Applying dynamic non-linear models to exchange rate determination

Nitus Patrayotin

ISU General Staff Papers from Iowa State University, Department of Economics

Abstract: There is a large theoretical and empirical literature that tries to explain and understand the movement of observed exchange rates. There are three major theories of exchange rate determination: the flexible-price approach, the sticky-price approach and the portfolio approach. These three approaches are combined together in this study. The model is modified further by incorporating information from the forward exchange market. This information is incorporated by using the relationship between the observed forward rate, the expected rate in the future and the forward parity rate;The theoretical models of exchange rate determination are mostly two country models. To extend it to multilateral situations involves using a "no-arbitrage condition." The statistical analysis is done in two ways: using fixed coefficient models and time-varying parameter models. The fixed parameter model considered is a bilateral exchange rate model. It is estimated by nonlinear least squares methods. The time-varying model is set up as a stochastic coefficient model. The Kalman filter algorithm is used to estimate the time-varying coefficient model. The no-arbitrage condition can be incorporated directly into the Kalman filter algorithm. The law of motion of these coefficients is assumed to be a first order vector autoregressive process. The first order vector autoregressive coefficients are estimated by using the maximum likelihood method;The results from statistical analysis in the two statistical models are different from each other. While the assumption of Purchasing Power Parity holding in the long run is confirmed by the fixed parameter estimation, it is rejected by the time-varying parameter model. In terms of the root-mean-square error of estimation, the fixed coefficient model fits the data used better than the time-varying parameter model. In the time-varying parameter model most of the coefficients estimated follow the return to nomality model;In comparing the forecasting performance between the theoretical models and a simple random walk, it is usually found in the literature that the theoretical model cannot improve upon the forecasting performance of the random walk model for a time horizon less than 12 months. In this study it is found that the time-varying model can out-perform the random walk model for a month ahead forecast in 5 out of 6 exchange rates. Hence, the time-varying parameter model can be used as a tool to trace the movements of exchange rates in the changing economic environment over short time periods.

Date: 1992-01-01
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