McCabe-Tremayne Test

TL;DR

Tests whether a time series has constant statistical properties (mean and variance) over time.
Works by splitting the series into consecutive segments, computing segment-wise means and variances, then summarizing those statistics.
If the segment-wise means and variances are stable, the series is considered stationary; systematic changes imply non-stationarity.

Definition

The McCabe-Tremayne test is a statistical test used to determine whether a time series is stationary or non-stationary.

Explanation

To perform the McCabe-Tremayne test, divide the time series into a chosen number of consecutive segments. For each segment, calculate the segment mean and segment variance. Then compute the mean and the variance of those segment means and the mean and variance of those segment variances. Comparing these aggregated values across segments indicates whether the time series’ mean and variance remain stable over time (stationary) or change over time (non-stationary).

Examples

Example 1

A time series has 100 data points. The series is divided into 10 consecutive time periods, each containing 10 data points. For each period, the mean is 10 and the variance is 5. The overall mean of the period means is 10 and the overall variance of the period variances is 5. This indicates the time series is stationary because the mean and variance do not change over time.

Example 2

A different time series has 100 data points and is again divided into 10 consecutive time periods of 10 data points each. The period means are 10 for the first 5 periods and increase to 15 for the last 5 periods. The period variances are 5 for the first 5 periods and increase to 10 for the last 5 periods. The overall mean of the period means is 12.5 and the overall variance of the period variances is 7.5. This indicates the time series is non-stationary because the mean and variance change over time.

Use cases

Determining whether a time series is stationary or non-stationary.

Time series
Stationarity
Mean
Variance