Hybrid versus Highbred -A New Approach to Combine Economic Models with Time-series Analyses

1. Hybrid versus Highbred-A New Approach to Combine Economic Models with Time-series Analyses Ming-Yuan Leon Li Quantitative Finance (SSCI journal), 10, 637-647 (2008)

3. Motivations • Economic models • They try to measure and quantify the relationships between exchange rates and a set of economic fundamentals • Meese and Rogoff (1983): the forecast performances of exchange rates produced by economic models based on fundamentals are no better than those using random walk models • Longer horizons or nonlinear methods

4. Motivations • Time-series approaches • The lagged values of the change in the lagged exchange rates could be used to predict their future values • ARMA (Auto-Regressive Moving Average) model

5. Motivations • Could we design a composite model that incorporated both of the economic models and time series techniques? • The information from both of fundamental variables derived from economic theory and their own lagged variables should be valuable for market participants

6. Motivations • Portfolio managers should weigh the information from fundamental variables from the economic theories and the own lagged data • Moreover, in some periods, we argue that managers should pay more attention to the economic models (time-series approach) and vice versa in other period • One of the main obstacles is how to decide the weights of each of these two different forecasting techniques

7. Motivations • Employ the Markov Switching (MS) mechanism to decide the time-varying weights of the various alternatives • In brief, we set up a framework with two states to capture two different forecasting alternatives. Moreover, one of the features of the MS model is to estimate the probabilities of the specific state at each time point by data itself • In this paper, we use the estimated and time-varying probabilities to serve as the weights of each technique.

8. Few Interesting Questions • The composite models with time-varying loading outperform each of these two techniques and the random walk models? • What are the relationships between the various volatility regimes and various forecasting techniques? • Examining the exchange rates of developing countries’ currencies and comparing the differences between them • Extreme Price Movements

9. Engle and Hamilton (1990) • Employed the MS techniques and examined the long term swing behaviors of exchange rates • Extend the MS system developed by Engle and Hamilton (1990) • Marsh (2000), Bessec (2003), Clarida, et al. (2003), De Grauwe and Vansteenkiste (2001), and Frommel, et al. (2005).

10. Unlike prior studies • The effects of fundamental variables on exchange rates would vary according to the phase of market state • Engle and Hamilton (1990) • two states on the constant term of regression equation versus a framework with two states on the slop terms • Highlighting the dynamics of return volatility in exchange rates.

11. Unlike prior studies • What are the relationships between various volatility states and forecasting techniques? • are investors more concerned with fundamental variables or lagged exchange rates during the volatile periods? • The comparative study of exchange rates in both mature and emerging economies. • To our knowledge, few if any, previous studies have explored these crucial exchange rate issues.

12. Model Specifications • Time-series Approach ,

13. Model Specifications • Economic Model ,

14. Model Specifications • Hybrid Model with Constant Weights

15. Model Specifications

16. Model Specifications • Hybrid versus highbred • Highbred= Hybrid model + a restriction • Shortcoming of the constant weight • the weights of w and (1-w) remain constant throughout the whole entire sample period.

17. Model Specifications • Hybrid Model with Time-varying Weights ,

18. Model Specifications • st is an unobservable state variable and follows a Markov chain with one order:

19. Model Specifications • p(st|It): filtering probability • p(st|IT): smoothing probability • p(st|It-1) : Predicting Probability

20. Model Specifications

21. Model Specifications • The difference between the two hybrid models • In contrast with studies by Engle and Hamilton (1990) and Frommel, et al. (2005)

22. Empirical Results • The monthly bilateral exchange rates (in U.S. dollars per unit of foreign currency) for the currency of four industrialized countries (France, Germany, U.K. and Japan) and two developing Asian countries (South Korea and Taiwan) • The data period is from January, 1980 to August, 2000 for 248 observations • The data source is AREMOS database

23. Forecasting Performance

25. Parameter Estimates

29. Parameter Estimates • The high volatility state (st=2) versus the low volatility state (st=1) • The high (low) volatility state corresponds to the forecasting technique of the Economic model (Time-series approach)

30. Parameter Estimates • The two ARMA components are significant in 1% • The fundamental variables are significant • South Korea: a special case

31. Explanations of Our Empirical Results • The composite model with non-constant loadings on two forecasting techniques outperforms the setting with constant loadings

32. Explanations of Our Empirical Results • The high (low) volatility state corresponds to the forecasting technique of the economic model (time-series approach)

33. Explanations of Our Empirical Results • The speed of convergence toward theoretical values which are derived from economic theories should be greater as the deviation from theoretical values rises in absolute value • The great/small deviation from theoretical values should be closely associated with the high/low volatility state

34. Explanations of Our Empirical Results • The state of the time-series approach with the own lagged values corresponds to the state of low volatility • Investors might well picture the future exchange rates via their own past values during the stable periods

35. Explanations of Our Empirical Results • However, during the volatile period, the fundamental variables are insignificant for the case of South Korea

36. High/Low Volatility

37. Explanations of Our Empirical Results

38. Explanations of Our Empirical Results • Asian financial crisis of 1997 • Substantial dollar depreciations and large scale of capital flights. • So the exchange rate volatility was a larger amount than what was originally planned. • Investors’ irrational overreaction behaviors

39. Out-off-sample Performance • The in-sample performance tests of various alternatives give an indication of their historical performance. • Investors in markets would be more concerned with how well they can do in the future using alternative forecasting techniques.

40. This paper withholds the last 12 twelve observations (namely one year data) of the sample for each market are withheld, and conducts a rolling estimation process is conducted • As in the in-sample test, the out-of-sample forecasting performances of alternative model specifications for exchange rates are also compared with the random walk model.

43. Conclusion and Extensions • First, market investors will more heavily emphasize on the fundamental variables derived from economic models when exchange rates are more volatile. By conversely, during the stable periods, market participants would increase the loadings of the effects of the lagged values of exchange rates.

44. Second, the hybrid model with time-varying loadings outperforms the highbred model for most cases. By contrast, the performancess of the hybrid model with constant weights are trivial.

45. Finally, compared with random walk models, the present findings lend support to the superiority of the hybrid model with time-varying loadings in the out-of-sample forecasting performances for mature economies such as Germany, Japan and U.K., but not for emerging markets such as South Korea and Taiwan.

46. Conclusion and Extensions • Two caveats should be mentioned • Future areas of work may include applying this approach to combine more complex time-series models (e.g., GARCH-based models) and other economic models (e.g., considering relative income levels, and explicitly including the crisis dummy variables) • Future researchers might employ other testing methods

47. Other applications of MRS models • Li, Ming-Yuan Leon* (2008) Could the jump diffusion technique enhance the effectiveness of futures hedging models? A reality test, Mathematics and Computers in Simulation, accepted and forthcoming 【SCI】 • Li, Ming-Yuan Leon* (2008) The dynamics of the relationship between spot and futures markets under high and low variance regimes, Applied Stochastic Models in Business and Industry, accepted and forthcoming 【SCI】 • Li, Ming-Yuan Leon* (2007) Purchasing power parity under high and low volatility regimes, Applied Economics Letters, 14, 581-589.【SSCI】

48. Li, Ming-Yuan Leon* (2007) Volatility state and international diversification of international stock markets, Applied Economics, 39, 1867-1876.【SSCI】 • Li, Ming-Yuan Leon*, Hsiou-wei William Lin and Hsiu-Hua Rau (2005) Performance of Markov-switching model on business cycle identification revisited, Applied Economics Letters, 12, 513-520.【SSCI】 • Li, Ming-Yuan Leon* and Hsiou-wei William Lin (2004) Estimating value at risk via Markov switching ARCH models - An empirical study on stock index returns, Applied Economics Letters, 11, 679-692.【SSCI】