The forward market is efficient if the lagged forward rate is an unbiased predictor of the current spot rate.
(a) Estimate the following model of the spot and the lagged 1-month forward rate
\[
\mathrm{s}_{t}=\beta_{0}+\beta_{1} \mathrm{f}_{t-4}+u_{t}
\]
where the forward rate is lagged four periods (the data are weekly). Verify that weekly data on the \$/AUD spot exchange rate and the 1 month forward rate yields
\[
s_{t}=0.066+0.916 f_{t-4}+e_{t}
\]
where a lag length of four is chosen as the data are weekly and the forward contract matures in one month. Test the restriction \(\beta_{1}=1\) and interpret the result.

(b) Compute the ACF and PACF of the least squares residuals, \(e_{t}\), for the first 8 lags. Verify that the results are as follows.

(c) There is evidence to suggest that the ACF decays quickly after 3 lags. Interpret this result and use this information to improve the specification of the model and redo the test of \(\beta_{1}=1\).
(d) Repeat parts (a) to (c) for the 3-month and the 6-month forward rates.

Transcribed Image Text:

Lag: 1 2 3 2 4 5 6 7 8 ACF 0.80 0.54 0.29 0.07 0.07 0.09 0.13 0.15 PACF 0.80 -0.28 -0.14 -0.07 0.40 -0.11 -0.04 -0.02