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A Note on Non‐Negative Arma Processes

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  • Henghsiu Tsai
  • K. S. Chan

Abstract

. Recently, there has been much research on developing models suitable for analysing the volatility of a discrete‐time process. Since the volatility process, like many others, is necessarily non‐negative, there is a need to construct models for stationary processes which are non‐negative with probability one. Such models can be obtained by driving autoregressive moving average (ARMA) processes with non‐negative kernel by non‐negative white noise. This raises the problem of finding simple conditions under which an ARMA process with given coefficients has a non‐negative kernel. In this article, we derive a necessary and sufficient condition. This condition is in terms of the generating function of the ARMA kernel which has a simple form. Moreover, we derive some readily verifiable necessary and sufficient conditions for some ARMA processes to be non‐negative almost surely.

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  • Henghsiu Tsai & K. S. Chan, 2007. "A Note on Non‐Negative Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 350-360, May.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:350-360
    DOI: 10.1111/j.1467-9892.2006.00513.x
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    1. Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, vol. 24(3), pages 823-828, June.
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    2. Site Wang & Harsha Gangammanavar & Sandra Ekşioğlu & Scott J. Mason, 2020. "Statistical estimation of operating reserve requirements using rolling horizon stochastic optimization," Annals of Operations Research, Springer, vol. 292(1), pages 371-397, September.
    3. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    4. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 838-862, June.

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