DEFINITIONS AND REPRESENTATIONS OF MULTIVARIATE LONG-RANGE DEPENDENT TIME SERIES

Stefanos Kechagias and Vladas Pipiras

Journal of Time Series Analysis, 2015, vol. 36, issue 1, 1-25

Abstract: type="main" xml:id="jtsa12086-abs-0001"> The notion of multivariate long-range dependence is reexamined here from the perspectives of time and spectral domains. The role of the so-called phase parameters is clarified and stressed throughout. In particular, examples of causal (one-sided) representations of multivariate long-range dependent time series with general-phase parameters are constructed. A multivariate extension of the autoregressive fractionally integrated moving-average series is introduced with explicit formulas for its autocovariance function.

Date: 2015
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