Hybrid versus highbred: combined economic models with time-series analyses

Abstract

While incorporating the Markov-switching (MS) mechanism, this work establishes a hybrid model with endogenous and time-varying loading in each economic model and time-series approach. The empirical data include the monthly exchange rates between the U.S. dollar and the currency of four mature economies, those of France, Germany, Japan and U.K., as well as two emerging Asian countries, South Korea and Taiwan, from 1980 to 2000. The empirical findings of this study are consistent with the following notions. First, market investors are more influenced by fundamental variables derived from economic models during volatile periods. Conversely, when markets stabilize, market participants increase the loadings of the values of lagged exchange rates. Second, a hybrid model with time-varying loading outperforms highbred models for each case. However, the performances of hybrid models with constant loadings are trivial. Third, compared with the random walk model, in-sample tests demonstrated the superior performance of the hybrid model with time-varying loading in all cases. Nevertheless, the out-of-sample performance was less promising, particularly in the case of South Korea.

Keywords:

• Applied econometrics
• Financial econometrics
• Foreign exchange markets
• International finance

Notes

†In brief, there is no strong evidence proving that any given economic models/specifications are particularly successful. In other words, one economic model might do well for one exchange rate, but not for another.

‡For a long time there has been very little communication between econometricians and time-series analysts. Econometricians have emphasized economic theory. Lagged variables were introduced but not in any systematic way and no serious attempts were made to study the temporal structure of the data.

†This investigation adopts the percentage changes in the exchange rates instead of the exchange rates to achieve stationarity. The Dickey–Fuller test (not reported here) shows that all of the data series adopted in this paper reject the null hypothesis of unit root.

†Undeniably, there are some other fundamental variables to explain the exchange rates, such as relative money supplies and relative real income as well as relative account balances. Restated, the target of this paper is not to find the best econometric model for the exchange rates. Therefore, for reasons of convenience, we only adopt the two fundamental variables to establish the econometric model.

‡The author would like to thank an anonymous referee for this suggestion.

§For any given value of the weights w and (1–w), one could find one corresponding value of each parameter estimate in equation (4) in equation (3). Just one example, if the estimate of α in equation (3) is 0.1 and one assumes that w is 0.2 in equation (4), then the corresponding value of the parameter estimate of α* in equation (4) would be 0.5 (=0.1×(1/0.2)). Notably, this paper thus estimates equation (3), not equation (4), for the results of the hybrid model with constant weights.

†To satisfy 1 > p_ij > 0, i(j)=1 or 2, this paper uses the following probability settings: 

‡The author is grateful to an anonymous referee for this suggestion.

†This study randomly generates 50 sets of initial values, and then derives the ML function value for each of the 100 sets of initial values. The mapped converged measure of the greatest ML function value then serves to estimate the parameter.

‡Undeniably, for the case of the U.K., only the β estimate is significant at 5%. However, both α and β are significant at 5% for the other five cases.

§One could also refer to Li (2007) for related discussions.

†Specifically, the inflation differentials (the interest rate differentials) are significant in the cases of France and Germany (U.K. and Japan).

‡One can also refers to ‘Taiwan Is Yet to Find Profit in Asia's Woes,’ A15, The Wall Street Journal, August 19, 1998.

†Except for the case of the U.K. in MAE, the hybrid model with time-varying loadings established in this paper performs lower MSE and MAE values in all cases.

†The author would like to thank an anonymous referee for this suggestion.

‡Compared with other alternatives, the hybrid model with time-varying loadings is associated with the second minimum values of forecasting errors in the case of South Korea.

†For example, Diebold and Mariano (1995) provide explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts.