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Stationarity and Persistence in the GARCH(1,1) Model

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  • Nelson, Daniel B.
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    This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition of persistence. We also develop necessary and sufficient conditions for the finiteness of absolute moments of any (including fractional) order.

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    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 6 (1990)
    Issue (Month): 03 (September)
    Pages: 318-334

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    Handle: RePEc:cup:etheor:v:6:y:1990:i:03:p:318-334_00
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    Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK

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