The content of this study is the following. The analysis is based on daily data for the USDPLN bilateral exchange rate, and for the Standard and Poors 500 and WIG20 stock indices, covering period since the beginning of the year 2000 until mid-May 2013.

In previous research [Syczewska, 2009, 2010] we compared behavior of exchange rates models before and just after the global financial crisis. We applied the ARMA and GARCH models to volatility and returns of the series, and also ARMAX or GARCH with additional variables, namely stock indices of the corresponding countries (SP500 and WIG20), following example of Bauwens, Rime and Succarat (2008).

Earlier research, performed with use of data up to the end of April 2009, has shown that although the volatility and risk of exchange rates substantially increased during the crisis (hence had negative effect on accuracy of forecasts both of volatility and of exchange rate returns), but since the beginning of 2009 the time series in question seemed to stabilize slightly, thus giving hope for improvement of forecasting quality of the models.

Here we extend the data set until the latest available observations (from the stooq.pl), partly repeat the previous comparisons for longer data series, and extend the analysis to the question of possible cointegration between the USDPLN, SP500 and WIG20.

All three variables are nonstationary with stationary logarithmic returns. Their volatility (measured as in Brooks (2008)) seems to decrease with time, as shown by means and standard deviations for subsamples.

The Johansen test statistic for the whole range of data clearly rejects cointegration of the variables. Hence we estimated an ADL(2) model, and compute a tentative long-run equilibrium equation based on its parameter estimates.

We check whether this linear combination is stationary. For the ADF test we use exact critical values for our sample size (over 3000 observations),  according to MacKinnon (2010) response surface equation. The ADF test shows that the null of non-stationarity has to be rejected (the computed ADF =  -2,87 is smaller than the 1% and 5% critical values).

At the same time, the Engle-Granger cointegration tests give ADF=-2.827 for error terms, while the appropriate critical value for our sample is -3,783 at 5% and -3,454 at 10%.

The Granger causality test for the whole sample does not reject the null of lack of causality for WIG20 and the USDPLN rate; clearly rejects the null for the pair of USDPLN and the SP500 index. This is in agreement with the Granger causality tests for subsample before the crisis. In contrast to that, for a sample covering period of crisis, the returns of the domestic stock index seem to influence the exchange rate.

In building the GARCH model for the USDPLN log returns we follow exactly the specification from previous study: GARCH(1,1) for conditional variance and AR(1) equation with log returns of the stock indices as additional variables. We estimate both models (with and without additional regressors) for the sample up to the end of April 2009 and compare the dynamic forecasts for the rest of sample.

As expected, the model with additional regressors performs slightly better: has lower values of the Akaike and Schwarz criteria, and RMSE and MSE decreased by 4%, and MAE by 8%. 

When the GARCH(1,1) is estimated for the whole sample, information criteria are lower for the version with additional variables (which prove to be significant).

To summarize: Behavior of the three series in question seems to stabilize with time, in comparison to the crisis year 2007-8;

- for longer data series the quality of bilateral exchange rate returns models improves due to use of corresponding pair of stock indices as additional variables;

- Cointegration for the three original closing values series is rejected for the whole sample by the Johansen and the Engle-Granger test, although the linear combination for equilibrium values, based on the ADL(2) model for the three variables seems to be stationary.

REFERENCES: 

Bauwens, L., Rime, D., Succarat, G. (2008) "Exchange Rate Volatility and the Mixture of Distribution Hypothesis", [in:] Bauwens, L., Pohlmeier, W., Veredas, D. (2008) "High Frequency Financial Econometrics. Recent Developments", Physica-Verlag A Springer Company, Heidelberg. 

 Brooks, Ch. (2008), "Introductory Econometrics for Finance", 2nd ed., Cambridge University Press, New York. 

Engle, R.F., Granger, C.W.J. (1987), "Cointegration and error correction: representation, estimation and testing", Econometrica, Vol. 55. 

Granger, C.W.J. (1980), "Testing for causality: A personal viewpoint", Journal of Dynamic Economic and Control, Vol. 2. 

MacKinnon, J.G. (2010), "Critical values for cointegration tests", Queen's Economic Department Working Paper No. 1227, http://ideas.repec.org/p/qed/wpaper/1227.html. 

Syczewska, E.M. (2009) "Changes of exchange rate behavior during and after crisis", Metody Ilościowe w Badaniach Ekonomicznych, X, Analiza rynków finansowych. 

Syczewska, E.M. (2010), "Increase of exchange rate risk during current crisis", Roczniki Kolegium Analiz Ekonomicznych, Warsaw School of Economics. 

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