[NEAS: We post only an extract from this student project. The dollar - Yen exchange rate from 1971 to 2005 is an excellent time series for ARIMA modeling.

Exchange rates follow interest rate parity and purchasing power parity, as explained in the NEAS project template on exchange rate time series modeling. The changing interest rates in the US and Japan allow you to examine ARIMA modeling with and without the adjustment for interest rates.

Dollar interest rates were high in the late 1970’s and early 1980’s, corresponding to the sharp depreciation of the dollar relative to the Yen in this candidate’s student project.

Dollar interest rates declined in the late 1980’s and early 1990’s, and the trend in the exchange rate leveled off.

Japanese interest rates fell in the 1990s’s, corresponding to a long recession and deflation. The dollar interest rates stayed about four or five points higher.

The exchange rate itself is stochastic. Some financial economists presume the exchange rate follows a random walk, after adjusting for interest rate parity. Other economists believe the exchange rate is influenced by economic and political conditions in each country. The different fortunes of the US and Japan over the past 35 years make this an interesting student project.

Your student project might compare the ARIMA processes fitted to the exchange rate itself vs the ARIMA processes fitted to the exchange rate adjusted for interest rate parity (that is, adjusted by the ratio of risk-free rates in the two currencies). If interest rate parity is correct, an ARIMA process is easier to fit after adjusting for interest rates. You examine this with the Box-Pierce Q statistic and Bartlett’s test.

Your comparison may be on the exchange rate itself or its first differences. If the exchange rate follows a random walk (perhaps with a drift), or if it has a trend, fit an ARIMA process to the first differences.]