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I wanted to see what I could do in a hurry using the commands found at Forecasting: Principles and Practice . I chose a simple enough data set of Wisconsin Unemployment from 1976 to the present (April 2013). I kept the last 12 months worth of data to test the accuracy of the models. The next blog post will include a multiple regression analysis. The analysis is lacking many important steps, particularly the ARIMA, but this is a down and dirty exercise.

library(forecast)

library(lmtest)

library(caret)

#State Unemployment seasonally adjusted

#http://www.quandl.com/FRED-Federal-Reserve-Economic-Data/WIUR-Unemployment-Rate-in-Wisconsin

#Using Quandl data, great little site

wi<-read.csv('http://www.quandl.com/api/v1/datasets/FRED/WIUR.csv?&auth_token=gigXwpxd6Ex91cjgz1B7&trim_start=1976-01-01&trim_end=2013-04-01&sort_order=desc', colClasses=c('Date'='Date'))

#some minor clean up

colnames(wi)<-c('date', 'rate')

wi$date<-as.Date(wi$date)

summary(wi)

#base data, 1-436, test data 437-448

wi.b<-wi[1:436,]

wi.p<-wi[437:448,]

wi.ts<-ts(wi.b$rate, start=c(1976, 1), frequency=12)

wi.p.ts<-ts(wi.p$rate, start=c(2012, 5), frequency=12)

plot.ts(wi.ts)

#Lets test some models

mean<-meanf(wi.ts, 12)

naive<-rwf(wi.ts, 12)

s.naive<-snaive(wi.ts, 12)

drift<-rwf(wi.ts, 12, drift=T)

#linear fit

m1<-tslm(wi.ts~trend)

m2<-tslm(wi.ts~trend+season)

#checking for autocorrelation

res1 <- residuals(m1)

par(mfrow=c(1,2))

plot(res1, ylab="Residuals",xlab="Year")

Acf(res1, main="ACF of residuals")

res2 <- residuals(m2)

par(mfrow=c(1,2))

plot(res2, ylab="Residuals",xlab="Year")

Acf(res2, main="ACF of residuals")

par(mfrow=c(1,1))

#Durbin-Watson Test

dwtest(m1, alt="two.sided")

dwtest(m2, alt="two.sided")

#yep autocorrelation city! No surprize here, due to the nature of unemployment

#STL ETS Decomposition

m3<-stl(wi.ts, s.window='periodic')

plot(m3)

m4<-ets(wi.ts, model='ZZZ')

plot(m4)

#ARIMA

m5<-auto.arima(wi.ts)

plot(forecast(m5, h=12))

#neural networks

m6<-nnetar(wi.ts)

m6

plot(forecast(m6, h=12))

#Testing for accuracy the first 4 models

a1<-accuracy(mean, wi.p.ts)

a2<-accuracy(naive, wi.p.ts)

a3<-accuracy(s.naive, wi.p.ts)

a4<-accuracy(drift, wi.p.ts)

a.table<-rbind(a1, a2, a3, a4)

#Creating the forecast and accuracy for the next 6 models

f1<-forecast(m1, h=12)

f2<-forecast(m2, h=12)

f3<-forecast(m3, h=12)

f4<-forecast(m4, h=12)

f5<-forecast(m5, h=12)

f6<-forecast(m6, h=12)

a5<-accuracy(f1, wi.p.ts)

a6<-accuracy(f2, wi.p.ts)

a7<-accuracy(f3, wi.p.ts)

a8<-accuracy(f4, wi.p.ts)

a9<-accuracy(f5, wi.p.ts)

a10<-accuracy(f6, wi.p.ts)

#Combining into a table with row names

a.table<-rbind(a.table, a5, a6, a7, a8, a9, a10)

row.names(a.table)<-c('Mean', 'Naive', 'S. Naive', 'Drift', 'Lm~Trend',

'Lm~Trend+Sea', 'STL', 'ETS', 'ARIMA', 'Neuro')

#make into a data frame so the best model is first, according to MAPE

a.table<-as.data.frame(a.table)

a.table<-a.table[order(a.table$MAPE),]

a.table

Results so far: Looks like the mean like forecasts are doing the best, the fancy models are not doing very well.

To

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