This student project applies ARIMA analysis to the residuals of a regression model. This is generally a good approach: the structural model (the regression) explains the known influences on the time series and the ARIMA model explains the remaining effects. Fitting an ARIMA process to interest rates (or their differences) is rarely sufficient, since government fiscal and monetary policy affect interest rates. This candidate begins with fiscal policy. A large budget deficit means more government borrowing: the FED issues long-term Treasury bonds, which pushes up long-term interest rates. Budget deficits are a primary influence on long-term interest rates. But interest rates are also a stochastic process. The yields on long-term Treasury bonds depends on the short rates expected each year, so the yields have high serial correlation. The candidate models the residuals from the regression on fiscal budget deficits by an ARIMA process.

The candidate knows that the regression model does not include all relevant explanatory variables, as he says: “the precise effects of the federal deficit on the long-term interest rate depend on a wide variety of factors, including whether the change in the deficit is caused by a change in taxes or a change in spending, how monetary policy reacts, and how foreign government react. All these factors are not included in this simple regression model.” The objective of the student project is to apply the statistical techniques to real data. Use a simple regression (as this candidate does) and examine the residuals with an ARIMA process.