second moments (volatility clustering) and in section 2.2.3 we showed that our data series also exhibit some autocorrelation. Therefore we further explore the statistical significance found in the first subperiod by estimating for each trading rule an econometric time series model which incorporates volatility clustering, autoregressive variables and a dummy for buy (sell) days in the regression function. We then determine the percentage of cases for which the dummy coefficients are significant, to check whether the trading rules as a group show signs of forecasting power.
We estimated some econometric time series models on the daily LIFFE cocoa return series for the period 1983:1-1987:12 and we find that the following exponential GARCH model developed by Nelson (1991)8 fits the data best9:
|
|
| rt |
=α + φ16 rt-16 + εt |
| εt |
=ηt ht; ηt iid N(0,1) |
| ln(ht) |
=α0+g(ηt-1)+β1 ln(ht-1) |
| g(ηt) |
|
|
(10) |
This model allows that future volatility depends differently on the sign of the current return. The coefficient θ measures the leverage effect. If θ is negative (positive), then a negative (positive) return is followed by larger volatility than a positive (negative) return. Table 2.10 shows the estimation results. The coefficient θ is significantly positive. This indicates that there is a positive correlation between return and volatility. Note that this is in contrast with the results found on stock markets and exchange rates where a negative correlation between return and volatility is found, see for example Nelson (1991). The estimation of γ is also significantly positive and this shows that there is volatility clustering in the data. The (partial) autocorrelation function of the (squared) standardized residuals shows no sign of dependence in the (squared) standardized residuals. Hence we conclude that this model fits the data well.
To explore the significance of the trading rules after correction for dependence the following regression function in the exponential GARCH model is estimated:
rt=α + δm Dm,t + φ16 rt-16 + εt,
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