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Sur un test d'égalité des autocovariances de deux séries chronologiques
Author(s) -
Melard Guy,
Roy Roch
Publication year - 1984
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314816
Subject(s) - mathematics , autocovariance , estimator , test statistic , covariance matrix , statistics , null distribution , statistical hypothesis testing , mathematical analysis , fourier transform
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.