
on Econometrics 
By:  Wang, Wenjie 
Abstract:  Under a framework with a small number of clusters but large numbers of observations per cluster for instrumental variable (IV) regression, we show that an unstudentized wild bootstrap test based on IV estimators such as the twostage least squares estimator is valid as long as the instruments are strong for at least one cluster. This is different from alternative methods proposed in the literature for inference with a small number of clusters, whose validity would require that the instruments be strong for all clusters. Moreover, for the leading case in empirical applications with a single instrument, the unstudentized wild bootstrap test generated by our procedure is fully robust to weak instrument in the sense that its limiting null rejection probability is no greater than the nominal level even if all clusters are ``weak". However, such robustness is not shared by its studentized version; the wild bootstrap test that is based on the ttest statistic can have serious size distortion in this case. Furthermore, in the general case with multiple instruments, we show that an unstudentized version of bootstrap AndersonRubin (AR) test is fully robust to weak instruments, and is superior with regard to both size and power properties to alternative asymptotic and bootstrap AR tests that employ clusterrobust variance estimators. By contrast, we �find that bootstrapping other weakinstrumentrobust tests such as the Lagrange multiplier test and the conditional quasilikelihood ratio test, no matter studentized or unstudentized, does not guarantee correct limiting null rejection probability when all clusters are ``weak". 
Keywords:  Weak Instrument, Wild Bootstrap, Clustered Data, Randomization Test 
JEL:  C12 C15 C26 
Date:  2021–02–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:106227&r=all 
By:  Magne Mogstad (University of Chicago  Department of Economics; NBER); Alexander Torgovitsky (University of Chicago  Department of Economics); Christopher R. Walters (University of California, Berkeley  Department of Economics) 
Abstract:  Marginal treatment effect methods are widely used for causal inference and policy evaluation with instrumental variables. However, they fundamentally rely on the wellknown monotonicity (thresholdcrossing) condition on treatment choice behavior. Recent research has shown that this condition cannot hold with multiple instruments unless treatment choice is effectively homogeneous. Based on these findings, we develop a new marginal treatment effect framework under a weaker, partial monotonicity condition. The partial monotonicity condition is implied by standard choice theory and allows for rich heterogeneity even in the presence of multiple instruments. The new framework can be viewed as having multiple different choice models for the same observed treatment variable, all of which must be consistent with the data and with each other. Using this framework, we develop a methodology for partial identification of clearly stated, policyrelevant target parameters while allowing for a wide variety of nonparametric shape restrictions and parametric functional form assumptions. We show how the methodology can be used to combine multiple instruments together to yield more informative empirical conclusions than one would obtain by using each instrument separately. The methodology provides a blueprint for extracting and aggregating information about treatment effects from multiple controlled or natural experiments while still allowing for rich heterogeneity in both treatment effects and choice behavior. 
JEL:  C01 C1 C26 C31 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:202099&r=all 
By:  Yoonseok Lee (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Donggyu Sul (Department of Economics, University of Texas at Dallas) 
Abstract:  This paper develops robust panel estimation in the form of trimmed mean group estimation for potentially heterogenous panel regression models. It trims outlying individuals of which the sample variances of regressors are either extremely small or large. The limiting distribution of the trimmed estimator can be obtained in a similar way to the standard mean group estimator, provided the random coefficients are conditionally homoskedastic. We consider two trimming methods. The first one is based on the order statistic of the sample variance of each regressor. The second one is based on the Mahalanobis depth of the sample variances of regressors. We apply them to the mean group estimation of the twoway fixed effects model with potentially heterogeneous slope parameters and to the common correlated effects regression, and we derive limiting distribution of each estimator. As an empirical illustration, we consider the effect of police on property crime rates using the U.S. statelevel panel data. 
Keywords:  Trimmed Mean Group Estimator, Robust Estimator, Heterogeneous Panel, Random Coefficient, TwoWay Fixed Effects, Common Correlated Effects 
JEL:  C23 C33 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:max:cprwps:237&r=all 
By:  Ruoyao Shi (Department of Economics, University of California Riverside) 
Abstract:  In a two step extremum estimation (M estimation) framework with a finite dimensional parameter of interest and a potentially infinite dimensional first step nuisance parameter, I propose an averaging estimator that combines a semiparametric estimator based on nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is the sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. I show that under mild conditions, the asymptotic lower bound of the truncated quadratic risk difference between the averaging estimator and the semiparametric estimator is strictly less than zero for a class of data generating processes (DGPs) that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero. 
Keywords:  two step M estimation, semiparametric model, averaging estimator, uniform dominance, asymptotic quadratic risk 
JEL:  C13 C14 C51 C52 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:ucr:wpaper:202105&r=all 
By:  Fischer, Manfred M.; Hauzenberger, Niko; Huber, Florian; Pfarrhofer, Michael 
Abstract:  Timevarying parameter (TVP) regressions commonly assume that timevariation in the coefficients is determined by a simple stochastic process such as a random walk. While such models are capable of capturing a wide range of dynamic patterns, the true nature of time variation might stem from other sources, or arise from different laws of motion. In this paper, we propose a flexible TVP VAR that assumes the TVPs to depend on a panel of partially latent covariates. The latent part of these covariates differ in their state dynamics and thus capture smoothly evolving or abruptly changing coefficients. To determine which of these covariates are important, and thus to decide on the appropriate state evolution, we introduce Bayesian shrinkage priors to perform model selection. As an empirical application, we forecast the US term structure of interest rates and show that our approach performs well relative to a set of competing models. We then show how the model can be used to explain structural breaks in coefficients related to the US yield curve. 
Keywords:  Bayesian shrinkage, interest rate forecasting, latent effect modifers, MCMC sampling, timevarying parameter regression 
Date:  2021–02–22 
URL:  http://d.repec.org/n?u=RePEc:wiw:wus046:8006&r=all 
By:  Jianqing Fan; Ricardo Masini; Marcelo C. Medeiros 
Abstract:  Factor and sparse models are two widely used methods to impose a lowdimensional structure in high dimension. They are seemingly mutually exclusive. In this paper, we propose a simple lifting method that combines the merits of these two models in a supervised learning methodology that allows to efficiently explore all the information in highdimensional datasets. The method is based on a very flexible linear model for panel data, called factoraugmented regression model with both observable, latent common factors, as well as idiosyncratic components as highdimensional covariate variables. This model not only includes both factor regression and sparse regression as specific models but also significantly weakens the crosssectional dependence and hence facilitates model selection and interpretability. The methodology consists of three steps. At each step, the remaining crosssection dependence can be inferred by a novel test for covariance structure in highdimensions. We developed asymptotic theory for the factoraugmented sparse regression model and demonstrated the validity of the multiplier bootstrap for testing highdimensional covariance structure. This is further extended to testing highdimensional partial covariance structures. The theory and methods are further supported by an extensive simulation study and applications to the construction of a partial covariance network of the financial returns for the constituents of the S\&P500 index and prediction exercise for a large panel of macroeconomic time series from FREDMD database. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.11341&r=all 
By:  Amaresh K Tiwari 
Abstract:  We propose a new control function (CF) method to estimate a binary response model in a triangular system with multiple unobserved heterogeneities The CFs are the expected values of the heterogeneity terms in the reduced form equations conditional on the histories of the endogenous and the exogenous variables. The method requires weaker restrictions compared to CF methods with similar imposed structures. If the support of endogenous regressors is large, average partial effects are pointidentified even when instruments are discrete. Bounds are provided when the support assumption is violated. An application and Monte Carlo experiments compare several alternative methods with ours. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.12927&r=all 
By:  Takaki Sato; Yasumasa Matsuda 
Abstract:  This paper proposes a spatial extension of mixed analysis of variance models for spatial multilevel data in which individual belongs to one of spatial regions, which are called spatial error models for multilevel data (SEMM). We have introduced empirical bayes estimation methods in two steps because SEMM models which are defined by two level equations, individual and regional levels, can be regarded as a Bayesian hierarchal model. The first step estimator based on quasimaximum likelihood estimation methods specifies the hyper parameters and has been justified in asymptotic situations, and posterior distributions for the parameters are evaluated with the hyperparameters estimated in the first step. The proposed models are applied to happiness survey data in Japan to demonstrate empirical properties. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:toh:dssraa:120&r=all 
By:  Jiangtao Duan; Jushan Bai; Xu Han 
Abstract:  This paper estimates the break point for largedimensional factor models with a single structural break in factor loadings at a common unknown date. First, we propose a quasimaximum likelihood (QML) estimator of the change point based on the second moments of factors, which are estimated by principal component analysis. We show that the QML estimator performs consistently when the covariance matrix of the pre or postbreak factor loading, or both, is singular. When the loading matrix undergoes a rotational type of change while the number of factors remains constant over time, the QML estimator incurs a stochastically bounded estimation error. In this case, we establish an asymptotic distribution of the QML estimator. The simulation results validate the feasibility of this estimator when used in finite samples. In addition, we demonstrate empirical applications of the proposed method by applying it to estimate the break points in a U.S. macroeconomic dataset and a stock return dataset. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.12666&r=all 
By:  Alfred Galichon; Marc Henry 
Abstract:  We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a KolmogorovSmirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.12257&r=all 
By:  Kohtaro Hitomi (Kyoto Institute of Technology); Masamune Iwasawa (Otaru University of Commerce); Yoshihiko Nishiyama (Institute of Economic Research, Kyoto University) 
Abstract:  This study investigates optimal minimax rates of specification testing for linear and nonlinear instrumental variable regression models. The rate implies that the uniform power of tests reduces when the dimension of instruments is large. The test constructed by nonparametric kernel techniques can be rate optimal when bandwidths satisfy two order conditions that depend on the dimensions of instruments and the smoothness of alternatives. Since bandwidths are often chosen in a datadependent way in empirical studies, the rate optimality of the test with datadriven bandwidths are investigated. Bandwidths selected by the least squares crossvalidation can satisfy conditions for the rate optimality. 
Keywords:  optimal minimax rate; specification test; instrumental variable regression; nonparametric kernel method; bandwidth selection 
JEL:  C12 C14 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:kyo:wpaper:1053&r=all 
By:  Chen, Yunxiao; Ying, Zhiliang; Zhang, Haoran 
Abstract:  Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a lowdimensional Euclidian space, in which respondents and items are represented by ideal points, with personperson, itemitem, and personitem similarities being captured by the Euclidian distances between the points. In this paper, we study the visualization of multidimensional unfolding from a statistical perspective. We cast multidimensional unfolding into an estimation problem, where the respondent and item ideal points are treated as parameters to be estimated. An estimator is then proposed for the simultaneous estimation of these parameters. Asymptotic theory is provided for the recovery of the ideal points, shedding lights on the validity of modelbased visualization. An alternating projected gradient descent algorithm is proposed for the parameter estimation. We provide two illustrative examples, one on users’ movie rating and the other on senate roll call voting. 
Keywords:  multidimensional unfolding; data visualization; distance matrix completion; item response data; embedding 
JEL:  C1 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:108876&r=all 
By:  Michael Gilraine; Jiaying Gu; Robert McMillan 
Abstract:  This paper proposes a computationally feasible nonparametric methodology for estimating teacher valueadded. Our estimator, drawing on Robbins (1956), permits the unobserved teacher valueadded distribution to be estimated directly, rather than assuming normality as is standard. Simulations indicate the estimator performs very well regardless of the true distribution, even in moderatelysized samples. Implementing our method in practice using two largescale administrative datasets, the estimated teacher valueadded distributions depart from normality and differ from each other. Further, compared with widelyused parametric estimates, we show our nonparametric estimates can make a significant difference to teacherrelated policy calculations, in both short and longer terms. 
Keywords:  Teacher ValueAdded, Nonparametric Empirical Bayes, Education Policy, Teacher Release Policy 
JEL:  C11 H75 I21 J24 
Date:  2021–02–13 
URL:  http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa689&r=all 
By:  Tobias Hartl 
Abstract:  This paper aims to provide reliable estimates for the COVID19 contact rate of a SusceptibleInfectedRecovered (SIR) model. From observable data on confirmed, recovered, and deceased cases, a noisy measurement for the contact rate can be constructed. To filter out measurement errors and seasonality, a novel unobserved components (UC) model is set up. It specifies the log contact rate as a latent, fractionally integrated process of unknown integration order. The fractional specification reflects key characteristics of aggregate social behavior such as strong persistence and gradual adjustments to new information. A computationally simple modification of the Kalman filter is introduced and is termed the fractional filter. It allows to estimate UC models with richer longrun dynamics, and provides a closedform expression for the prediction error of UC models. Based on the latter, a conditionalsumofsquares (CSS) estimator for the model parameters is set up that is shown to be consistent and asymptotically normally distributed. The resulting contact rate estimates for several countries are well in line with the chronology of the pandemic, and allow to identify different contact regimes generated by policy interventions. As the fractional filter is shown to provide precise contact rate estimates at the end of the sample, it bears great potential for monitoring the pandemic in real time. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.10067&r=all 
By:  Müller, Henrik; Hornig, Nico; Rieger, Jonas 
Abstract:  This paper deals with the problem of deriving consistent timeseries from newspaper contentbased topic models. In the first part, we recapitulate a few our own failed attempts, in the second one, we show some results using a twin strategy, that we call prototyping and seeding. Given the popularity newsbased indicators have assumed in econometric analyses in recent years, this seems to be a valuable exercise for researchers working on related issues. Building on earlier writings, where we use the topic modelling approach Latent Dirichlet Allocation (LDA) to gauge economic uncertainty perception, we show the difficulties that arise when a number of oneshot LDAs, performed at different points in time, are used to produce something akin of a timeseries. The models' topic structures differ considerably from computation to computation. Neither parameter variations nor the accumulation of several topics to broader categories of related content are able solve the problem of incompatibleness. It is not just the content that is added at each observation point, but the very properties of LDA itself: since it uses random initializations and conditional reassignments within the iterative process, fundamentally different models can emerge when the algorithm is executed several times, even if the data and the parameter settings are identical. To tame LDA's randomness, we apply a newish "prototyping" approach to the corpus, upon which our Uncertainty Perception Indicator (UPI) is built. Still, the outcomes vary considerably over time. To get closer to our goal, we drop the notion that LDA models should be allowed to take various forms freely at each run. Instead, the topic structure is fixated, using a "seeding" technique that distributes incoming new data to our model's existing topic structure. This approach seems to work quite well, as our consistent and plausible results show, but it is bound to run into difficulties over time either. 
Keywords:  uncertainty,economic policy,business cycles,Covid19,Latent Dirichlet Allocation,Seeded LDA 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:zbw:docmaw:3&r=all 
By:  Charles F Manski; Michael Gmeiner; Anat Tamburc 
Abstract:  Researchers regularly perform conditional prediction using imputed values of missing data. However, applications of imputation often lack a firm foundation in statistical theory. This paper originated when we were unable to find analysis substantiating claims that imputation of missing data has good frequentist properties when data are missing at random (MAR). We focused on the use of observed covariates to impute missing covariates when estimating conditional means of the form E(yx, w). Here y is an outcome whose realizations are always observed, x is a covariate whose realizations are always observed, and w is a covariate whose realizations are sometimes unobserved. We examine the probability limit of simple imputation estimates of E(yx, w) as sample size goes to infinity. We find that these estimates are not consistent when covariate data are MAR. To the contrary, the estimates suffer from a shrinkage problem. They converge to points intermediate between the conditional mean of interest, E(yx, w), and the mean E(yx) that conditions only on x. We use a type of genotype imputation to illustrate. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.11334&r=all 
By:  Yoonseok Lee (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Donggyu Sul (Department of Economics, University of Texas at Dallas) 
Abstract:  We develop a novel forecast combination based on the order statistics of individual predictability when many forecasts are available. To this end, we define the notion of forecast depth, which measures the size of forecast errors during the training period and provides a ranking among different forecast models. The forecast combination is in the form of a depthweighted trimmed mean, where the group of models with the worst forecasting performance during the training period is dropped. We derive the limiting distribution of the depthweighted forecast combination, based on which we can readily construct forecast confidence intervals. Using this novel forecast combination, we forecast the national level of new COVID19 cases in the U.S. and compare it with other approaches including the ensemble forecast from the Centers for Disease Control and Prevention. We find that the depthweighted forecast combination yields more accurate predictions compared with other forecast combinations. 
Keywords:  Forecast Combination, Forecast depth, Depthweighted trimmed mean, COVID19 
JEL:  C32 C53 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:max:cprwps:238&r=all 
By:  Tengyuan Liang (University of Chicago  Booth School of Business) 
Abstract:  This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GAN), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions, under a host of objective evaluation metrics. We investigate how to obtain a good statistical guarantee for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks), that characterizes the interplay on the choice of generator and discriminator pair. We discover and isolate a new notion of regularization, called the generatordiscriminatorpair regularization, that sheds light on the advantage of GANs compared to classical parametric and nonparametric approaches for explicit distribution estimation. We develop novel oracle inequalities as the main technical tools for analyzing GANs, which is of independent interest. 
Keywords:  Generative adversarial networks, implicit distribution estimation, simulated method of moments, oracle inequality, neural network learning, mini max problem, pair regularization 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:2020154&r=all 
By:  Moehring, Katja (University of Mannheim) 
Abstract:  Multilevel models that combine individual and contextual factors are increasingly popular in comparative social science research; however, their application in countrycomparative studies is often associated with several problems. First of all, most datasets utilized for multilevel modeling include only a small number (N<30) of macrolevel units, and therefore, the estimated models have a small number of degrees of freedom on the country level. If models are correctly specified paying regard to the small, level2 N, only a few macrolevel indicators can be controlled for. Furthermore, the introduction of random slopes and crosslevel interaction effects is then hardly possible. Consequently, (1) these models are likely to suffer from omitted variable bias regarding the countrylevel estimators, and (2) the advantages of multilevel modeling cannot be fully exploited. The fixed effects approach is a valuable alternative to the application of conventional multilevel methods in countrycomparative analyses. This method is also applicable with a small number of countries and avoids the countrylevel omitted variable bias through controlling for countrylevel heterogeneity. Following common practice in panel regression analyses, the moderator effect of macrolevel characteristics can be estimated also in fixed effects models by means of crosslevel interaction effects. Despite the advantages of the fixed effects approach, it is rarely used for the analysis of crossnational data. In this paper, I compare the fixed effects approach with conventional multilevel regression models and give practical examples using data of the International Social Survey Programme (ISSP) from 2006. As it turns out, the results of both approaches regarding the effect of crosslevel interactions are similar. Thus, fixed effects models can be used either as an alternative to multilevel regression models or to assess the robustness of multilevel results. 
Date:  2021–02–22 
URL:  http://d.repec.org/n?u=RePEc:osf:socarx:3xw7v&r=all 
By:  Zacharias Psaradakis; Marian Vavra (National Bank of Slovakia) 
Abstract:  The problem of assessing symmetry about an unspecified center of the onedimensional marginal distribution of strictly stationary random processes is considered. A wellknown Ustatistic based on data triples is used to detect deviations from symmetry, allowing the underying process to satisfy suitable mixing or nearepoch dependence conditions. We suggest using subsampling for inference on the target parameter, establish the asymptotic validity of the method in our setting, and discuss datadriven rules for selecting the size of subsamples. The smallsample properties of the proposed procedures are examined by means of Monte Carlo simulations and an application to real output growth rates is also presented. 
JEL:  C12 C22 
Date:  2020–12 
URL:  http://d.repec.org/n?u=RePEc:svk:wpaper:1075&r=all 
By:  Tengyuan Liang (University of Chicago  Booth School of Business); Pragya Sur (Harvard University  Department of Statistics) 
Abstract:  This paper establishes a precise highdimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider the setting where the number of features (weak learners) p scales with the sample size n, in an overparametrized regime. Under a broad class of statistical models, we provide an exact analysis of the generalization error of boosting, when the algorithm interpolates the training data and maximizes the empirical L1margin. The relation between the boosting test error and the optimal Bayes error is pinned down explicitly. In turn, these precise characterizations resolve several open questions raised in [15, 81] surrounding boosting. On the computational front, we provide a sharp analysis of the stopping time when boosting approximately maximizes the empirical L1 margin. Furthermore, we discover that the larger the overparametrization ratio p/n, the smaller the proportion of active features (with zero initialization), and the faster the optimization reaches interpolation. At the heart of our theory lies an indepth study of the maximum L1margin, which can be accurately described by a new system of nonlinear equations; we analyze this margin and the properties of this system, using Gaussian comparison techniques and a novel uniform deviation argument. Variants of AdaBoost corresponding to general Lq geometry, for q > 1, are also presented, together with an exact analysis of the highdimensional generalization and optimization behavior of a class of these algorithms. 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:bfi:wpaper:2020152&r=all 
By:  Alain Hecq; Marie Ternes; Ines Wilms 
Abstract:  Mixedfrequency Vector AutoRegressions (MFVAR) model the dynamics between variables recorded at different frequencies. However, as the number of series and highfrequency observations per lowfrequency period grow, MFVARs suffer from the "curse of dimensionality". We curb this curse through a regularizer that permits various hierarchical sparsity patterns by prioritizing the inclusion of coefficients according to the recency of the information they contain. Additionally, we investigate the presence of nowcasting relations by sparsely estimating the MFVAR error covariance matrix. We study predictive Granger causality relations in a MFVAR for the U.S. economy and construct a coincident indicator of GDP growth. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.11780&r=all 
By:  Xiuqin Xu; Ying Chen 
Abstract:  Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to automatically detect the dependence of the future volatility on past returns, past volatilities and the stochastic noise, and thus provides a flexible volatility model without the need to manually select features. We develop a scalable inference and learning algorithm based on variational inference. In real data analysis, the DSVM outperforms several popular alternative volatility models. In addition, the predicted volatility of the DSVM provides a more reliable risk measure that can better reflex the risk in the financial market, reaching more quickly to a higher level when the market becomes more risky and to a lower level when the market is more stable, compared with the commonly used GARCH type model with a huge data set on the U.S. stock market. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.12658&r=all 
By:  Ding, Y. 
Abstract:  We propose a model that extends Smetanina's (2017) original RTGARCH model by allowing conditional heteroskedasticity in the variance of volatility process. We show we are able to filter and forecast both volatility and volatility of volatility simultaneously in this simple setting. The volatility forecast function follows a secondorder difference equation as opposed to firstorder under GARCH(1,1) and RTGARCH(1,1). Empirical studies confirm the presence of conditional heteroskedasticity in the volatility process and the standardised residuals of return are close to Gaussian under this model. We show we are able to obtain better insample nowcast and outofsample forecast of volatility. 
Keywords:  GARCH, diffusion limit, forecasting, volatility of volatility 
JEL:  C22 C32 C53 C58 
Date:  2021–02–16 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2112&r=all 
By:  Andrea Carriero; Todd E. Clark; Massimiliano Marcellino; Elmar Mertens 
Abstract:  Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with timevarying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with timevarying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt an outlieradjusted stochastic volatility (SV) model for VAR residuals that combines transitory and persistent changes in volatility. In addition, we consider the treatment of outliers as missing data. Evaluating forecast performance over the last few decades in quasireal time, we find that the outlieraugmented SV scheme does at least as well as a conventional SV model, while both outperform standard homoskedastic VARs. Point forecasts made in 2020 from heteroskedastic VARs are much less sensitive to outliers in the data, and the outlieradjusted SV model generates more reasonable gauges of forecast uncertainty than a standard SV model. At least preCOVID, a close alternative to the outlieradjusted model is an SV model with tdistributed shocks. Treating outliers as missing data also generates betterbehaved forecasts than the conventional SV model. However, since uncertainty about the incidence of outliers is ignored in that approach, it leads to strikingly tight predictive densities. 
Keywords:  Bayesian VARs; stochastic volatility; outliers; pandemics; forecasts 
JEL:  C53 E17 E37 F47 
Date:  2021–02–02 
URL:  http://d.repec.org/n?u=RePEc:fip:fedcwq:89757&r=all 