Rolling t-Statistics and Signal Stability
A single full-sample t-statistic can hide a signal that worked brilliantly for years and then stopped — tracking the t-statistic on a rolling window instead reveals whether an edge is stable or decaying.
A ten-year backtest with a full-sample t-statistic of 3.0 sounds reassuringly significant. But that single number is an average over the whole period — it can't tell you whether the strategy produced steady, modest outperformance every year, or made all its money in one spectacular early stretch and has been flat or losing ever since. Both histories can produce the same headline t-statistic.
Computing the t-statistic on a rolling window — say, the trailing two years, recalculated every month — turns one static number into a time series, exposing whether a signal's edge has been consistent or is fading, which the full-sample statistic alone can never show.
To build one, pick a window length long enough to contain a reasonable number of independent return observations (too short and the rolling statistic is just noise), compute the mean return and its standard error over that window, and slide it forward one period at a time. Plotting the resulting series of t-statistics against time turns an abstract single number into a visible trend line: a rolling t-statistic that steadily declines toward zero over the last few years of a ten-year backtest is a strong warning sign that the strategy's edge has decayed, even though the full-sample number still looks solid because it's propped up by the earlier, stronger years.
This diagnostic is standard practice before allocating capital to any systematic signal, precisely because full-sample statistics are backward-looking averages that reward strategies for having once worked, not for still working now.
Related concepts
Practice in interviews
Further reading
- Harvey and Liu, 'Backtesting'