Tests for Randomness in Multiple Financial Time Series

There exist tests for randomness in multiple time series but the exact distributions of these test statistics are unknown. The asymptotic distributions do not provide adequate approximation to the exact ones in small samples. In this paper there are suggested modified test statistics asymptotically equivalent to their original counterparts. The adequacy of the approximations is examined by simulation experimens. The modified statistics are obtained using the asymptotic means and covariances. These moments involve nuisance parameters which are replaced by their sample counterparts giving consistent estimates of the parameters. It is suggested to use these statistics for testing the hypotheses based on randomness of multiple time series e.g. the weak form of financial market efficiency at small and new financial markets. Results of such a test are reported using the stock prices data of Budapest Exchange.