548 946.3548
## 38 946.8766 947.5375 947.5375
## 39 947.2497 946.8392 946.8392
## 40 947.6513 947.4306 947.4306
## 41 948.1840 948.1415 948.1415
## 42 948.3492 948.7607 948.7607
## 43 948.0322 948.4813 948.4813
## 44 947.1065 947.9116 947.9116
## 45 946.0796 944.5752 944.5752
## 46 946.1838 945.9564 945.9564
## 47 946.2258 945.9004 945.9004
## 48 945.9978 946.0669 946.0669
## 49 945.5183 945.8488 945.8488
## 50 945.3514 945.8293 945.8293
## 51 945.2918 946.3258 946.3258
## 52 945.4008 945.5979 945.5979
## 53 945.9058 944.0544 944.0544
## 54 945.9035 946.4640 946.4640
## 55 946.3190 945.6220 945.6220
## 56 946.5796 945.7052 945.7052
## 57 946.7800 947.8771 947.8771
## 58 947.6283 948.4362 948.4362
## 59 948.6221 949.1711 949.1711
## 60 949.3992 949.4798 949.4798
## 61 949.9481 949.1474 949.1474
## 62 949.7945 949.1506 949.1506
## 63 949.9534 949.6592 949.6592
## 64 950.2502 951.0461 951.0461
## 65 950.5380 950.1564 950.1564
## 66 950.7871 949.8888 949.8888
## 67 950.8695 951.5676 951.5676
## 68 950.9281 952.6469 952.6469
## 69 951.8457 952.2905 952.2905
## 70 952.6005 951.7949 951.7949
## 71 953.5976 951.9520 951.9520
## 72 954.1434 953.5076 953.5076
## 73 954.5426 955.1312 955.1312
## 74 955.2631 956.0166 956.0166
## 75 956.0561 955.9302 955.9302
## 76 956.7966 957.3131 957.3131
## 77 957.3865 958.3134 958.3134
## 78 958.0634 957.8100 957.8100
## 79 958.7166 958.0994 958.0994
## 80 959.4881 956.9243 956.9243Dada la transformación sugerida por Harvey (1978) utiliza en \(w_{1,t}\), \((\frac{1}T) ^\frac{1}2\), poner en fase el regresor \(X_{1,t}\), simplemente requiere
\(\frac{(\frac{1}T) ^\frac{1}2}{(\frac{1}{T+m}) ^\frac{1}2}\). En el resto de regresores, el desfase es una función de función de t.
Se representa el desfase del regresor \(X_{2,t}\)
plot(ts(regresores1[,3],frequency=4))
lines(ts(regresores2[,3],frequency=4),col="red")
Dado que la transformación de Harvey (1978) es ortogonal, pueden utilizarse como regresores los armónicos auxiliares seleccionados de \(X_{j,t}\) extendidos con los \(m\) primeros datos.
NX <- data.frame(cdf(PIBC))
regresores3 <- data.frame(
XC=c(rep(1,84)),
X1=gdt(NX$X1)*((1/80)^(1/2))/((1/84)^(1/2)),
X2=c(regresores2$X2,regresores2$X2[1:4]),
X3=c(regresores2$X3,regresores2$X3[1:4]),
X4=c(regresores2$X4,regresores2$X4[1:4]),
X5=c(regresores2$X5,regresores2$X5[1:4]),
X8=c(regresores2$X8,regresores2$X8[1:4]),
X9=c(regresores2$X9,regresores2$X9[1:4]),
X6=c(regresores2$X6,regresores2$X6[1:4]),
X7=c(regresores2$X7,regresores2$X7[1:4]),
X34=c(regresores2$X34,regresores2$X34[1:4]),
X35=c(regresores2$X35,regresores2$X35[1:4]),
X12=c(regresores2$X12,regresores2$X12[1:4]),
X13=c(regresores2$X13,regresores2$X13[1:4]),
X22=c(regresores2$X22,regresores2$X22[1:4]),
X23=c(regresores2$X23,regresores2$X23[1:4]),
X14=c(regresores2$X14,regresores2$X14[1:4]),
X15=c(regresores2$X15,regresores2$X15[1:4]),
X10=c(regresores2$X10,regresores2$X10[1:4]),
X11=c(regresores2$X11,regresores2$X11[1:4]),
X16=c(regresores2$X11,regresores2$X16[1:4]),
X17=c(regresores2$X11,regresores2$X17[1:4])
)
regresores3 <- as.matrix(regresores3,nrow=84)
coeficientes <- as.matrix(eq6$coefficient)
proyectados2 <-regresores3%*%coeficientes
plot(ts(proyectados2,frequency=4))
lines(ts(E,frequency=4),col="red")
lines(ts(reg6$datos$F,frequency=4),col="green")
Esta forma de obtener la predicción lógicamente no incorpora la información en \(T+m\) de las oscilaciones armnónicas del regresor \(X_{T+m}\). Para ello, habría que poner el fase dichas oscilaciones armónicas.
En base a las identidades trigonometricas, la matriz \(Z\), cuyo elemento \(z_{j,t}\) se define como: \[\begin{equation} z_{jt} = \left\lbrace\begin{array}{ll}\left( \frac{T}{T+m}\right)^\frac{1}2 & \forall j=1\\ \left(\frac{T}{T+m}\right) ^\frac{1}2 \cos\left[\pi j (t-1)\left(\frac{1}{T}-\frac{1}{T+m}\right)\right] - \tan\left[\pi j (t-1)T\right] \sin\left[\pi j (t-1)\left(\frac{1}{T}-\frac{1}{T+m}\right)\right] & \forall j=2,4,6,..\frac{(T+m-2)}{(T+m-1)}\\ \left(\frac{T}{T+m}\right) ^\frac{1}2 \cos\left[\pi j (t-1)\left(\frac{1}{T}+\frac{1}{T+m}\right)\right] -\frac{1}{\tan\left[\pi j (t-1)T\right]} \sin\left[\pi j (t-1)\left(\frac{1}{T}-\frac{1}{T+m}\right)\right] & \forall j=3,5,7,..\frac{(T-2)}T\\ \left( \frac{T}{T+m}\right)^\frac{1}2 (-1)^\frac{1}2 & \forall j=T\end{array}\right.\end{equation}\]
Serviría para poner en fase \(T\) los regresores \(T+m\) que utilizamos en el MCO en dominio temporal.
Se plantea solo una proyección de los predictores correspondientes a los armónicos utilizados en la ecuación. No presentan indeterminación, pero en todo caso habría que ofrecer una solución en base a distancias cuando se presentara. Se representan los resultados y se comparan con el anterior pronóstico. No obstante, esta conversión tiene indeterminaciones, en los angulos en los que el seno o coseno \(\left[\frac{\pi j (t-1})T\right]\) sea cero \(\pi\), \(2\pi\), \(3\pi\), etc…
Se realiza este pronostico para el PIBC
NX <- data.frame(cdf(PIBC))
regresores4 <- data.frame(
XC=c(rep(1,84)),
X1=gdt(NX$X1),
X2=gdt(NX$X2),
X3=gdt(NX$X3),
X4=gdt(NX$X4),
X5=gdt(NX$X5),
X8=gdt(NX$X8),
X9=gdt(NX$X9),
X6=gdt(NX$X6),
X7=gdt(NX$X7),
X34=gdt(NX$X4),
X35=gdt(NX$X35),
X12=gdt(NX$X12),
X13=gdt(NX$X13),
X22=gdt(NX$X22),
X23=gdt(NX$X23),
X14=gdt(NX$X14),
X15=gdt(NX$X15),
X10=gdt(NX$X10),
X11=gdt(NX$X11),
X16=gdt(NX$X16),
X17=gdt(NX$X17)
)
# parametrizacion de los regresores
#lista <- as.list(data.frame(regresores1))
# 2,3,4,5,8,9,6,7,34,35,12,13,22,23,14,15,10,11,16,17
names <- c(colnames(regresores2))
L <- substring(names, 2)
L <- as.numeric(L)
#Lista2 <- as.list(matrix(L,nrow=1))
m<- 84
n <- (m-4)
uno <- as.numeric (1:m)
Xf <- c(rep(1,4))
X1f <- c(rep(sqrt(n/m),4))
X1f <- rbind(Xf,X1f)
L <- L[3:length(L)]
for (i in L)
{if(i%%2==0) {
A1f <- matrix(sqrt(n/m)*(cos(pi*(i)*(uno-1)*(1/m-1/n))-tan(pi*(i)*(uno-1)/n)*sin(pi*(i)*(uno-1)*(1/m-1/n))), nrow=1)
X2f <- A1f[(n+1):m]
X1f <- rbind(X1f,X2f)} else {
j=i-1
A2f <- matrix(sqrt(n/m)*(cos(pi*(j)*(uno-1)*(1/m-1/n))+(1/tan(pi*(j)*(uno-1)/n))*sin(pi*(j)*(uno-1)*(1/m-1/n))), nrow=1)
X3f <- A2f[(n+1):m]
X1f <- rbind(X1f,X3f)}
}
# Final
predict <- t(regresores4[81:84,])/X1f
t(predict)## XC X1 X2 X3 X4 X5 X8
## 81 1 46.60719 65.91252 -1.614391e-14 65.91252 -3.228782e-14 65.91252
## 82 1 46.69026 65.82645 5.180654e+00 65.21706 1.032937e+01 62.79826
## 83 1 46.73415 65.27837 1.033908e+01 62.85730 2.042357e+01 53.46961
## 84 1 46.65183 64.15274 1.540171e+01 58.78474 2.995232e+01 38.77952
## X9 X6 X7 X34 X35 X12
## 81 -6.457565e-14 65.91252 -4.843174e-14 149.06479 1.938901e-13 65.91252
## 82 2.040439e+01 64.20559 1.541440e+01 -17.76328 6.420559e+01 58.83316
## 83 3.884795e+01 58.88847 3.000517e+01 68.10649 3.000517e+01 38.84795
## 84 5.337543e+01 50.16828 4.284776e+01 -143.74366 -5.016828e+01 10.32087
## X13 X22 X23 X14 X15 X10
## 81 -9.686347e-14 65.91252 -6.459197e-13 65.91252 -1.130074e-13 65.91252
## 82 2.997699e+01 42.88306 5.020961e+01 65.18109 3.450058e+01 61.00377
## 83 5.346961e+01 -10.33908 6.527837e+01 30.00517 5.888847e+01 46.73415
## 84 6.516339e+01 -56.25349 3.447219e+01 -5.17639 6.577227e+01 25.24779
## X11 X16 X17
## 81 -8.071956e-14 65.91252 -1.291513e-13
## 82 2.526859e+01 53.41939 3.881146e+01
## 83 4.673415e+01 20.42357 6.285730e+01
## 84 6.095356e+01 -20.38760 6.274658e+01proyectados3 <-t(predict)%*%coeficientes
EE <- c(reg6$datos$F,proyectados3)
plot(ts(E,frequency=4))
lines(ts(EE,frequency=4),col="red")
Descomposición temporal de las series de PIB y empleo de Canada.
Se calcula la tendencia, factores estacionales e irregular del PIB y se realiza el test de durbin sobre la serie irregular,se representan los resultados y se comparan con los procedimientos “descompose” y “stl” de R
Analisis con el PIB y empleo de Canada:
desc <- descomponer(PIBC,4,1)
str(desc)## List of 5
## $ datos :'data.frame': 84 obs. of 5 variables:
## ..$ y : num [1:84] 405 405 404 404 405 ...
## ..$ TDST: num [1:84] 405 405 404 404 404 ...
## ..$ TD : num [1:84] 405 405 405 405 404 ...
## ..$ ST : num [1:84] 0.0896 0.0377 -0.0987 -0.0285 0.0897 ...
## ..$ IR : num [1:84] 0.4826 -0.0228 -0.6433 -0.2657 0.6218 ...
## $ regresoresTD :'data.frame': 84 obs. of 23 variables:
## ..$ X1 : num [1:84] 43.8 43.8 43.9 43.9 43.9 ...
## ..$ X2 : num [1:84] 62 61.8 61.3 60.5 59.3 ...
## ..$ X3 : num [1:84] 1.90e-13 4.63 9.24 1.38e+01 1.83e+01 ...
## ..$ X4 : num [1:84] 62 61.3 59.3 55.9 51.3 ...
## ..$ X5 : num [1:84] -3.33e-13 9.24 1.83e+01 2.69e+01 3.50e+01 ...
## ..$ X6 : num [1:84] 62 60.4 55.9 48.5 38.7 ...
## ..$ X7 : num [1:84] 2.01e-13 1.38e+01 2.69e+01 3.87e+01 4.85e+01 ...
## ..$ X8 : num [1:84] 62 59.2 51.2 38.7 22.7 ...
## ..$ X9 : num [1:84] 5.13e-13 1.83e+01 3.49e+01 4.85e+01 5.78e+01 ...
## ..$ X10: num [1:84] 61.98 57.72 45.47 26.92 4.64 ...
## ..$ X11: num [1:84] 3.28e-13 2.27e+01 4.22e+01 5.59e+01 6.19e+01 ...
## ..$ X12: num [1:84] 62 55.9 38.7 13.8 -13.8 ...
## ..$ X13: num [1:84] -1.07e-13 2.69e+01 4.85e+01 6.05e+01 6.05e+01 ...
## ..$ X14: num [1:84] 6.20e+01 5.37e+01 3.10e+01 1.99e-13 -3.10e+01 ...
## ..$ X15: num [1:84] -2.69e-13 3.10e+01 5.37e+01 6.20e+01 5.38e+01 ...
## ..$ X16: num [1:84] 62 51.2 22.7 -13.8 -45.5 ...
## ..$ X17: num [1:84] 2.55e-13 3.49e+01 5.77e+01 6.05e+01 4.22e+01 ...
## ..$ X18: num [1:84] 62 48.5 13.8 -26.9 -55.9 ...
## ..$ X19: num [1:84] 1.26e-13 3.87e+01 6.05e+01 5.59e+01 2.69e+01 ...
## ..$ X20: num [1:84] 61.98 45.45 4.64 -38.69 -61.38 ...
## ..$ X21: num [1:84] -1.53e-13 4.22e+01 6.19e+01 4.85e+01 9.25 ...
## ..$ X22: num [1:84] 61.98 42.17 -4.64 -48.51 -61.38 ...
## ..$ X23: num [1:84] -3.93e-14 4.55e+01 6.19e+01 3.87e+01 -9.25 ...
## $ regresoresST :'data.frame': 84 obs. of 4 variables:
## ..$ X1: num [1:84] 43.8 43.8 43.9 43.9 43.9 ...
## ..$ X2: num [1:84] 6.20e+01 -2.78e-14 -6.20e+01 -1.17e-13 6.21e+01 ...
## ..$ X3: num [1:84] -9.11e-13 6.20e+01 9.75e-13 -6.20e+01 3.48e-13 ...
## ..$ X4: num [1:84] 43.8 -43.8 43.9 -43.9 43.9 ...
## $ coeficientesTD: num [1:23, 1] 9.16515 0.026997 0.009631 -0.000658 -0.024758 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:23] "1" "2" "3" "4" ...
## .. ..$ : NULL
## $ coeficientesST: num [1:4, 1] 1.02e-06 1.52e-03 5.34e-04 -1.04e-04
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:4] "X1" "X2" "X3" "X4"
## .. ..$ : NULLgtd(desc$datos$IR,3)
plot(ts(descomponer(PIBC,4,1)$datos,frequency=4))
plot(ts(descomponer(E,4,1)$datos,frequency=4))
plot(decompose(ts(PIBC,frequency=4),type="additive"))
plot(stl(ts(PIBC,frequency=4), s.window=4))
plot(decompose(ts(E,frequency=4),type="additive"))
plot(stl(ts(E,frequency=4), s.window=4))
Bibliografia
DURBIN, J., “Tests for Serial Correlation in Regression Analysis based on the Periodogram ofLeast-Squares Residuals,” Biometrika, 56, (No. 1, 1969), 1-15.
Engle, Robert F. (1974), Band Spectrum Regression,International Economic Review 15,1-11.
Harvey, A.C. (1978), Linear Regression in the Frequency Domain, International Economic Review, 19, 507-512.
Parra F (2014): Seasonal Adjustment by Frequency Analysis. Package R Version 1.1. URL:http://cran.r-project.org/web/packages/descomponer/index.html