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[NEAS: Monthly unemployment rates are a good choice for a time series student project. They show the four patterns we analyze in this course: stochasticity, trend, seasonality, and cycles. Your ARIMA modeling disentangles these four patterns.

Unemployment often lasts many months, so the time series is not a white noise process. It surely has one or more autoregressive terms. You can compare AR(1), AR(2), MA(1), and ARMA(1,1) processes.

Illustration: If the April 20X7 unemployment rate rises unexpectedly and the average duration of unemployment is three months, the May, June, and July unemployment rates will also be higher than expected.

Unemployment rates are seasonal, with higher unemployment in the summer months when more college students look for work and lower unemployment in November and December, when retail stores hire temporary workers. The seasonality differs by location, industry, and population group. An ARIMA process that fits well to one set of data may not fit well to another set.

Illustration: In college towns, unemployment may rise in the summer. In a rural area, unemployment may fall in the summer (harvest season).

We use different methods to adjust for exogenous vs endogenous seasonality.

For unemployment rates, it is unclear which method is preferred. You can use both methods and compare which time series can be better fit by an ARIMA process.

Unemployment rates show long-term trends. The rates may rise gradually for a decade or decline for a decade. Both trends can be seen in the post-World War II U.S. data.

If a time series has a trend, we model first differences or first differences of logarithms. You may fit the ARIMA process to the first differences of the unemployment rates.

Be careful with taking differences. Most countries have relatively monetary growth and monetary inflation. To fit an ARIMA process to the CPI, we take logarithms and first differences. But unemployment does not naturally have a trend. It has cycles, seasonality, and stochasticity, but the trends may reflect economic conditions or legislation.

Unemployment rates are affected by economic conditions. Unemployment is higher during recessions and lower during prosperous years. You may regress the unemployment rate on GDP growth and fit an ARIMA process to the residuals.

Unemployment rates are affected by legislation for unemployment benefits, minimum wages, and termination procedures. You can examine unemployment rates before and after a law change and fit an ARIMA process to each time period.

The effects of legislation are best seen in European nations. The labor laws and unemployment benefits in the US have remained relatively stable for the past fifty years. The minimum wage laws have risen with inflation but have not changed much.

The time series for unemployment differ for males vs females, for young vs older workers, and for workers of different ethnic groups. You can compare the ARIMA processes for two sets of workers.

This candidate looks at monthly unemployment rates in Bloomington, Illinois. The monthly figures themselves don’t indicate the type of process. The sample autocorrelation function shows the geometric decay and the 12 month seasonality. The 12 month differences eliminate the seasonal effect, and the candidate fits AR(1) and AR(2) processes.]