Obtain data on bilateral exchange rates and consumer price index for three countries: France, Belgium and Germany. The frequency of the data should be monthly and should span a period post-Bretton-Woods system and before introduction of a single currency, that is, from 1973 to 1990. Take the natural log of the variables and split the sample period into two parts: one part containing all of the observations excluding the last 10 observations and the other part containing the last 10 observations. The larger sub-sample is to be used to answer questions (1) to (4) and the smaller sample is to be used in the forecasting question (question (5)).
Analyse the time-series properties of your series as follows;
(1) Identify the summary statistics which describe the statistical properties of each series and provide a rationale for your choice. Calculate the chosen summary statistics and analyse briefly the results obtained.
(2) Test for the presence of unit roots in all series. Explain carefully the testing procedure used.
(3) Explain what you can do to test the hypothesis of the long-run Purchasing Power Parity (PPP) for a given pair of countries, with the reference to the appropriate theoretical and empirical literature. Find if there is evidence in your data in support of the long-run PPP hypothesis for each pair of countries.
(4) Identify and estimate a suitable autoregressive (AR) model for any one of the exchange rate series. Test for ARCH effects in the chosen series. Re-estimate your model using an appropriate GARCH model for the conditional variance. Comment succinctly on the usefulness of your GARCH model in finance.
(5) Forecast the mean and the variance of the model obtained in question (4) for the last 15 observations. Re-estimate your model using an asymmetric GARCH model. Critically compare the properties of the two models in the context of their usefulness in finance.