Another explanation for the bias observed in the filter rule test

Substantial bias in profits is observed when Alexander’s filter rule is applied to the piecewise linear function formed by the linear interpolation of a past daily (weekly or monthly) stock price sequence. The only explanation for this phenomenon reported up to now is the possible discontinuity of the original price path. This paper demonstrates that the autocorrelation generated by the linear interpolation procedure causes this phenomenon even if the original path is a realization of the Brownian motion. It is also shown that the bias for the TOPIX index in the Tokyo Stock Exchange is substantially explained in the present theoretical framework.