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On the Transmission of Memory in Garch-in-Mean Models

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  • Neil Kellard
  • Denise Osborn
  • Jerry Coakley
  • Christian Conrad
  • Menelaos Karanasos

Abstract

type="main" xml:id="jtsa12119-abs-0001"> In this article, we show that in times series models with in-mean and level effects, persistence will be transmitted from the conditional variance to the conditional mean and vice versa. Hence, by studying the conditional mean/variance independently, one will obtain a biased estimate of the true degree of persistence. For the specific example of an AR(1)-APARCH(1,1)-in-mean-level process, we derive the autocorrelation function, the impulse response function and the optimal predictor. Under reasonable assumptions, the AR(1)-APARCH(1,1)-in-mean-level process will be observationally equivalent to an autoregressive moving average (ARMA)(2,1) process with the largest autoregressive root being close to one. We illustrate the empirical relevance of our results with applications to S&P 500 return and US inflation data.

Suggested Citation

  • Neil Kellard & Denise Osborn & Jerry Coakley & Christian Conrad & Menelaos Karanasos, 2015. "On the Transmission of Memory in Garch-in-Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 706-720, September.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:5:p:706-720
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    File URL: http://hdl.handle.net/10.1111/jtsa.12119
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    2. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
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    5. Canepa, Alessandra, 2022. "Ination Dynamics and Time-Varying Persistence: The Importance of the Uncertainty Channel," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202211, University of Turin.

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