Zaffaroni, Paolo (2000) Stationarity and memory of ARCH models. EM, 383. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case of hyperbolically decaying coefficients are included, such as the autoregressive coefficients of ARFIMA(p,d,q), once the non-negativity constraints are imposed. Second, we show the necessary and sufficient conditions for covariance stationarity of ARCH(8), both for the levels and the squares. These prove to be much stronger than the strict stationarity conditions. The covariance stationarity condition for the levels rules out long memory in the squares.
|Item Type:||Monograph (Discussion Paper)|
|Additional Information:||© 2000 Paolo Zaffaroni|
|Uncontrolled Keywords:||ARCH(); GARCH(p,q); nonlinear moving average representation; strict and weak stationarity; memory|
|Library of Congress subject classification:||H Social Sciences > HB Economic Theory|
|Journal of Economic Literature Classification System:||C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models|
|Sets:||Collections > Economists Online
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
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