INVERSE AUTOCOVARIANCES AND A MEASURE OF LINEAR DETERMINISM FOR A STATIONARY PROCESS

Francesco Battaglia

Journal of Time Series Analysis, 1983, vol. 4, issue 2, 79-87

Abstract: Abstract. The inverse autocorrelations and autocovariances of a stationary stochastic process are generally used in the identification of ARMA models and linear systems, but they are also useful for studying linear relations inside the process as a whole. Using inverse autocovariances, for any stationary process an ‘inverse process’ may be defined which may be considered a minimum variance linear filter, and turns out to be the best linear two‐sided interpolator for one unknown value. Basing on these results an index of linear determinism is introduced to measure to what degree a stationary process satisfies a linear deterministic constraint. The behaviour of the index for ARMA processes is finally examined.

Date: 1983
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