On the Exact Discretization of a Continuous Time AR(1) Model driven by either Long Memory or Antipersistent Innovations: A Fractional Algebra Approach

Theodore Simos

doi:10.1515/1941-1928.1145

Published by De Gruyter November 14, 2012

On the Exact Discretization of a Continuous Time AR(1) Model driven by either Long Memory or Antipersistent Innovations: A Fractional Algebra Approach

Theodore Simos

From the journal Journal of Time Series Econometrics

https://doi.org/10.1515/1941-1928.1145

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Abstract

Exact discretization formulae are established for a first-order stochastic differential equation driven by a fractional noise of either long memory or antipersistent type. We assume that the underlying process is sampled at non-unit equispaced observational intervals. Using fractional algebra techniques the exact discretization formulae are derived in terms of confluent hypergeometric and incomplete gamma functions which admit infinite order series expansions.

Keywords: stochastic differential equations; fractional noise; exact discretization formulae; special functions

Published Online: 2012-11-14

On the Exact Discretization of a Continuous Time AR(1) Model driven by either Long Memory or Antipersistent Innovations: A Fractional Algebra Approach

Abstract

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