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

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)

2

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

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Economic Model

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14


Hybrid Model with Constant Weights

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16


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


Hybrid Model with Time-varying Weights

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1),,0(~,.

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st is an unobservable state variable and follows a Markov chain with one order:

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19


p(st|It): filtering probability

p(st|IT): smoothing probability

p(st|It-1) : Predicting Probability

20


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21


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

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Forecasting Performance

Table 3 In-sample Forecasting Performances of Various Model Specifications for Exchange Rates (a) Mean Square Error (MSE)

Highbred Model Hybrid Model ARMA (1, 1)

Model Economic

Model Constant Weights

Time-varying Weights

Mature Countries

France 10.218

[2.623%] 10.300

[1.843%] 10.616

[-1.169%] 9.931*

[5.356%]

Germany 10.648

[0.896%] 10.694

[0.467%] 10.547

[1.830%] 10.139*

[5.633%]

Japan 12.442

[0.471%] 12.120

[3.044%] 12.753

[-2.013%] 12.070*

[3.449%]

U.K. 9.318

[3.208%] 9.358

[2.795%] 9.434

[2.008%] 9.222*

[4.207%] Emerging Countries

South Korea 11.274

[0.718%] 11.420

[-0.567%] 11.465

[-0.957%] 11.061*

[2.597%]

Taiwan 1.970

[4.067%] 2.062

[-0.446%] 2.065

[-0.595%] 1.892*

[7.866%]

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(b) Mean Absolute Error (MAE) Highbred Model Hybrid Model

ARMA (1, 1) Model

Economic Model

Constant Weights Time-varying

Weights Mature Countries

France 2.487

[1.982%] 2.519

[0.713%] 2.568

[-1.229%] 2.407*

[5.141%]

Germany 2.532

[0.357%] 2.545

[-0.159%] 2.549

[-0.318%] 2.442*

[3.905%]

Japan 2.782

[-1.444%] 2.713

[1.074%] 2.777

[-1.259%] 2.663*

[2.896%]

U.K. 2.345

[0.206%] 2.305

[1.932%] 2.284*

[2.795%] 2.303


South Korea 1.267

[0.639%] 1.313

[-2.958%] 1.340

[-5.116%] 1.189*

[6.713%]

Taiwan 0.851

[1.390%] 0.879

[-1.854%] 0.882

[-2.202%] 0.827*

[4.114%]

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Parameter Estimates

(a) Highbred Model: ARMA (1, 1) Model cont. α β σ Log-Lik. Mature Countries

France 0.001

(0.011) 0.968*** (0.019)

-0.955*** (0.034)

3.201*** (0.144)

-637.873

Germany 0.026

(0.098) 0.638

(0.632) -0.565 (0.675)

3.258*** (0.147)

-642.236

Japan -0.273 (0.226)

0.201 (0.361)

-0.141 (0.344)

3.530*** (0.159)

-661.986

U.K, -0.330 (0.397)

-0.885*** (0.034)

0.975*** (0.014)

3.212*** (0.145)

-638.718

Emerging Countries

South Korea 0.177

(0.184) 0.328

(0.277) -0.217 (0.281)

3.347*** (0.151)

-648.864

Taiwan -0.006 (0.02)

0.896*** (0.066)

-0.785*** (0.089)

1.391*** (0.063)

-431.968

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(b) Highbred Model: Economic Model cont. γ δ σ Log-Lik. Mature Countries

France 0.398

(0.249) 1.119* (0.649)

-1.240 (0.967)

3.214*** (0.145)

-638.863

Germany 0.017*** (0.001)

0.493 (0.572)

-1.289 (0.930)

3.265*** (0.147)

-642.778

Japan -0.964***

(0.322) -0.323 (0.348)

-2.641** (1.072)

3.484*** (0.157)

-658.753

U.K. -0.753***

(0.291) 0.332

(0.406) 2.726*** (1.031)

3.219*** (0.145)

-639.244

Emerging Countries

South Korea 0.302

(0.230) -0.151 (0.356)

-0.034 (0.239)

3.368*** (0.152)

-650.449

Taiwan -0.034 (0.086)

0.048 (0.094)

0.908* (0.529)

1.423*** (0.064)

-437.601

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(c) Hybrid Model with Constant Weights cont. α β γ δ σ Log-Lik. Mature Countries

France 0.145

(0.131) 0.630*** (0.198)

-1.868*** (0.648)

0.843* (0.492)

-0.532 (0.500)

3.187*** (0.143)

-636.798

Germany 0.085

(0.447) -0.400* (0.243)

1.511* (0.799)

1.082* (0.593)

-2.038 (1.507)

3.252*** (0.146)

-641.727

Japan -0.866** (0.377)

0.111 (0.255)

-0.301 (0.864)

-0.319 (0.355)

-2.354** (1.182)

3.482*** (0.157)

-658.666

U.K. -1.263***

(0.445) -0.561** (0.242)

1.653** (0.816)

0.445 (0.341)

5.227*** (1.554)

3.008*** (0.135)

-622.515

Emerging Countries

South Korea 0.187

(0.232) 0.421

(0.342) -0.993 (0.834)

-0.351 (0.312)

0.098 (0.628)

3.338*** (0.15)

-648.240

Taiwan -0.038 (0.177)

0.885*** (0.086)

-0.776*** (0.117)

0.039 (0.09)

1.033 (0.826)

1.403*** (0.190)

-429.745

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(d) Hybrid Model with Time-varying Weights cont. α β γ δ σ1 σ2 P11 P22 Log-Lik. Mature Countries

France -0.013 (0.029)

0.994*** (0.043)

-0.894*** (0.088)

0.604* (0.363)

0.481 (1.779)

2.307*** (0.357)

4.100*** (0.555)

0.571** (0.293)

0.359* (0.221)

-633.096

Germany 0.133

(0.292) -0.606***

(0.089) 0.900*** (0.033)

1.056* (0.613)

-1.165 (1.581)

2.424*** (0.198)

3.854*** (0.290)

0.973*** (0.020)

0.971*** (0.023)

-634.158

Japan -0.975***

(0.389) -0.673***

(0.192) 0.844*** (0.124)

-0.232 (0.424)

-2.706** (1.364)

2.335*** (0.308)

3.813 (0.238)

0.951 (0.036)

0.984 (0.014)

-656.062

U.K. -0.160 (0.168)

0.079 (0.246)

-0.370* (0.230)

0.171 (0.520)

1.895*** (0.897)

2.026*** (0.172)

3.460*** (0.197)

0.994*** (0.197)

0.996*** (0.006)

-615.810

Emerging Countries

South Korea 0.017

(0.025) 0.877*** (0.100)

-0.564*** (0.250)

-1.193 (2.026)

1.469 (2.938)

0.635*** (0.068)

8.600 (1.270)

0.981 (0.013)

0.884 (0.070)

-355.370

Taiwan -0.013 (0.017)

0.793*** (0.096)

-0.701*** (0.110)

0.256 (0.470)

4.640* (2.698)

0.652*** (0.063)

2.711*** (0.365)

0.881*** (0.045)

0.553*** (0.140)

-367.134

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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

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Explanations of Our Empirical Results

The composite model with non-constant loadings on two forecasting techniques outperforms the setting with constant loadings

32


The high (low) volatility state corresponds to the forecasting technique of the economic model (time-series approach)

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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

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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

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However, during the volatile period, the fundamental variables are insignificant for the case of South Korea

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High/Low Volatility

Table 2 Measurement of Volatility at High Volatility State Relative to Low Volatility State for the Hybrid Model with Time-varying weights Mature Countries Emerging Countries

France Germany Japan U.K. South Korea Taiwan (σ2/σ1) 1.777 1.590 1.6191 1.708 13.543 4.158

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-15

-10

-5

0

5

10

15

1980/1 1982/1 1984/1 1986/1 1988/1 1990/1 1992/1 1994/1 1996/1 1998/1 2000/1

-20

-10

0

10

20

30

40

50

1980/1 1982/1 1984/1 1986/1 1988/1 1990/1 1992/1 1994/1 1996/1 1998/1 2000/1

0

0.25

0.5

0.75

1

1980/1 1982/1 1984/1 1986/1 1988/1 1990/1 1992/1 1994/1 1996/1 1998/1 2000/1

0

0.25

0.5

0.75

1

1980/1 1982/1 1984/1 1986/1 1988/1 1990/1 1992/1 1994/1 1996/1 1998/1 2000/1

(a) France (b) South Korea Unusual Regime Crisis Regime

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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

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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.

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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.

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(a) Mean Square Error (MSE) Highbred Model Hybrid Model

ARMA (1, 1) Model

Economic Model



France 9.504

[-25.319%] 8.129

[-7.191%] 10.965

[-44.581%] 8.062*

[-6.309%]

Germany 6.874

[14.519%] 8.099

[-0.712%] 7.992

[0.619%] 6.565*

[18.365%]

Japan 19.927

[-84.178 %] 11.107

[-2.664%] 19.325

[-78.620%] 10.746*

[0.671%]

U.K. 4.942

[-19.428%] 4.490

[-8.523%] 6.120

[-47.912 %] 3.656*


South Korea 4.491

[-48.958%] 3.257*

[-8.037%] 4.743

[-57.320] 3.294

[-9.272%]

Taiwan 0.735

[-3.521%] 0.739

[-4.101%] 0.970

[-36.532%] 0.725*

[-2.070%]

42

(b) Mean Absolute Error (MAE) Highbred Model Hybrid Model

ARMA (1, 1) Model

Economic Model



France 2.573

[-16.004%] 2.421

[-9.173 %] 2.961

[-33.504%] 2.372*

[-6.939%]

Germany 2.201

[5.184%] 2.310

[0.493%] 2.512

[-8.199%] 2.200*

[5.220%]

Japan 3.639

[-32.458%] 2.679*

[2.501%]] 3.509

[-27.721%] 2.741

[2.061%]

UK 1.792

[-4.116%] 1.736

[-0.861%] 2.088

[-21.269%] 1.640*


South Korea 1.661

[-19.805%] 1.486*

[-5.886%] 1.869

[-34.801%] 1.546

[-11.499%]

Taiwan 0.646

[-4.531%] 0.664

[-7.442] 0.869

[-40.581%] 0.641*

[-3.733%]

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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.

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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

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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 】

Documents

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