hw2-q3 new

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…{r} #download data

install.packages(“Quandl”)

library(“Quandl”) …

…{r} #(1) data identification

hou <- Quandl(“FRED/HOUSTNSA”, type=“zoo”)

summary(hou)

plot(hou)

str(hou)

head(hou)

tail(hou) …

…{r} # split sample into two parts - estimation sample and prediction sample y <- hou y1 <- window(y,end=c(2012,12)) y2 <- window(y,start=c(2013,1)) # first part used to identify and estimate the model y <- y1 # log, log-change, seasonal log change ly <- log(y) dly1 <- diff(ly) dly12 <- diff(ly,12) dly12_1 <- diff(diff(ly),12) …

…{r}

par(mfrow=c(2,3)) plot(y, main=expression(y)) plot(ly, main=expression(log(y))) plot.new

plot(dly,main=expression(paste(Delta,“log(y)”))) plot(dly12,main=expression(paste(Delta[12],“log(y)”))) plot(dly12_1,main=expression(paste(Delta,Delta[12],“log(y)”)))

…

plot ACF and PACF

library(zoo)

maxlag <-36

par(mfrow=c(2,2)) …{r}

plot(acf(coredata(ly), type=‘correlation’, lag=maxlag, plot=FALSE), ylab=“”, main=expression(paste(“ACF for log(y)”)))

acf(coredata(dly),type=“correlation”,lag=maxlag,ylab=“”,main=expression(paste(Delta,“log (y)-ACF”)))

acf(coredata(dly12),type=“correlation”,lag=maxlag,ylab=“”,main=expression(paste(Delta[12],“log (y)-ACF”)))

acf(coredata(dly12_1),type=“correlation”,lag=maxlag,ylab=“”,main=expression(paste(Delta, Delta[12],“log (y)-ACF”)))

acf(coredata(ly),type=“partial”,lag=maxlag,ylab=“”,main=“PACF-log y”)

acf(coredata(dly),type=“partial”,lag=maxlag,ylab=“”,main=“PACF-delta,log y”)

acf(coredata(dly12),type=“partial”,lag=maxlag,ylab=“”,main=“PACF-delta[12],log y”)

acf(coredata(dly12_1),type=“partial”,lag=maxlag,ylab=“”,main=“PACF-delta[12],log y”) …

…{r}

estimate model -

m1 <- arima(dly12_1,order=c(2,0,0),seasonal=list(order=c(0,0,1),period=12)) m1

…

…{r} #Check model m1 for adequacy tsdiag(m1,gof.lag=36)

BIC(m1) AIC(m1)

m2<-arima(dly,order=c(0,0,3),seasonal = list(order=c(0,1,1),period=12)) m2 tsdiag(m2,gof.lag=36) BIC(m2) AIC(m2)

```

…{r} m3<-arima(ly,order=c(0,1,3),seasonal =list(order=c(0,1,1),period=12)) m3 tsdiag(m3,gof.lag=36) BIC(m3) AIC(m3)

…