The null distribution of sample serial correlation coefficient

 The null distribution of the lag-k sample serial correlation coefficient (r _k , k=1,2,3) was investigated by Monte Carlo simulation. For a time series with normal, exponential, Pearson 3, EV1 (Gumbel), or generalized Pareto (GP) distribution type, the null distribution of its r _k can be approximated by the normal distribution with mean −1/(n−k) and variance 1/(n−1). But for a time series with the lognormal, EV2 or EV3 (Weibull) distribution type, the null distribution of r _k is skewed distributed. In such cases, a simulation technique is suggested to construct percentile confidence intervals at a given significance level.