Noising the GARCH volatility: A random coefficient GARCH model

Aknouche, Abdelhakim and Almohaimeed, Bader and Dimitrakopoulos, Stefanos (2024): Noising the GARCH volatility: A random coefficient GARCH model. Forthcoming in: Journal of Time Series Analysis

Abstract

This paper proposes a noisy GARCH model with two volatility sequences (an unobserved and an observed/predictive one) and a stochastic time-varying conditional kurtosis. The unobserved volatility equation, equipped with random coefficients, is a linear function of the past squared observations and of the past predictive volatility. The predictive volatility is the conditional mean of the unobserved volatility, thus following the standard GARCH specification, where its coefficients are equal to the means of the random coefficients. The means and the variances of the random coefficients as well as the unobserved volatilities are estimated using a three-stage procedure. First, we estimate the means of the random coefficients using the Gaussian quasi-maximum likelihood estimator (QMLE), then the variances of the random coefficients, using a weighted least squares estimator (WLSE), and finally the latent volatilities through a volatility filtering process under the assumption that the random parameters follow an Inverse Gaussian distribution, with the innovation being normally distributed. Hence, the conditional distribution of the model is the Normal Inverse Gaussian (NIG), which entails a closed form expression for the posterior mean of the unobserved volatility and of the random coefficients. Consistency and asymptotic normality of the QMLE and WLSE are established under quite tractable assumptions. The proposed methodology is illustrated with various simulated and real examples. It is shown that the filtered volatility can improve both in-sample and out-of-sample forecasts of the predictive volatility, even when the future observations are unknown and are replaced by their predictions.

• Item Type: MPRA Paper
• Language: English
• Keywords: Noised volatility GARCH, Random coefficient GARCH, Markov switching GARCH, QMLE, Weighted least squares, filtering volatility, time-varying conditional kurtosis.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

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