A new approach for testing the randomness of heteroskedastic time series data

Proposed is a conditional approach for testing the randomness of heteroskedastic time series data as well as for checking the validity of this testing. It is shown that the ordinary serial correlation test works correctly neither for daily sequence of the TOPIX index in Tokyo Stock Exchange nor for heteroskedastic models, while our approach works well for them. It is also shown that our approach is enough powerful for detecting the departure from the randomness. An advantage of this approach is that it allows us to use any quantity for testing. Its application to the TOPIX index detected statistically significant long term correlation which causes both the mean reversion and the outperformance of the Alexander's filter rule over the buy-and-hold strategy.