Testing for a Shift in Mean Without Having to Estimate Serial-Correlation Parameters

Abstract

Tests for detecting a shift in the mean of a univariate time series that do not require estimation of serial-correlation parameters are proposed. The statistics are valid whether the errors are stationary or have a unit root. The date of the shift may be known or unknown. The statistics are based on a simple transformation of the data and are functions of partial sums of the data. These so-called partial sum statistics are shown to be asymptotically invariant to serial-correlation parameters. The statistics are shown to have good size and power properties asymptotically and in finite samples.

KEY WORDS:

• HACE
• Partial sum
• Structural change
• Unit root
• Wald test