Asymptotic properties of QMLE for seasonal threshold GARCH model with periodic coefficients

Abdelouahab Bibi ()
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Abdelouahab Bibi: University Larbi Ben M’hidi

Statistical Methods & Applications, 2021, vol. 30, issue 2, No 5, 477-514

Abstract: Abstract Periodic models for volatility process constitute an alternative representation for the seasonal patterns observed in data exhibits a strong seasonal volatility driven by periodic coefficients of high and law variation. Moreover, these varying-parameters can arise also when seasonality is incorporated into the theory of economic decision-making So, in this paper, we propose an extension of time-invariant coefficients threshold GARCH (TGARCH) processes to periodically time-varying coefficients (PTGARCH) one. This parametrization allows us to describe the dynamic volatility through a TGARCH model within each regime (or season), and therefore a new stylized fact that characterize the volatility by seasonal patterns. Hence, theoretical probabilistic properties of this model are derived. The necessary and sufficient conditions which ensure the strict stationarity and ergodicity (in periodic sense) solution of PTGARCH are given. We extend the standard results of the popular quasi-maximum likelihood estimator (QMLE) for estimating the unknown parameters in model. More precisely, the strong consistency and the asymptotic normality of QMLE are studied for the cases when the innovation process is an i.i.d (Strong case) or is not (Semi-strong case). A Monte Carlo study is further conducted to examine the finite sample properties of the QMLE. The simulation results reveal that the QMLE is approximately unbiased and consistent for modest sample sizes when the stationarity conditions hold. Empirical work on the exchange rates of the Algerian Dinar against the single European currency (Euro) shows that our approach also outperforms and fits the data well.

Keywords: Periodic threshold GARCH model; Strict periodic stationarity; Strong consistency; Asymptotic normality (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10260-020-00531-9

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