Introducción R

Este es un ejemplo de crear notebooks

Librerias

rm(list=ls())
library(dplyr) ## pandas python
library(ggplot2)## Graficos en R
library(lubridate)## Fechas
library(readxl)
### Modelos de Series de Tiempo
library(MTS)
library(forecast)
library(TSstudio)
library(vars)
library(urca)
library(dygraphs)

Importar Base Datos

BuscarV para Unir la Variable Fecha

fecha= as.data.frame(read_excel("MaestroFecha.xlsx"))
names(fecha)[1]="Fecha"
str(fecha)

## 'data.frame':    76 obs. of  2 variables:
##  $ Fecha: chr  "2001-1" "2001-2" "2001-3" "2001-4" ...
##  $ date : POSIXct, format: "2001-03-31" "2001-06-30" ...

## corregir 
fecha$date=as.Date(fecha$date)
## Left Join

df= dplyr::left_join(df,fecha,by="Fecha")

Vista Previa

## Seleccion de Variables 

df=df[,c("date","Infla","Desem","Int")]
head(df)

Analisis Gráfico

ts_plot(df[,c("date","Infla","Int")],title = "Evolución Series Macroeconomicas Colomibia 2001-2019",
        Xtitle = "Fecha",Ytitle = "Indicadores")

Formato Series de Tiempo

df1=ts(cbind(Int=df$Int,Infla=df$Infla),
       frequency = 4,
       start = c(2001),
       end = c(2019))

head(df1)

##               Int    Infla
## 2001 Q1 11.892473 8.120000
## 2001 Q2 11.500000 7.926667
## 2001 Q3 10.583513 8.030000
## 2001 Q4  8.983333 7.813333
## 2002 Q1  7.994624 6.653333
## 2002 Q2  6.096595 5.913333

Gráfico Simple

plot.ts(df1,type="o", cex=0.4,col="darkred")

## Tasa de Crecimiento

df1_C=diff(log(df1))
head(df1_C)

##                 Int       Infla
## 2001 Q2 -0.03355865 -0.02409755
## 2001 Q3 -0.08304967  0.01295193
## 2001 Q4 -0.16392636 -0.02735285
## 2002 Q1 -0.11660174 -0.16071369
## 2002 Q2 -0.27103886 -0.11790829
## 2002 Q3 -0.14950234  0.02064230

plot.ts(df1_C,type="o", cex=0.4,col="darkred")

Identificación del modelo VARMA(p,q): No exite tendencia

VARselect(data.frame(df1_C),lag.max = 12)

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      4      1      1      4 
## 
## $criteria
##                    1             2             3             4             5
## AIC(n) -9.493256e+00 -9.523320e+00 -9.582553e+00 -9.615103e+00 -9.491531e+00
## HQ(n)  -9.411335e+00 -9.386784e+00 -9.391404e+00 -9.369339e+00 -9.191153e+00
## SC(n)  -9.283822e+00 -9.174263e+00 -9.093873e+00 -8.986799e+00 -8.723605e+00
## FPE(n)  7.537091e-05  7.318316e-05  6.906803e-05  6.701857e-05  7.612413e-05
##                    6             7             8             9            10
## AIC(n) -9.411072e+00 -9.360482e+00 -9.431854e+00 -9.390568e+00 -9.359242e+00
## HQ(n)  -9.056080e+00 -8.950875e+00 -8.967633e+00 -8.871733e+00 -8.785792e+00
## SC(n)  -8.503523e+00 -8.313310e+00 -8.245058e+00 -8.064150e+00 -7.893200e+00
## FPE(n)  8.296306e-05  8.794219e-05  8.272603e-05  8.735908e-05  9.165614e-05
##                  11            12
## AIC(n) -9.345135713 -9.2666436245
## HQ(n)  -8.717072188 -8.5839658805
## SC(n)  -7.739471548 -7.5213564894
## FPE(n)  0.000094906  0.0001052993

Otra Forma

tc_desv=df1_C-colMeans(df1_C)
VARorder(tc_desv,maxp = 13)

## selected order: aic =  4 
## selected order: bic =  1 
## selected order: hq =  4 
## Summary table:  
##        p     AIC     BIC      HQ    M(p) p-value
##  [1,]  0 -8.6480 -8.6480 -8.6480  0.0000  0.0000
##  [2,]  1 -9.5585 -9.4321 -9.5082 56.7033  0.0000
##  [3,]  2 -9.6138 -9.3608 -9.5131  8.8990  0.0637
##  [4,]  3 -9.6919 -9.3125 -9.5409  9.7481  0.0449
##  [5,]  4 -9.7461 -9.2402 -9.5447  8.1801  0.0852
##  [6,]  5 -9.6454 -9.0130 -9.3936  0.4934  0.9741
##  [7,]  6 -9.5981 -8.8392 -9.2960  2.9055  0.5738
##  [8,]  7 -9.5739 -8.6885 -9.2214  3.7803  0.4366
##  [9,]  8 -9.6744 -8.6625 -9.2716  8.7809  0.0668
## [10,]  9 -9.6450 -8.5067 -9.1918  3.2285  0.5203
## [11,] 10 -9.6439 -8.3791 -9.1404  4.1263  0.3892
## [12,] 11 -9.6530 -8.2617 -9.0991  4.2655  0.3713
## [13,] 12 -9.5938 -8.0760 -8.9896  1.7407  0.7833
## [14,] 13 -9.6672 -8.0230 -9.0126  5.8119  0.2136

Modelo Var(4)

var_p=vars::VAR(df1_C,p=4)
summary(var_p)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: Int, Infla 
## Deterministic variables: const 
## Sample size: 68 
## Log Likelihood: 150.011 
## Roots of the characteristic polynomial:
## 0.8293 0.8293 0.808 0.808 0.6396 0.6396 0.352 0.352
## Call:
## vars::VAR(y = df1_C, p = 4)
## 
## 
## Estimation results for equation Int: 
## ==================================== 
## Int = Int.l1 + Infla.l1 + Int.l2 + Infla.l2 + Int.l3 + Infla.l3 + Int.l4 + Infla.l4 + const 
## 
##           Estimate Std. Error t value Pr(>|t|)    
## Int.l1    0.754141   0.139921   5.390  1.3e-06 ***
## Infla.l1  0.236777   0.070850   3.342  0.00145 ** 
## Int.l2   -0.276420   0.167397  -1.651  0.10399    
## Infla.l2  0.007800   0.074788   0.104  0.91729    
## Int.l3   -0.008376   0.167646  -0.050  0.96032    
## Infla.l3 -0.008425   0.073733  -0.114  0.90942    
## Int.l4   -0.077335   0.122646  -0.631  0.53077    
## Infla.l4  0.038807   0.074070   0.524  0.60229    
## const    -0.002372   0.008051  -0.295  0.76935    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.06549 on 59 degrees of freedom
## Multiple R-Squared: 0.6825,  Adjusted R-squared: 0.6394 
## F-statistic: 15.85 on 8 and 59 DF,  p-value: 3.469e-12 
## 
## 
## Estimation results for equation Infla: 
## ====================================== 
## Infla = Int.l1 + Infla.l1 + Int.l2 + Infla.l2 + Int.l3 + Infla.l3 + Int.l4 + Infla.l4 + const 
## 
##           Estimate Std. Error t value Pr(>|t|)   
## Int.l1    0.222211   0.266052   0.835  0.40696   
## Infla.l1  0.412934   0.134716   3.065  0.00328 **
## Int.l2    0.229294   0.318296   0.720  0.47414   
## Infla.l2 -0.148676   0.142205  -1.046  0.30005   
## Int.l3   -0.377991   0.318770  -1.186  0.24046   
## Infla.l3  0.263439   0.140199   1.879  0.06518 . 
## Int.l4    0.030277   0.233205   0.130  0.89714   
## Infla.l4 -0.309457   0.140839  -2.197  0.03194 * 
## const    -0.007748   0.015309  -0.506  0.61467   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.1245 on 59 degrees of freedom
## Multiple R-Squared: 0.3852,  Adjusted R-squared: 0.3018 
## F-statistic:  4.62 on 8 and 59 DF,  p-value: 0.0002047 
## 
## 
## 
## Covariance matrix of residuals:
##            Int    Infla
## Int   0.004289 0.003357
## Infla 0.003357 0.015507
## 
## Correlation matrix of residuals:
##          Int  Infla
## Int   1.0000 0.4117
## Infla 0.4117 1.0000

options(repr.plot.width=15, repr.plot.height=8)
plot(var_p)

Valores Atipicos

(sigma2_Infla=sum(var_p$varresult$Infla$residuals^2)/var_p$varresult$Infla$df.residual)

## [1] 0.01550674

(sigma2_Int=sum(var_p$varresult$Int$residuals^2)/var_p$varresult$Int$df.residual)

## [1] 0.004288978

Residuales Estandarizados Para Ver Observaciones Atipicas

res_est_Infla=var_p$varresult$Infla$residuals/sigma2_Infla^0.5
res_est_Int=var_p$varresult$Int$residuals/sigma2_Int^0.5

plot.ts(res_est_Infla)
abline(a=-3,b=0, col="blue")
abline(a=3, b=0, col="blue")

plot.ts(res_est_Int)
abline(a=-3, b=0, col="blue")
abline(a=3, b=0, col="blue")

Normalidad

normalitytest = normality.test(var_p)
normalitytest

## $JB
## 
##  JB-Test (multivariate)
## 
## data:  Residuals of VAR object var_p
## Chi-squared = 47.548, df = 4, p-value = 1.173e-09
## 
## 
## $Skewness
## 
##  Skewness only (multivariate)
## 
## data:  Residuals of VAR object var_p
## Chi-squared = 17.595, df = 2, p-value = 0.0001511
## 
## 
## $Kurtosis
## 
##  Kurtosis only (multivariate)
## 
## data:  Residuals of VAR object var_p
## Chi-squared = 29.952, df = 2, p-value = 3.133e-07

No se Cumple Normalidad

Ajustar los Valores Atipicos

out_Infla=(abs(res_est_Infla)>2.7)
sum(out_Infla)

## [1] 0

subset(res_est_Infla, out_Infla==1)

## named numeric(0)

out_Int=(abs(res_est_Int)>2.7)
sum(out_Int)

## [1] 2

subset(res_est_Int, out_Int==1)

##         1        29 
## -2.901584 -3.709579

Efecto de Valores Atípicos

#df1_C

out1=as.matrix((seq(df1_C[,1]==1)))
out29=as.matrix((seq(df1_C[,1]==29)))

OUT=cbind(out1,out29)

Ajustamos el Modelo de Nuevo

var_p1= vars::VAR(df1_C,p=4,exogen = as.matrix(OUT))

## Warning in vars::VAR(df1_C, p = 4, exogen = as.matrix(OUT)): No column names supplied in exogen, using: exo1, exo2 , instead.

summary(var_p1)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: Int, Infla 
## Deterministic variables: const 
## Sample size: 68 
## Log Likelihood: 150.023 
## Roots of the characteristic polynomial:
## 0.8302 0.8302 0.8078 0.8078 0.6395 0.6395 0.3537 0.3537
## Call:
## vars::VAR(y = df1_C, p = 4, exogen = as.matrix(OUT))
## 
## 
## Estimation results for equation Int: 
## ==================================== 
## Int = Int.l1 + Infla.l1 + Int.l2 + Infla.l2 + Int.l3 + Infla.l3 + Int.l4 + Infla.l4 + const + exo1 
## 
##            Estimate Std. Error t value Pr(>|t|)    
## Int.l1    7.543e-01  1.411e-01   5.344 1.59e-06 ***
## Infla.l1  2.365e-01  7.157e-02   3.305  0.00163 ** 
## Int.l2   -2.768e-01  1.689e-01  -1.638  0.10678    
## Infla.l2  7.850e-03  7.543e-02   0.104  0.91748    
## Int.l3   -8.283e-03  1.691e-01  -0.049  0.96110    
## Infla.l3 -8.312e-03  7.439e-02  -0.112  0.91142    
## Int.l4   -7.798e-02  1.242e-01  -0.628  0.53256    
## Infla.l4  3.896e-02  7.475e-02   0.521  0.60419    
## const    -3.296e-03  1.799e-02  -0.183  0.85523    
## exo1      2.375e-05  4.123e-04   0.058  0.95426    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.06605 on 58 degrees of freedom
## Multiple R-Squared: 0.6825,  Adjusted R-squared: 0.6332 
## F-statistic: 13.85 on 9 and 58 DF,  p-value: 1.441e-11 
## 
## 
## Estimation results for equation Infla: 
## ====================================== 
## Infla = Int.l1 + Infla.l1 + Int.l2 + Infla.l2 + Int.l3 + Infla.l3 + Int.l4 + Infla.l4 + const + exo1 
## 
##            Estimate Std. Error t value Pr(>|t|)   
## Int.l1    0.2227413  0.2683119   0.830  0.40985   
## Infla.l1  0.4118018  0.1360731   3.026  0.00369 **
## Int.l2    0.2275756  0.3211891   0.709  0.48145   
## Infla.l2 -0.1484363  0.1434089  -1.035  0.30494   
## Int.l3   -0.3775451  0.3214631  -1.174  0.24501   
## Infla.l3  0.2639813  0.1414268   1.867  0.06702 . 
## Int.l4    0.0271935  0.2361265   0.115  0.90871   
## Infla.l4 -0.3087091  0.1421166  -2.172  0.03394 * 
## const    -0.0121661  0.0341941  -0.356  0.72329   
## exo1      0.0001135  0.0007838   0.145  0.88536   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.1256 on 58 degrees of freedom
## Multiple R-Squared: 0.3854,  Adjusted R-squared:  0.29 
## F-statistic: 4.041 on 9 and 58 DF,  p-value: 0.0004667 
## 
## 
## 
## Covariance matrix of residuals:
##            Int    Infla
## Int   0.004439 0.003474
## Infla 0.003474 0.016045
## 
## Correlation matrix of residuals:
##          Int  Infla
## Int   1.0000 0.4116
## Infla 0.4116 1.0000

normalitytest = normality.test(var_p1)
normalitytest

## $JB
## 
##  JB-Test (multivariate)
## 
## data:  Residuals of VAR object var_p1
## Chi-squared = 46.942, df = 4, p-value = 1.568e-09
## 
## 
## $Skewness
## 
##  Skewness only (multivariate)
## 
## data:  Residuals of VAR object var_p1
## Chi-squared = 17.506, df = 2, p-value = 0.000158
## 
## 
## $Kurtosis
## 
##  Kurtosis only (multivariate)
## 
## data:  Residuals of VAR object var_p1
## Chi-squared = 29.436, df = 2, p-value = 4.056e-07

Simplificar el Modelo

ModeloSimplificado=restrict(var_p1,method = "ser",thresh = 2)
summary(ModeloSimplificado)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: Int, Infla 
## Deterministic variables: const 
## Sample size: 68 
## Log Likelihood: 146.837 
## Roots of the characteristic polynomial:
## 0.8023 0.8023 0.789 0.789 0.5506 0.5506     0     0
## Call:
## vars::VAR(y = df1_C, p = 4, exogen = as.matrix(OUT))
## 
## 
## Estimation results for equation Int: 
## ==================================== 
## Int = Int.l1 + Infla.l1 + Int.l2 
## 
##          Estimate Std. Error t value Pr(>|t|)    
## Int.l1    0.76089    0.11763   6.469 1.49e-08 ***
## Infla.l1  0.25592    0.06264   4.085 0.000123 ***
## Int.l2   -0.30318    0.10276  -2.950 0.004409 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.06283 on 65 degrees of freedom
## Multiple R-Squared: 0.6804,  Adjusted R-squared: 0.6657 
## F-statistic: 46.13 on 3 and 65 DF,  p-value: 4.276e-16 
## 
## 
## Estimation results for equation Infla: 
## ====================================== 
## Infla = Infla.l1 + Infla.l3 + Infla.l4 
## 
##          Estimate Std. Error t value Pr(>|t|)    
## Infla.l1   0.4665     0.1026   4.549 2.42e-05 ***
## Infla.l3   0.2709     0.1129   2.399 0.019327 *  
## Infla.l4  -0.4007     0.1128  -3.552 0.000718 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 0.1233 on 65 degrees of freedom
## Multiple R-Squared: 0.3401,  Adjusted R-squared: 0.3097 
## F-statistic: 11.17 on 3 and 65 DF,  p-value: 5.288e-06 
## 
## 
## 
## Covariance matrix of residuals:
##            Int    Infla
## Int   0.004498 0.003593
## Infla 0.003593 0.017272
## 
## Correlation matrix of residuals:
##          Int  Infla
## Int   1.0000 0.4077
## Infla 0.4077 1.0000

ModeloSimplificado$restrictions

##       Int.l1 Infla.l1 Int.l2 Infla.l2 Int.l3 Infla.l3 Int.l4 Infla.l4 const
## Int        1        1      1        0      0        0      0        0     0
## Infla      0        1      0        0      0        1      0        1     0
##       exo1 exo2
## Int      0    0
## Infla    0    0

plot(ModeloSimplificado)