Testing financial time series for autocorrelation: Robust Tests

Two modified Portmanteau statistics are studied under dependence assumptions common in financial applications which can be used for testing that heteroskedastic time series are serially uncorrelated without assuming independence or Normality. Their asymptotic distribution is found to be null and their small sample properties are examined via Monte Carlo. The power of the tests is studied under the MA and GARCH-in-mean alternatives. The tests exhibit an appropriate empirical size and are seen to be more powerful than a robust Box-Pierce to the selected alternatives. Real data on daily stock returns and exchange rates is used to illustrate the tests.

TESTING CHAOS OF TIME SERIES: PORTMANTEAU STATISTICS UNDER AN ORDER TRANSFORMATION

This paper studies several portmanteau test statistics with a nonparametric order transformation for distinguishing independent and identically distributed (i.i.d.) random processes from noisy chaotic time series. These portmanteau test statistics are asymptotically distributed as a chi-square random variable under the null hypothesis of i.i.d. Gaussian series. In this Letter, we show that the asymptotic distributions of these portmanteau test statistics on the transformed series are still chi-square under the null hypothesis. The simulations indicate that direct use of these portmanteau test statistics yields low power in identifying chaos. However, with the proposed order transformation, the simulations show that these test statistics are still effective for identifying noisy low dimensional chaos in some cases.