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Intertemporal stationarity tests of the variance‐covariance matrix of monthly returns on seven international equity indices are conducted over the most recent period. Pairwise covariances are then decomposed into their component statistics for further examination of the source(s) of stationarity or nonstationarity. Historical analysis reveals that pairwise covariances were invariably highly nonstationary over forecast intervals that varied in length between one month and five years. Reliance on historical covariances to estimate future covariances over a hold‐out sample produced suboptimal results in comparison to an alternative naive forecasting model. These findings were robust in that they were invariant to whether nominal or real returns were used. Evidence on the intertemporal stationarity of the vector of mean returns is also provided.

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