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The candidate examines interest rates on municipal bonds from 1970 through 1998. He properly examines the graph and divides the time series into three time periods, based on the means, trends, and volatility of the interest rates. He does not just use the interest rate eras on the NEAS web site; he carefully examines whether the time series justifies the division.
The three interest rate eras affecting Treasury yields and corporate bonds also affect municipal bonds. The NEAS faculty comments also discuss the different tax eras that affect municipal bond spreads.
Some candidates try to model the full time series by taking second differences. The results are spurious, and do not forecast well. The original time series need not be stationary, but it must by homogeneous. It reflects a single process, not an amalgam of two processes in different periods.
Choosing eras is not easy. Use three rules:
(1) A distinct change in trend indicates a different ARIMA process. If interest rates first increase and then decrease, we divide the time series into two eras to fit ARIMA processes. When you examine the trends, consider several items:
~ Seasonality and cycles are not trends. The expected daily temperature rises in the Spring and declines in the Autumn. This is seasonality, not a trend. GDP rises in prosperous years and declines in recessions; this is a cycle, not a trend. We adjust for seasonality and cycles to see the trends.
~ Stochasticity obscures trends. Average claim severities by month for a small insurer have so much stochasticity that the inflationary trend is hard to see. Simple moving averages help you quantify the trends.
~ A continuous change in a trend may require taking logarithms, not separating the time series into eras.
(2) A change in volatility indicates a different ARIMA process. We see only the realization of the time series, not the underlying process, so it is not easy to discern if a higher standard deviation is higher volatility or a random fluctuation. For interest rates, the higher volatility in the second time period is clear. A high dispersion in daily temperatures one year is random fluctuation, not a change in volatility.
(3) A change in the mean indicates a different ARIMA process. Changes in the mean are most often caused by exogenous factors, such as marginal tax rates. Two examples are
~ The 1986 reduction of the corporate tax rate narrowed the municipal bond spread. Actual ARIMA modeling of municipal bond yields must distinguish tax eras (You are not expected to know tax law for the student project. We point out exogenous factors to help you understand why the means differ by time period.)
~ A change from a high and progressive income tax to a low and flat income tax raises employment and GDP. This type of change occurred (to different degrees) in the U.S., Ireland, Eastern Europe, and Asia. The change is relatively rapid, though it takes five to ten years for the change in GDP growth to be clear.]