Time Series And Forecasting

Problem 2.3

Kevin Wunderlich

First we read in the data, install the appropriate packages, load the packages into our working directory using the “library()” function, and create a timeseries variable “tsrate”

## Warning: package 'broom' was built under R version 3.2.3

hw <- read.csv("C:/Users/kgwunderlich1s/Desktop/hw.txt", sep="")
ymd(paste(hw$Year,hw$Mon,hw$Day,sep = "/"))->hw$date
ts(hw$Rate)->tsrate

Now we use the “auto.arima()” function to achieve a forecast model with p=4,d=1,q=4

fit <- auto.arima(tsrate)

## Warning in auto.arima(tsrate): Unable to fit final model using maximum
## likelihood. AIC value approximated

fcast <- forecast(fit)
fcast$fitted->hw$forecast
dates<-hw$date[735]+months(1:10)

tidy(fit)

##   term     estimate  std.error
## 1  ar1 -0.006933305 0.18409084
## 2  ar2  0.307028265 0.12285361
## 3  ar3 -0.434984420 0.12831388
## 4  ar4  0.323025540 0.10868138
## 5  ar5  0.221112357 0.05109936
## 6  ma1  0.029766416 0.18606073
## 7  ma2 -0.069541925 0.12713478
## 8  ma3  0.632318825 0.10420285
## 9  ma4 -0.236353283 0.09434336

The above model implies cycles because of the +,- alternating estimates for AR p’s and MA q’s

From here we can see the following plots in the respective order:

1)Observed Rates

2)Forecast Rates (plus 10 forecasted values)

3)Observed Rates against Forecast Rates

plot(hw$Rate,x = hw$date,main="True Rates",ylab="Return Rates",xlab="date",type="l")

plot(fcast,xlab="Rate Observation Value",ylab="Return Rates")

plot(y=hw$forecast,x=hw$Rate,ylab="Forecasted Rates",xlab="True Rates")

cbind(as.character(dates),fcast$mean)->ans

Finally, the forecasted rates for 2009 are:

## Time Series:
## Start = 736 
## End = 745 
## Frequency = 1 
##     as.character(dates)       fcast$mean
## 736          2009-04-01 8.73062653174108
## 737          2009-05-01 8.98999141104361
## 738          2009-06-01  9.1646731184688
## 739          2009-07-01 9.34213812460723
## 740          2009-08-01 9.44466344831955
## 741          2009-09-01 9.55723141694743
## 742          2009-10-01 9.62451004103085
## 743          2009-11-01 9.70995822094358
## 744          2009-12-01 9.75341491317477
## 745          2010-01-01 9.80911541266399