
on Econometric Time Series 
Issue of 2020‒01‒13
eleven papers chosen by Jaqueson K. Galimberti Auckland University of Technology 
By:  Aknouche, Abdelhakim; Francq, Christian 
Abstract:  General parametric forms are assumed for the conditional mean λ_{t}(θ₀) and variance υ_{t}(ξ₀) of a time series. These conditional moments can for instance be derived from count time series, Autoregressive Conditional Duration (ACD) or Generalized Autoregressive Score (GAS) models. In this paper, our aim is to estimate the conditional mean parameter θ₀, trying to be as agnostic as possible about the conditional distribution of the observations. QuasiMaximum Likelihood Estimators (QMLEs) based on the linear exponential family fulfill this goal, but they may be inefficient and have complicated asymptotic distributions when θ₀ contains zero coefficients. We thus study alternative weighted least square estimators (WLSEs), which enjoy the same consistency property as the QMLEs when the conditional distribution is misspecified, but have simpler asymptotic distributions when components of θ₀ are null and gain in efficiency when υ_{t} is well specified. We compare the asymptotic properties of the QMLEs and WLSEs, and determine a data driven strategy for finding an asymptotically optimal WLSE. Simulation experiments and illustrations on realized volatility forecasting are presented. 
Keywords:  Autoregressive Conditional Duration model; Exponential, Poisson, Negative Binomial QMLE; INtegervalued AR; INtegervalued GARCH; Weighted LSE. 
JEL:  C13 C14 C18 C25 C52 C53 C58 
Date:  2019–12–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:97382&r=all 
By:  Andrii Babii; Eric Ghysels; Jonas Striaukas 
Abstract:  Time series regression analysis in econometrics typically involves a framework relying on a set of mixing conditions to establish consistency and asymptotic normality of parameter estimates and HACtype estimators of the residual longrun variances to conduct proper inference. This article introduces structured machine learning regressions for highdimensional time series data using the aforementioned commonly used setting. To recognize the time series data structures we rely on the sparsegroup LASSO estimator. We derive a new FukNagaev inequality for a class of $\tau$dependent processes with heavier than Gaussian tails, nesting $\alpha$mixing processes as a special case, and establish estimation, prediction, and inferential properties, including convergence rates of the HAC estimator for the longrun variance based on LASSO residuals. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that the text data can be a useful addition to more traditional numerical data. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.06307&r=all 
By:  Raffaella Giacomini (Institute for Fiscal Studies and cemmap and UCL); Toru Kitagawa (Institute for Fiscal Studies and cemmap and University College London); Matthew Read (Institute for Fiscal Studies) 
Abstract:  We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the impulse responses or forecast error variance decompositions of interest are setidenti?ed using external instruments (or ‘proxy SVARs’). Existing Bayesian approaches to inference in proxy SVARs require researchers to specify a single prior over the model’s parameters. When parameters are setidenti?ed, a component of the prior is never updated by the data. Giacomini and Kitagawa (2018) propose a method for robust Bayesian inference in setidentifed models that delivers inference about the identi?ed set for the parameter of interest. We extend this approach to proxy SVARs, which allows researchers to relax potentially controversial pointidentifying restrictions without having to specify an unrevisable prior. We also explore the e?ect of instrument strength on posterior inference. We illustrate our approach by revisiting Mertens and Ravn (2013) and relaxing the assumption that they impose to obtain point identi?cation. 
Date:  2019–07–23 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:38/19&r=all 
By:  Fries, Sébastien 
Abstract:  Noncausal, or anticipative, alphastable processes generate trajectories featuring locally explosive episodes akin to speculative bubbles in financial time series data. For (X_t) a twosided infinite alphastable moving average (MA), conditional moments up to integer order four are shown to exist provided (X_t) is anticipative enough. The functional forms of these moments at any forecast horizon under any admissible parameterisation are obtained by extending the literature on arbitrary bivariate alphastable random vectors. The dynamics of noncausal processes simplifies during explosive episodes and allows to express ex ante crash odds at any horizon in terms of the MA coefficients and of the tail index alpha. The results are illustrated in a synthetic portfolio allocation framework and an application to the Nasdaq and S&P500 series is provided. 
Keywords:  Noncausal processes, Multivariate stable distributions, Conditional dependence, Extremal dependence, Explosive bubbles, Prediction, Crash odds, Portfolio allocation 
JEL:  C22 C53 C58 
Date:  2018–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:97353&r=all 
By:  Holger Dette; Weichi Wu 
Abstract:  We develop an estimator for the highdimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in nonstationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a simulation study and a financial indices study. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.00419&r=all 
By:  Serge Darolles (DRM  Dauphine Recherches en Management  Université ParisDauphine  CNRS  Centre National de la Recherche Scientifique); Gaëlle Le Fol (DRM  Dauphine Recherches en Management  Université ParisDauphine  CNRS  Centre National de la Recherche Scientifique); Yang Lu (CEPN  Centre d'Economie de l'Université Paris Nord  UP13  Université Paris 13  USPC  Université Sorbonne Paris Cité  CNRS  Centre National de la Recherche Scientifique); Ran Sun (DRM  Dauphine Recherches en Management  Université ParisDauphine  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  We propose a new family of bivariate nonnegative integerautoregressive (BINAR) models for count process data. We first generalize the existing BINAR(1) model by allowing for dependent thinning operators and arbitrary innovation distribution. The extended family allows for intuitive interpretation, as well as tractable aggregation and stationarity properties. We then introduce higher order BINAR(p) and BINAR(∞) dynamics to accommodate more flexible serial dependence patterns. So far, the literature has regarded such models as computationally intractable. We show that the extended BINAR family allows for closedform predictive distributions at any horizons and for any values of , which significantly facilitates nonlinear forecasting and likelihood based estimation. Finally, a BINAR model with memory persistence is applied to openended mutual fund purchase and redemption order counts. 
Keywords:  Multivariate low event count process,memory persis tence,Compound autoregressive process,Memory persistence,Mutual funds,Nonlinear forecasting,liquidity risk,mutual funds MSC code: 6215,JEL code: C32,C53 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs02418967&r=all 
By:  Zijian Zeng; Meng Li 
Abstract:  We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes timevarying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used meanbased methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure of autoregressive (AR) models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging (BMA) is used to account for model uncertainty including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulation and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performances than the selected meanbased alternatives under various loss functions. The proposed methods are generic and can be used to complement a rich class of methods that builds on the AR models. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.01116&r=all 
By:  Ruben LoaizaMaya; Gael M. Martin; David T. Frazier 
Abstract:  We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After observing data, we update the prior to a posterior over these models, via a criterion that captures a userspecified measure of predictive accuracy. Under regularity, this update yields posterior concentration onto the element of the predictive class that maximizes the expectation of the accuracy measure. In a series of simulation experiments and empirical examples we find notable gains in predictive accuracy relative to conventional likelihoodbased prediction. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.12571&r=all 
By:  Jiahe Lin; George Michailidis 
Abstract:  We consider the estimation of approximate factor models for time series data, where strong serial and crosssectional correlations amongst the idiosyncratic component are present. This setting comes up naturally in many applications, but existing approaches in the literature rely on the assumption that such correlations are weak, leading to misspecification of the number of factors selected and consequently inaccurate inference. In this paper, we explicitly incorporate the dependent structure present in the idiosyncratic component through lagged values of the observed multivariate time series. We formulate a constrained optimization problem to estimate the factor space and the transition matrices of the lagged values {\em simultaneously}, wherein the constraints reflect the low rank nature of the common factors and the sparsity of the transition matrices. We establish theoretical properties of the obtained estimates, and introduce an easytoimplement computational procedure for empirical work. The performance of the model and the implementation procedure is evaluated on synthetic data and compared with competing approaches, and further illustrated on a data set involving weekly logreturns of 75 US large financial institutions for the 20012016 period. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.04123&r=all 
By:  Mike Tsionas; Marwan Izzeldin; Lorenzo Trapani 
Abstract:  This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. With our new methodology, the original multivariate, n dimensional model is treated as a set of n univariate estimation problems, and crossdependence is handled through the use of a copula. Thus, only univariate distribution functions are needed when estimating the individual equations, which are often available in closed form, and easy to handle with MCMC (or other techniques). Estimation is carried out in parallel for the individual equations. Thereafter, the individual posteriors are combined with the copula, so obtaining a joint posterior which can be easily resampled. We illustrate our approach by applying it to a large timevarying parameter VAR with 25 macroeconomic variables. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.12527&r=all 
By:  Jiahe Lin; George Michailidis 
Abstract:  A factoraugmented vector autoregressive (FAVAR) model is defined by a VAR equation that captures leadlag correlations amongst a set of observed variables $X$ and latent factors $F$, and a calibration equation that relates another set of observed variables $Y$ with $F$ and $X$. The latter equation is used to estimate the factors that are subsequently used in estimating the parameters of the VAR system. The FAVAR model has become popular in applied economic research, since it can summarize a large number of variables of interest as a few factors through the calibration equation and subsequently examine their influence on core variables of primary interest through the VAR equation. However, there is increasing need for examining leadlag relationships between a large number of time series, while incorporating information from another highdimensional set of variables. Hence, in this paper we investigate the FAVAR model under highdimensional scaling. We introduce an appropriate identification constraint for the model parameters, which when incorporated into the formulated optimization problem yields estimates with good statistical properties. Further, we address a number of technical challenges introduced by the fact that estimates of the VAR system model parameters are based on estimated rather than directly observed quantities. The performance of the proposed estimators is evaluated on synthetic data. Further, the model is applied to commodity prices and reveals interesting and interpretable relationships between the prices and the factors extracted from a set of global macroeconomic indicators. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.04146&r=all 