Abstract.
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.
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Yue, S., Wang, C. The null distribution of sample serial correlation coefficient. Stochastic Environmental Research and Risk Assessment 16, 77–100 (2002). https://doi.org/10.1007/s00477-001-0086-9
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DOI: https://doi.org/10.1007/s00477-001-0086-9