the total number of observations. However the variance of µk-µ is equal to

V(µk-µ) =V(µk)+V(µ)-2Cov(µk, µ)
 
=V(
1
Nk
 
∑
t ∈ k
rt) + V(
1
N
N
∑
t=1
rt) -2 Cov(
1
Nk
 
∑
t ∈ k
rt,
1
N
N
∑
t=1
rt)
 
=
1
Nk
σ2 +
1
N
σ2 -2
1
Nk
1
N
Nk σ2
 
=
1
Nk
σ2 -
1
N
σ2.
    (9)
Thus the expression in the denominator of (2.8) is not correct, because the covariance term in (2.9) is unequal to zero. This is because the set of buy or sell days is a subset of the total set of observations. However the adjustment would have little effect on the results of Brock et al. (1992), because as we have shown the variance of their test statistic is actually smaller than the one they used and therefore their tests are too conservative.

The best strategy applied to the full sample has a significantly positive mean daily excess return of 0.039%, 10.38% yearly, which is considerably large. The mean daily excess return of the CSCE series during buy (sell) days is equal to 0.056% (-0.101%), 15.2% (-22.5%) yearly. The mean daily sell return is significantly negative at a 5% significance level using a one tailed test, while the mean daily buy return is not significantly positive. The mean buy-sell difference is significantly positive at a 5% significance level and equal to 0.158% (48.9% yearly). The four other strategies yield similar results. The mean daily excess return is significantly positive in all cases at a 10% significance level using a one tailed t-test. The mean return of the CSCE series during buy days is positive, but not significant, and the mean return during sell days is significantly negative. For all five strategies the mean buy-sell differences are significantly positive at a 5% significance level using a one sided test. The sixth and seventh column show that for all five listed strategies more than 50% of the buy and sell trades have a strictly positive excess return and that these trades consist of more than 50% of the total number of buy and sell days. The results above show that the best five technical trading strategies applied to the CSCE series in the period 83:1-97:6 have an economically as well as a statistically significant forecasting power.

For the three subperiods similar results are found, but now the best five strategies found have a higher mean daily excess return. The best strategy has a significantly positive mean yearly excess return of about 20%. Thus when looking at subperiods, strategies can be found that perform better than when applied to the full period.

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