Rank-based statistics for testing the whiteness hypothesis of time series

ABSTRACT

There are several statistics in time series either based on sample autocorrelation or partial autocorrelation to test the whiteness hypothesis. In this manuscript we show that departure from normality may mislead the decision making based on the common statistics. The main objective of this article is using the ranks instead of the original data as a non-parametric approach. By an extensive simulation study, we compare the power and significance level of the common statistics and rank-based statistics under different non-normal distributions including heavy-tail and skew-normal distributions.

KEYWORDS:

• Autocorrelation
• Partial autocorrelation
• Simulation
• Skew-normal distribution
• Stable distribution
• Whiteness

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62G10