The data set "wages" in the package "TSA" contains monthly data on average hourly wages in the apparel industry. The data can be accessed by doing the following

library(TSA)

data(wages)

A description of the data can be found by doing

help(wages)

Some (potentially) helpful functions for this problem are

plot() -will plot a time series

diff() - will create a differenced time series

acf() - will create an autocorrelation plot

pacf() - will create a partial autocorrelation plot

To fit an ARIMA(p,d,m) model with seasonal component of (sp,sd,sm) of period k you would use the following code

arima(wages, order=c(p,d,m), seasonal = list(order=c(sp,sd,sm), period = k))

A plot() of an ARIMA model will provide forecasts with interval bounds for future observations.

Note this is monthly data.

a)Create a time series plot of the raw wages data and the monthly change in wages.

a.Do you believe average wages is a stationary time series? Explain.

b.Do you believe that monthly difference in average wages is a stationary time series? Explain.

b)Fit an ARIMA model to this data. Explain why you selected the model you fit.

c)Use the plot() function to provide future forecasts from the model. Discuss any concerns you have about the model and the future forecasts. If you have no concerns, explain why.