Practica 4

R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

X<-numeric(1000)
W<-rnorm(1000)
for(t in 2:1000)
X[t]<-1/3*W[t-1]+W[t]

plot(X, type='l')

acf(X)

A)Xt=3W(t-1)+Wt

X<-numeric(1000)
W<-rnorm(1000)
for(t in 2:1000)
X[t]<-3*W[t-1]+W[t]

plot(X, type='l')

acf(X)

B)Xt=2W(t-2)+0.5W(t-1)+Wt

X<-numeric(1000)
W<-rnorm(1000)
for(t in 3:1000)
X[t]<-2*W[t-2]+0.5*W[t-1]+W[t]

plot(X, type='l')

acf(X)

C) Xt = 0.2Xt−1 + 0.15Xt−2 + Wt con X1 = 2 con X2 = 4

X<-numeric(1000)
W<-rnorm(1000)
X1<-2
X2<-4
for (t in 3:1000)
X[t]<-.2*X[t-1]+0.15*X[t-2]+W[t]

plot(X, type='l')

acf(X1,X2)

D)Xt = 0.2Xt−1 + 0.24Xt−2 + Wt con X1 = 2 con X2 = 6

X<-numeric(1000)
W<-rnorm(1000)
X1<-2
X2<-6
for (t in 3:1000)
X[t]<-.2*X[t-1]+0.24*X[t-2]+W[t]

plot(X, type='l')

acf(X1,X2)

2. Calcula de manera anal´ıtica la funci´on de autocorrelaci´on de los procesos dados, para los primeros 5 periodos: ρ0, ρ1, ρ2, ρ3, ρ4. (CUADERNO)

3. Compara los valores estimados por R y los valores que calculaste analıticamente. Todas las gráficas y resultados son iguales.Algunos datos pueden interpretarse como 0 ya que en la gráfica se encuentran dentro del rango azul, independientemente de que en lo analítico es más específico.