Mixed difference integer-valued GARCH model for Z-valued time series

Aknouche, Abdelhakim and Francq, Christian and Goto, Yuichi (2026): Mixed difference integer-valued GARCH model for Z-valued time series.

Abstract

In this paper, we introduce flexible observation-driven Z-valued time series models constructed from mixtures of negative and non-negative components. Compared to models based on the standard Skellam distribution or on a difference of two integer-valued variables, our specification offers greater versatility. For example, it easily allows for skewness and bimodality. Furthermore, the observation of one component of the mixture makes interpretation and statistical analysis easier. We establish conditions for stationarity and mixing, and develop a mixed Poisson quasi-maximum likelihood estimator with proven asymptotic properties. A portmanteau test is proposed to diagnose residual serial dependence. The finite-sample performance of the methodology is assessed via simulation, and an empirical application on tick prices demonstrates its practical usefulness.

• Item Type: MPRA Paper
• Language: English
• Keywords: Discrete difference distribution; GARCH for tick-by-tick data, Mixed difference; Mixed Poisson QMLE; Random-weighting bootstrap; Z-valued time series.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; 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 > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

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