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Working paper

Укорочение набора весов, соответствующих квадратическому спектральному окну, при оценке ковариационной матрицы

Панов Е. В., Шведов А. С.
Let, X1 , X 2 , ..., XT , ... be a multivariate random process in discrete time. For its asymptotic covariance matrix one can use estimators of the form ˆΣ =Cˆ (0) + wk (Cˆ (k) +Cˆʹ(k)) k =1 T −1 Σ , where Cˆ (k) is the sample autocovariance matrix of order k. Usually such estimator is efficient when weights wk correspond to a quadratic spectral window. However the drawback of such approach is the large number of summands used in the formula above. The estimator offered in this paper has much less non-zero weights, but its weights converge to quadratic spectral ones when the sample size grows. This estimator is also guaranteed to always be positive semi-definite.