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1. Testing for parameter change epochs in GARCH time series

   https://doi.org/10.1093/ectj/utad006  

   Richter, Stefan; Wang, Weining; Wu, Wei Biao (February 2023, The Econometrics Journal)

   Summary We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against the alternative that there is an ‘abnormal’ period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process. Simulations in the Appendix show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e., the Bitcoin returns. 

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2. GARCH quasi-likelihood ratios for SV model and the diffusion limit

   https://doi.org/DOI:10.1016/j.spl.2020.108817  

   Song, Xinyu; Wang, Yazhen (June 2020, Statistics probability letters)

   Xiao, Yimin; Sangalli, Laura (Ed.)

   There is a widely known intriguing phenomenon that discrete-time GARCH and stochastic volatility (SV) models share the same continuous-time diffusion model as their weak convergence limit, but statistically, the GARCH model is not asymptotically equivalent to the SV or diffusion model. This paper investigates GARCH-type quasi-likelihood ratios for the SV and diffusion models whose own likelihoods are analytically intractable. We show that the two quasi-likelihood ratios for the SV and diffusion models asymptotically have the same closed-form expression that is different from the limiting likelihood ratio of the GARCH model. 

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3. Profile estimation of generalized semiparametric varying-coefficient additive models for longitudinal data with within-subject correlations

   Sun, Yanqing and (October 2022, Springer)

   In this paper, we study several profile estimation methods for the generalized semiparametric varying-coefficient additive model for longitudinal data by utilizing the within-subject correlations. The model is flexible in allowing timevarying effects for some covariates and constant effects for others, and in having the option to choose different link functions which can used to analyze both discrete and continuous longitudinal responses.We investigated the profile generalized estimating equation (GEE) approaches and the profile quadratic inference function (QIF) approach. The profile estimations are assisted with the local linear smoothing technique to estimate the time-varying effects. Several approaches that incorporate the within-subject correlations are investigated including the quasi-likelihood (QL), the minimum generalized variance (MGV), the quadratic inference function and the weighted least squares (WLS). The proposed estimation procedures can accommodate flexible sampling schemes. These methods provide a unified approach that work well for discrete longitudinal responses as well as for continuous longitudinal responses. Finite sample performances of these methods are examined through Monto Carlo simulations under various correlation structures for both discrete and continuous longitudinal responses. The simulation results show efficiency improvement over the working independence approach by utilizing the within-subject correlations as well as comparative performances of different approaches. 

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4. A conditional density estimation partition model using logistic Gaussian processes

   https://doi.org/10.1093/biomet/asz064  

   Payne, R D; Guha, N; Ding, Y; Mallick, B K (December 2019, Biometrika)

   Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution. 

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5. A model-free approach to do long-term volatility forecasting and its variants

   https://doi.org/10.1186/s40854-023-00466-6  

   Wu, Kejin; Karmakar, Sayar (March 2023, Financial Innovation)

   Abstract Volatility forecasting is important in financial econometrics and is mainly based on the application of various GARCH-type models. However, it is difficult to choose a specific GARCH model that works uniformly well across datasets, and the traditional methods are unstable when dealing with highly volatile or short-sized datasets. The newly proposed normalizing and variance stabilizing (NoVaS) method is a more robust and accurate prediction technique that can help with such datasets. This model-free method was originally developed by taking advantage of an inverse transformation based on the frame of the ARCH model. In this study, we conduct extensive empirical and simulation analyses to investigate whether it provides higher-quality long-term volatility forecasting than standard GARCH models. Specifically, we found this advantage to be more prominent with short and volatile data. Next, we propose a variant of the NoVaS method that possesses a more complete form and generally outperforms the current state-of-the-art NoVaS method. The uniformly superior performance of NoVaS-type methods encourages their wide application in volatility forecasting. Our analyses also highlight the flexibility of the NoVaS idea that allows the exploration of other model structures to improve existing models or solve specific prediction problems. 

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