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1. Volatility analysis with realized GARCH-Itô models

   https://doi.org/DOI: 10.1016/j.jeconom.2020.07.007  

   Song, Xinyu; Kim, Donggyu; Yuan, Huiling; Cui, Xiangyu; Lu, Zhiping; Zhou, Yong; Wang, Yazhen (August 2021, Journal of econometrics)

   Andersen, Torben; Chen, Xiaohong (Ed.)

   This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump–diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in the continuous instantaneous volatility process. The key feature of the proposed model is that the corresponding conditional daily integrated volatility adopts an autoregressive structure, where both integrated volatility and jump variation serve as innovations. We name it as the realized GARCH-Itô model. Given the autoregressive structure in the conditional daily integrated volatility, we propose a quasi-likelihood function for parameter estimation and establish its asymptotic properties. To improve the parameter estimation, we propose a joint quasi-likelihood function that is built on the marriage of daily integrated volatility estimated by high-frequency data and nonparametric volatility estimator obtained from option data. We conduct a simulation study to check the finite sample performance of the proposed methodologies and an empirical study with the S&P500 stock index and option data. 

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2. Dynamic Shrinkage Processes

   https://doi.org/10.1111/rssb.12325  

   Kowal, Daniel R; Matteson, David S; Ruppert, David (May 2019, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Summary We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods. 

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3. 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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4. Climate Risks and Stock Market Volatility over a Century in an Emerging Market Economy: The Case of South Africa

   https://doi.org/10.3390/cli12050068  

   Wu, Kejin; Karmakar, Sayar; Gupta, Rangan; Pierdzioch, Christian (May 2024, Climate)

   Because climate change broadcasts a large aggregate risk to the overall macroeconomy and the global financial system, we investigate how a temperature anomaly and/or its volatility affect the accuracy of forecasts of stock return volatility. To this end, we do not apply only the classical GARCH and GARCHX models, but rather we apply newly proposed model-free prediction methods, and use GARCH-NoVaS and GARCHX-NoVaS models to compute volatility predictions. These two models are based on a normalizing and variance-stabilizing transformation (NoVaS transformation) and are guided by a so-called model-free prediction principle. Applying the new models to data for South Africa, we find that climate-related information is helpful in forecasting stock return volatility. Moreover, the novel model-free prediction method can incorporate such exogenous information better than the classical GARCH approach, as revealed by the the squared prediction errors. More importantly, the forecast comparison test reveals that the advantage of applying exogenous information related to climate risks in prediction of the South African stock return volatility is significant over a century of monthly data (February 1910–February 2023). Our findings have important implications for academics, investors, and policymakers. 

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5. Stochastic Approximation for Multi-period Simulation Optimization with Streaming Input Data

   https://doi.org/10.1145/3617595  

   He, Linyun; Shanbhag, Uday V; Song, Eunhye (April 2024, ACM Transactions on Modeling and Computer Simulation)

   We consider a continuous-valued simulation optimization (SO) problem, where a simulator is built to optimize an expected performance measure of a real-world system while parameters of the simulator are estimated from streaming data collected periodically from the system. At each period, a new batch of data is combined with the cumulative data and the parameters are re-estimated with higher precision. The system requires the decision variable to be selected in all periods. Therefore, it is sensible for the decision-maker to update the decision variable at each period by solving a more precise SO problem with the updated parameter estimate to reduce the performance loss with respect to the target system. We define this decision-making process as the multi-period SO problem and introduce a multi-period stochastic approximation (SA) framework that generates a sequence of solutions. Two algorithms are proposed: Re-start SA (ReSA) reinitializes the stepsize sequence in each period, whereas Warm-start SA (WaSA) carefully tunes the stepsizes, taking both fewer and shorter gradient-descent steps in later periods as parameter estimates become increasingly more precise. We show that under suitable strong convexity and regularity conditions,ReSAandWaSAachieve the best possible convergence rate in expected sub-optimality either when an unbiased or a simultaneous perturbation gradient estimator is employed, whileWaSAaccrues significantly lower computational cost as the number of periods increases. In addition, we present theregularizedReSA, which obviates the need to know the strong convexity constant and achieves the same convergence rate at the expense of additional computation. 

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