price series is equal to {Pt*=exp(rt*) Pt-1*: t=2,3,...,T}, where rt* is the redrawn return series. The initial value of the bootstrapped price series is set equal to the initial original price: P1*=P1. By construction the returns in the bootstrapped data series are iid. There is no dependence in the data anymore that can be exploited by technical trading rules. Only by chance a trading rule will generate good forecasting results. Hence under the null of a random walk with a drift we test whether the results of the technical trading rules in the original data series are just the result of pure luck.

Autoregressive process

The second null model we test upon is an AR model:
rt=α + φ16 rt-16 + εt, |φ16|<1,     (11)
where rt is the return on day t and εt is iid10. The coefficients α, φ16 and the residuals εt are estimated with ordinary least squares. The estimated residuals are redrawn with replacement and the bootstrapped return series are generated using the estimated coefficients and residuals:
rt*=α + φ16 rt-16* + εt*,
for t=18,...,T and where εt* is the redrawn estimated residual at day t and where rt* is the bootstrapped return at day t. For t=2,..,17 we set rt*=rt. The bootstrapped price series is now equal to {Pt*=exp(rt*) Pt-1*: t=2,...,T} and P1*=P1. The autoregressive model tests whether the results of the technical trading strategies can be explained by the high order autocorrelation in the data. OLS estimation with White's (1980) heteroskedasticity-consistent standard errors gives the following results with t-ratios within parenthesis:
α φ16
-0.000235 0.110402
(-0.68) (4.00)
The coefficient of the lagged return is significantly different from zero. This shows that the LIFFE series contains high order autocorrelation.

Exponential GARCH process

The third null model we test upon is the exponential GARCH model as given by (2.10). The model is estimated with maximum likelihood. The estimated coefficients and standardized residuals are used to generate new bootstrapped price series. The estimated
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