ProblemSet#3

fred_qd <- read.csv("fred_qd.csv")
fred <- fred_qd
fred <- fred[-(1:2),]
fred$NX <- (fred$EXPGSC1-fred$IMPGSC1)

timeseries <- ts(fred[,-1],start=c(1959,1),frequency = 4)
gdp_ts <- timeseries[,("GDPC1")]
consumption_ts <- timeseries[,("PCECC96")]
investment_ts <- timeseries[,("GPDIC1")]
government_ts <- timeseries[,("GCEC1")]
netexports_ts <- timeseries[,("NX")]

Part 1: Random Walk

plot(gdp_ts)

plot(consumption_ts)

plot(investment_ts)

plot(government_ts)

plot(netexports_ts)

1. Using an eye test on the plotted time series, I determined that a random walk with drift is most appropriate for GDP, consumption, investment, and goverment spending since they all have distinct upward trends. Net exports on the other hand flucuates around 0 and does not have a clear trend so a random walk would be appropriate.

pacf(gdp_ts, plot = FALSE)

## 
## Partial autocorrelations of series 'gdp_ts', by lag
## 
##   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25   2.50   2.75 
##  0.988  0.003 -0.003 -0.008  0.000 -0.002 -0.003 -0.007 -0.004 -0.003 -0.009 
##   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75   5.00   5.25   5.50 
## -0.014  0.010 -0.001  0.008  0.004  0.001  0.074 -0.099 -0.030 -0.003  0.004 
##   5.75   6.00 
## -0.001 -0.005

pacf(consumption_ts)

pacf(investment_ts, plot = FALSE)

## 
## Partial autocorrelations of series 'investment_ts', by lag
## 
##   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25   2.50   2.75 
##  0.985 -0.015  0.006 -0.003 -0.017  0.000  0.013 -0.029 -0.001 -0.032 -0.029 
##   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75   5.00   5.25   5.50 
##  0.003  0.060  0.029 -0.017 -0.023  0.025  0.146 -0.132 -0.030 -0.025 -0.002 
##   5.75   6.00 
## -0.003  0.005

pacf(government_ts, plot = FALSE)

## 
## Partial autocorrelations of series 'government_ts', by lag
## 
##   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25   2.50   2.75 
##  0.988  0.002 -0.006 -0.020 -0.016  0.006  0.003  0.005  0.011 -0.005 -0.010 
##   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75   5.00   5.25   5.50 
## -0.014 -0.005 -0.014 -0.019  0.008 -0.022 -0.035  0.033 -0.002  0.000  0.005 
##   5.75   6.00 
##  0.007  0.006

pacf(netexports_ts, plot = FALSE)

## 
## Partial autocorrelations of series 'netexports_ts', by lag
## 
##   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25   2.50   2.75 
##  0.979 -0.051  0.010 -0.018 -0.032 -0.009 -0.046 -0.023 -0.027 -0.136 -0.041 
##   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75   5.00   5.25   5.50 
##  0.075 -0.023  0.029  0.002  0.010  0.068  0.142 -0.016 -0.002 -0.095 -0.061 
##   5.75   6.00 
## -0.006 -0.055

1. For all five variables of interest AR(1) seems the most appropriate according to the lags.

library(forecast)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo