On the Transmission of Memory in GARCH‐In‐Mean Models

15 Pages Posted: 28 Jul 2015

See all articles by Christian Conrad

Christian Conrad

Heidelberg University - Alfred Weber Institute for Economics; ETH Zürich - KOF Swiss Economic Institute

Menelaos Karanasos

Brunel University London - Economics and Finance

Date Written: September 2015

Abstract

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.

Keywords: Conditional heteroscedasticity, GARCH‐in‐mean, persistence, unit root tests

Suggested Citation

Conrad, Christian and Karanasos, Menelaos, On the Transmission of Memory in GARCH‐In‐Mean Models (September 2015). Journal of Time Series Analysis, Vol. 36, Issue 5, pp. 706-720, 2015, Available at SSRN: https://ssrn.com/abstract=2636574 or http://dx.doi.org/10.1111/jtsa.12119

Christian Conrad (Contact Author)

Heidelberg University - Alfred Weber Institute for Economics ( email )

Grabengasse 14
Heidelberg, D-69117
Germany
+49 (06)221 543173 (Phone)

HOME PAGE: http://www.uni-heidelberg.de/conrad

ETH Zürich - KOF Swiss Economic Institute ( email )

Zurich
Switzerland

Menelaos Karanasos

Brunel University London - Economics and Finance ( email )

Uxbridge UB8 3PH
United Kingdom

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