Financial modelling and business forecasting
SUMMATIVE ASSIGNMENT
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;
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(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.
(10 marks)
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(2) Test for the presence of unit roots in all series. Explain carefully the testing procedure used.
(10 marks)
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(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.
(30 marks)
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(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.
(25 marks)
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(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.
(25 marks)
