On the size and power of normalized autocorrelation coefficients

Tests based on normalized autocorrelation coefficients have been commonly used by applied researchers to examine the randomness of economic and financial time series. This paper investigates via Monte Carlo simulation the finite-sample properties of these tests for randomness, paying special attention to empirical sizes and power levels. Monte Carlo simulation results indicate that parametric autocorrelation coefficients suffer from severe size distortions, namely their empirical sizes are often too small in the case of nonnormal distributions. However, these size distortions are well corrected by nonparametric autocorrelation coefficient proposed previously. Moreover, the power levels of the nonparametric test are very close to those of the parametric tests in commonly used samples, suggesting that there is no noticeable loss from using this 'robust autocorrelation' test in the area of testing for the randomness of a time series. On the whole, results strongly favour the use of the nonparametric autocorrelation coefficient in empirical applications.