Quadratic random coefficient autoregression with linear-in-parameters volatility

Abdelhakim Aknouche ()

Statistical Inference for Stochastic Processes, 2015, vol. 18, issue 2, 99-125

Abstract: This paper proposes a class of generalized random coefficient autoregressions ( $$GRCA$$ G R C A ) in which the autoregressive coefficient is a linear regression of the innovation, so that the corresponding volatility is linear in parameters while having a quadratic expression. The proposed model allows a flexible representation, including level and volatility asymmetries, while being fairly simple to implement. We study the dynamic structure of the model and we propose a four-stage weighted least squares estimate ( $$4SWLSE$$ 4 S W L S E ) for which we establish consistency and asymptotic normality in both stationary and nonstationary cases. The proposed $$4SWLSE$$ 4 S W L S E , with a closed form, has the same asymptotic distribution as the quasi-maximum likelihood estimate under the same mild assumptions. Application to real data is given. Copyright Springer Science+Business Media Dordrecht 2015

Keywords: Generalized random coefficient autoregression; Quadratic $$ ARCH$$ A R C H; Four-stage weighted least squares; Consistency and asymptotic normality; Stationarity testing; Primary 62M10; Secondary 62M04 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11203-014-9108-3

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