
on Econometric Time Series 
By:  Yayi Yan; Jiti Gao; Bin Peng 
Abstract:  Moving average infinity (MA(∞)) processes play an important role in modeling time series data. While a strand of literature on time series analysis emphasizes the importance of modeling smooth changes over time and therefore is shifting its focus from parametric models to nonparametric ones, MA(∞) processes with constant parameters are often part of the fundamental data generating mechanism. Along this line of research, an intuitive question is how to allow the underlying data generating mechanism evolves over time. To better capture the dynamics, this paper considers a new class of timevarying vector moving average infinity (VMA(∞)) processes. Accordingly, we establish some new asymptotic properties, including the law of large numbers, the uniform convergence, the central limit theory, the bootstrap consistency, and the longrun covariance matrix estimation for the class of timevarying VMA(∞) processes. Finally, we demonstrate the empirical relevance and usefulness of the newly proposed model and estimation theory through extensive simulated and real data studies. 
Keywords:  multivariate time series, nonparametric kernel estimation, timevarying Beveridgeâ€“Nelson decomposition 
JEL:  C14 C32 E52 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:202122&r= 
By:  Peter Reinhard Hansen; Zhuo Huang; Chen Tong; Tianyi Wang 
Abstract:  We show that the Realized GARCH model yields closeform expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and riskneutral measures that can explain timevariation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the Realized GARCH model significantly outperforms conventional GARCH models. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.05302&r= 
By:  Alessandro Casini 
Abstract:  We show that the nonstandard limiting distribution of HAR test statistics under fixedb asymptotics is not pivotal (even after studentization) when the data are nonstationarity. It takes the form of a complicated function of Gaussian processes and depends on the integrated local longrun variance and on on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, existing fixedb inference methods based on stationarity are not theoretically valid in general. The nuisance parameters entering the fixedb limiting distribution can be consistently estimated under smallb asymptotics but only with nonparametric rate of convergence. Hence, We show that the error in rejection probability (ERP) is an order of magnitude larger than that under stationarity and is also larger than that of HAR tests based on HAC estimators under conventional asymptotics. These theoretical results reconcile with recent finitesample evidence in Casini (2021) and Casini, Deng and Perron (2021) who showing that fixedb HAR tests can perform poorly when the data are nonstationary. They can be conservative under the null hypothesis and have nonmonotonic power under the alternative hypothesis irrespective of how large the sample size is. 
Date:  2021–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2111.14590&r= 
By:  Salman Huseynov (Aarhus University, Department of Economics and Business Economics and CREATES) 
Abstract:  I provide a unified theoretical framework for long memory term structure models and show that the recent statespace approach suffers from a parameter identification problem. I propose a different framework to estimate long memory models in a statespace setup, which addresses the shortcomings of the existing approach. The proposed framework allows asymmetrically treating the physical and riskneutral dynamics, which simplifies estimation considerably and helps to conduct an extensive comparison with standard term structure models. Relying on a battery of tests, I find that standard term structure models perform just as well as the more complicated long memory models and produce plausible term premium estimates. 
Keywords:  Dynamic term structure models, Long memory, Affine model, Shadow rate model 
JEL:  C32 E43 G12 
Date:  2021–12–20 
URL:  http://d.repec.org/n?u=RePEc:aah:create:202115&r= 
By:  Chen Tong; Peter Reinhard Hansen; Zhuo Huang 
Abstract:  We introduce a new volatility model for option pricing that combines Markov switching with the Realized GARCH framework and leads to a novel pricing kernel with a regimespecific variance risk premium. An analytical approximation method based on an Edgeworth expansion of cumulative returns enables us to derive the pricing formula for European options in this setting. The Markov switching Realized GARCH model is easy to estimate because inferences about regimes can be deduced with realized volatility measures. In an empirical application with S&P 500 index options from 1990 to 2019, we find that investors' aversion to volatilityspecific risk is time varying. The proposed framework outperforms competing methods and reduces option pricing errors by 15% or more both insample as well as outofsample. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.05308&r= 
By:  Gael M. Martin; David T. Frazier; Christian P. Robert 
Abstract:  The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain `intractable' statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, highdimensional models, and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular  and more generally those interested in adopting a Bayesian approach to empirical work  distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways in which they can can be combined. 
Keywords:  Approximate Bayesian inference, intractable Bayesian problems, approximate Bayesian computation, Bayesian synthetic likelihood, variational Bayes, integrated nested Laplace approximation 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:msh:ebswps:202124&r= 