论文信息 - Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

In this article we shall consider a class of strongly T-periodically correlated processes with values in a separable complex Hilbert space H. The periodograms of these processes and their statistical properties were previously studied by the authors. In this paper we derive the asymptotic distribution of the periodogram, that appears to be a certain Wishart distribution on H^T.

Ali Zamani | Z. Shishebor | A. R. Soltani

[1] S. Resnick. A Probability Path , 1999 .

[2] Z. Shishebor,et al. On Infinite Dimensional Discrete Time Periodically Correlated Processes , 2007 .

[3] E. J. Hannan,et al. Multiple time series , 1970 .

[4] D. Pollard. Convergence of stochastic processes , 1984 .

[5] Sophie Dabo-Niang,et al. Functional and operatorial statistics , 2008 .

[6] Richard A. Davis,et al. Time Series: Theory and Methods , 2013 .

[7] N. N. Vakhania,et al. Random Vectors with Values in Complex Hilbert Spaces , 1997 .

[8] Harry L. Hurd,et al. Periodically correlated random sequences : spectral theory and practice , 2007 .

[9] Ali Zamani,et al. Inference on periodograms of infinite dimensional discrete time periodically correlated processes , 2010, J. Multivar. Anal..

[10] A. Soltani,et al. Periodically correlated autoregressive Hilbertian processes , 2011 .

[11] K. Mukherjee,et al. Central limit theorems revisited , 2000 .

[12] M. Azimmohseni,et al. Periodograms asymptotic distributions in periodically correlated processes and multivariate stationary processes: An alternative approach☆ , 2007 .