hw3-q3

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

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.

q3

install.packages(“Quandl”)

library(“Quandl”) library(tseries)

c<-Quandl(“FRED/CPILFENS”,type=“zoo”)

str(c)

A<-diff(c) B<-(A/c)*100 Inflation<-ts(B,start=c(1957,2),frequency=12)

plot(Inflation,xlab=“”,ylab=“INF”,main=“INF”)

DInflation=diff(Inflation)

plot(DInflation,xlab=“”,ylab=" INF“,main=” InF“)

adf.test(Inflation)

adf.test(DInflation)

kpss.test(Inflation)

kpss.test(DInflation)

acf(coredata(DInflation),type=“correlation”,lag=40,ylab=“”,main=“ACF”)

acf(coredata(DInflation),type=“partial”,lag=40,ylab=“”,main=“PACF”)

estimate model

ARMA1<-arima(DInflation,order=c(2,0,2)) ARMA1

tsdiag(ARMA1,gof.lag=12)

AIC(ARMA1)

BIC(ARMA1)

ARMA2<-arima(DInflation,order=c(4,0,4)) ARMA2

tsdiag(ARMA2,gof.lag=12)

AIC(ARMA2)

BIC(ARMA2)

ARMA3<-arima(DInflation,order=c(4,0,2)) ARMA3

tsdiag(ARMA3,gof.lag=12)

AIC(ARMA3)

BIC(ARMA3)

ARMA4<-arima(DInflation,order=c(3,0,3)) ARMA4

tsdiag(ARMA4,gof.lag=12)

AIC(ARMA4)

BIC(ARMA4)

#based on AIC values and Ljunb-Box tests we choose model 3

forecasting

library(“forecast”)

ARMA3.fcast<-forecast(ARMA3,h=12)

plot(ARMA3.fcast,type=“o”,pch=16,xlim=c(2005,2017),ylim=c(-0.5,0.5))