Sur un test d'égalité des autocovariances de deux séries chronologiques

We propose a test for the equality of the autocovariance functions of two independent and stationary time series. The test statistic is a quadratic form in the vector of differences of the first J + 1 autocovariances. Its asymptotic distribution is derived under the null hypothesis, and the finite‐sample properties of the test, namely the bias and the power, are investigated by Monte Carlo methods. A by‐product of this study is a new estimator of the covariance between two sample autocovariances which provides a positive definite covariance matrix. We establish the convergence of this estimator in the L 1 norm.