Page 47 - Contributed Paper Session (CPS) - Volume 8

CPS2176 Chiraz KARAMTI et al.
on the basis of root mean square error (RMSE) and absolute mean error (AME)
are also reported in Table 3. When looking at the two sub periods depicted in
Table 3, we can see that on average the forecast error of the three EGARCH
models decreased significantly in higher scales (long-run) compared to lower
scales (short-run). Specially, after Brexit, it is obvious that the uncertainty is
higher, so a longer-term forecast seems more reliable (d6 and d7). It follows
that a forecast at a period of high volatility is better in the long run and that
the accuracy of the euro/dollar exchange rate forecast depends on the
frequency of the data.

Tableau 1. The AIC, RMSE and MAE comparisons for different EGARCH
models

Full sample Before Brexit After Brexit
α γ β α γ β α γ β
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0.0017 0.0212 0.3253 -0.0048 0.0408 0.0203 -0.0422 0.0110 0.0165
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0.0136 0.0235 0.2020 0.0818 -0.0047 0.0645 -0.0115 0.0360 0.1916
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0.1719 0.0587 0.9264 0.0401 0.0140 0.0924 -0.0007 0.0121 0.0613
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0.2768 -0.0001 0.9834 0.2798 -0.0004 0.9807 0.2758 0.0001 0.9741
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0.2743 0.0011 0.9783 0.2936 -0.0012 0.9737 0.2686 0.0018 0.9696
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0.2580 0.0004 0.9596 0.2058 0.0005 0.9656 0.2721 8.15E-05 0.9582
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0.1156 -0.0061 0.3188 0.1937 -0.0004 0.9721 0.1866 -0.00003 0.9625
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5. Discussion and Conclusion
This paper proposes the application of the Wavelet-EGARCH technique for
the modelling of euro/dollar exchange rate series. The MODWT-EGARCH
models are obtained by combining two methods, an EGARCH model and
discrete wavelet transforms. The main objective is to verify if the frequency of
the data would have an impact on the reliability of the forecasts. Accordingly,
the series was decomposed at 7 decomposition levels (10mn until one day).
The sum of the effective details and the approximation component were used
as inputs to the EGARCH model. The performance of the proposed MODWT-
EGARCH models was compared to forecasting using regular criteria.
Comparison of the results indicated that the MODWT-EGARCH model was
substantially more accurate in higher scales, i.e. the medium and long-terms.
This study shows that wavelet transform technique, joined with GARCH
models, are particularly useful in forecasting foreign exchange volatility in
periods of either low or high volatility. Indeed, forecasts seem less reliable in
periods characterized by greater uncertainty, in our case due to the Brexit
announcement. Thus, over a period of high volatility, a long-term scale is
found to be the most effective in yielding an accurate forecast, whereas before
Brexit, the best forecast is given by medium-term wavelets. In all cases a short-
term forecast has proved unreliable.
Finally, the frequency component affects the predictive performance of
various models at both short horizons and long horizons. The volatility
dynamics are not uniform across scales. Accordingly, as might have been
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