Structural modelling and analysis of the behavioural dynamics of foreign exchange rate
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Date
2006
Authors
Yip, Chee Yin
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Abstract
This thesis deals specifically with the foreign exchange rates that resulted from free float regimes. In general, we study the structural modelling and analysis of the behavioural dynamics of foreign exchange rates. We start with the recognition that foreign exchange rate is a financial time series. We model the foreign exchange rate by using two popular methodologies: ARFIMA and a Kalman filter based method (KFBM) with the hope that it can produce the best exchange rate model. Our objective is to use this best model to show the mean reverting behaviour of the exchange rates. In the course of carrying out the experiments and analysis, we would like to study the behavioural dynamics of the exchange rate.
We have developed a dynamic YQ-specified ARFIMA model for the long and short term memory modelling. Here ‘dynamic’ simply means that the model parameters can be altered according to the characteristics of the particular time series. This seemingly easy alteration is made possible by using sequential t tests. This YQ-specified ARFIMA model performs very well and much better than the Kalman filter based method. We have shown without any doubts that YQ-ARFIMA is about 12 times better in term of the RMSE values and 10.6 times better in term of the MAPE values, than the Kalman filter based method in long-term memory modelling. Moreover, for short-term memory, the YQ-ARFIMA performs even better, giving a RMSE value of 40 times and a MAPE value of 36 times
better than the Kalman filter based method. However, KFBM seems to do better in analysing structural breaks. The possible reason is that KFBM is more suitable for series with cyclical components. In addition, output results show that for short-term memory modelling, the ideal sample size is about 200 to 1300 observations while for long-memory modelling the ideal sample size is between 1500 and 2000 observations.
The output of experimental results shows that this YQ-specified ARFIMA model is robust across 22 foreign exchange markets and across sample sizes. We have found that this YQ-ARFIMA beats the random walk model soundly in out of sample forecasting in terms of the loss functions RMSE and MAPE. With this positive result, we use this YQ-ARFIMA model as a tool to show the mean reverting behaviour of the exchange rates.
We investigated the influence of the breaks on our predictive models. We found that it is costly to ignore structural breaks in forecasting. We have devised a practical method, which we refer to as the dissection method for the correction of outliers when there are not many of them in the series. However, we have found that discarding the section of the data that contains extreme outliers can improve the predictive power of the model tremendously.
We have shown that the cyclical components (stationary) of the exchange rate series are positively related with the corresponding cyclical components of the consumption series. This implies exchange rate series have a long run relationship with consumption. To put it differently, they move together. With this result, we can at least keep track of the sign of the exchange rate by examining the consumption rate.
In the single equation dynamic specification modelling, we have shown that adding only one cyclical component of consumption into the model can deteriorate the predictive ability of the YQ-ARFIMA model. However, we have found that adding the appropriate cyclical component of the LQBritpus series together with that of Lconsumption to models other than the best-fitted model can improve its predictive ability substantially. For the best fitted-model, no combination of the cyclical components can improve its predictive ability at all.
Description
PhD
Keywords
Mathematical science , Behavioural dynamics , Foreign exchange rate