Formulae for the covariance structure of the sampled autocovariances from series generated by general autoregressive integrated moving average processes of order \((p,d,q)\), \(d=0\) or 1. (English) Zbl 0533.62084

Anderson, Oliver D.; de Gooijer, Jan G.

Sankhyā, Ser. B 45, 249-256 (1983).

Summary: We provide exact formulae for the variances and covariances of the sampled variances and autocovariances, given a time series realisation from any stationary or once integrated stationary mixed autoregressive moving average process generated by normal shocks, and indicate how these can then yield approximate first and second order moments for the associated sampled serial correlation behaviour.

MSC:

62M10

Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

covariance structure; sampled autocovariances; autoregressive integrated moving average processes; exact formulae; moments