[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.

~ Form two time series: one is the original exchange rates and the other is adjusted for interest rate parity.

~ Fit ARIMA models to each time series. You can use the same models for each time series, since the focus is on the comparison.

~ For each ARIMA process you fit, calculate the Box-Pierce Q statistic.

~ Compare the Box-Pierce Q statistics for the two time series.

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.]

[This is just an FYI from a student who had considered modeling the USD/JPY exchange rate.]

In theory, the USD/JPY exchange rate should follow purchasing power and interest rate parity (PPP and IRP).  But in practice, interest rate parity does not hold.  According to Thaler ("The Winners Curse," 1992, pp 182-198), there is a very large literature that shows currencies with higher interest rates appreciating relative to lower interest rate currencies.  There is no firm conclusion as to why IRP does not hold, but Thaler presents two prevailing theories, including expectational errors ("inefficient" markets) and time-varying exchange rate risk premiums.  A current case in point is USD appreciation versus JPY (also EUR appreciation versus JPY), where Japanese interest rates are much lower than U.S. rates.  This practical conclusion is literally opposite of what is predicted in theory by IRP.

Although my project did not look at exchange rates, I had considered studying the USD/JPY exchange rate given the conclusions above.  I would have specifically looked at regressing changes in real interest rate differentials against the USD/JPY exchange rate, with the expectation that rising real rates would lead to currency appreciation, i.e. higher real U.S. interest rates would lead to higher USD/JPY.  I would then model the residuals according to an ARIMA process.  I don't know how this would have turned out, but thought it might be an interesting approach given the failure in IRP.  At the least, it may keep you from losing money betting against the carry-trade.

It is indicated above that there is a project template for an exchange rate student project, can someone please direct me to this? I am interested in doing my project on this.

Thanks!