
on Econometric Time Series 
Issue of 2020‒03‒09
twelve papers chosen by Jaqueson K. Galimberti Auckland University of Technology 
By:  Bernd Funovits 
Abstract:  This paper deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly noninvertible structural vector autoregressive moving average (SVARMA) models driven by independent and nonGaussian shocks. We introduce a new parameterisation of the MA polynomial matrix based on the WienerHopf factorisation (WHF) and show that the model is identified in this parametrisation for a generic set in the parameter space (when certain justidentifying restrictions are imposed). When the SVARMA model is driven by Gaussian errors, neither the static shock transmission matrix, nor the location of the determinantal zeros of the MA polynomial matrix can be identified without imposing further identifying restrictions on the parameters. We characterise the classes of observational equivalence with respect to second moment information at different stages of the modelling process. Subsequently, crosssectional and temporal independence and nonGaussianity of the shocks is used to solve these identifiability problems and identify the true root location of the MA polynomial matrix as well as the static shock transmission matrix (up to permutation and scaling).Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator. The estimation procedure is illustrated with various examples from the economic literature and implemented as Rpackage. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.04346&r=all 
By:  James A. Duffy; Jerome R. Simons 
Abstract:  It has been known since Elliott (1998) that efficient methods of inference on cointegrating relationships break down when autoregressive roots are near but not exactly equal to unity. This paper addresses this problem within the framework of a VAR with nonunit roots. We develop a characterisation of cointegration, based on the impulse response function implied by the VAR, that remains meaningful even when roots are not exactly unity. Under this characterisation, the longrun equilibrium relationships between the series are identified with a subspace associated to the largest characteristic roots of the VAR. We analyse the asymptotics of maximum likelihood estimators of this subspace, thereby generalising Johansen's (1995) treatment of the cointegrated VAR with exactly unit roots. Inference is complicated by nuisance parameter problems similar to those encountered in the context of predictive regressions, and can be dealt with by approaches familiar from that setting. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.08092&r=all 
By:  Robert J. Hodrick 
Abstract:  This paper uses simulations to explore the properties of the HP filter of Hodrick and Prescott (1997), the BK filter of Baxter and King (1999), and the H filter of Hamilton (2018) that are designed to decompose a univariate time series into trend and cyclical components. Each simulated time series approximates the natural logarithms of U.S. Real GDP, and they are a random walk, an ARIMA model, two unobserved components models, and models with slowly changing nonstationary stochastic trends and definitive cyclical components. In basic time series, the H filter dominates the HP and BK filters in more closely characterizing the underlying framework, but in more complex models, the reverse is true. 
JEL:  E32 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:26750&r=all 
By:  Niko Hauzenberger; Florian Huber; Luca Onorante 
Abstract:  Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a straightforward means of postprocessing posterior estimates of a conjugate Bayesian VAR to effectively perform equationspecific covariate selection. Compared to existing techniques using shrinkage alone, our approach combines shrinkage and sparsity in both the VAR coefficients and the error variancecovariance matrices, greatly reducing estimation uncertainty in large dimensions while maintaining computational tractability. We illustrate our approach by means of two applications. The first application uses synthetic data to investigate the properties of the model across different datagenerating processes, the second application analyzes the predictive gains from sparsification in a forecasting exercise for US data. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.08760&r=all 
By:  Shaolong Suna; Dan Bi; Jue Guo; Shouyang Wang 
Abstract:  The accurate seasonal and trend forecasting of tourist arrivals is a very challenging task. In the view of the importance of seasonal and trend forecasting of tourist arrivals, and limited research work paid attention to these previously. In this study, a new adaptive multiscale ensemble (AME) learning approach incorporating variational mode decomposition (VMD) and least square support vector regression (LSSVR) is developed for short, medium, and longterm seasonal and trend forecasting of tourist arrivals. In the formulation of our developed AME learning approach, the original tourist arrivals series are first decomposed into the trend, seasonal and remainders volatility components. Then, the ARIMA is used to forecast the trend component, the SARIMA is used to forecast seasonal component with a 12month cycle, while the LSSVR is used to forecast remainder volatility components. Finally, the forecasting results of the three components are aggregated to generate an ensemble forecasting of tourist arrivals by the LSSVR based nonlinear ensemble approach. Furthermore, a direct strategy is used to implement multistepahead forecasting. Taking two accuracy measures and the DieboldMariano test, the empirical results demonstrate that our proposed AME learning approach can achieve higher level and directional forecasting accuracy compared with other benchmarks used in this study, indicating that our proposed approach is a promising model for forecasting tourist arrivals with high seasonality and volatility. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.08021&r=all 
By:  Wenjing Wang; Minjing Tao 
Abstract:  Multivariate volatility modeling and forecasting are crucial in financial economics. This paper develops a copulabased approach to model and forecast realized volatility matrices. The proposed copulabased time series models can capture the hidden dependence structure of realized volatility matrices. Also, this approach can automatically guarantee the positive definiteness of the forecasts through either Cholesky decomposition or matrix logarithm transformation. In this paper we consider both multivariate and bivariate copulas; the types of copulas include Student's t, Clayton and Gumbel copulas. In an empirical application, we find that for oneday ahead volatility matrix forecasting, these copulabased models can achieve significant performance both in terms of statistical precision as well as creating economically meanvariance efficient portfolio. Among the copulas we considered, the multivariatet copula performs better in statistical precision, while bivariatet copula has better economical performance. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.08849&r=all 
By:  Burkhart, Michael C. 
Abstract:  Given a stationary statespace model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earthbased radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes’ rule to build a nonlinear, nonGaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closedform updates for the posterior. We argue there are many cases where the distribution of state given measurement is betterapproximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein—von Mises theorem applies. Online neural decoding for braincomputer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an onscreen cursor in realtime using mental imagery alone. Participant “T9” used the DKF to type out messages on a tablet PC. Nonstationarities, or changes to the statistical relationship between states and measurements that occur after model training, pose a significant challenge to effective filtering. In braincomputer interfaces, one common type of nonstationarity results from wonkiness or dropout of a single neuron. We show how a robust measurement model can be used within the DKF framework to effectively ignore large changes in the behavior of a single neuron. At BrainGate2, a successful online human neural decoding experiment validated this approach against the commonlyused Kalman filter. 
Date:  2019–05–01 
URL:  http://d.repec.org/n?u=RePEc:osf:thesis:4j3fu&r=all 
By:  Daniel Buncic 
Abstract:  Holston, Laubach and Williams' (2017) estimates of the natural rate of interest are driven by the downward trending behaviour of `other factor' $z_{t}$. I show that their implementation of Stock and Watson's (1998) Median Unbiased Estimation (MUE) to determine the size of $\lambda_{z}$ is unsound. It cannot recover the ratio of interest $\lambda _{z}=a_{r}\sigma _{z}/\sigma _{\tilde{y}}$ from MUE required for the estimation of the full structural model. This failure is due to their Stage 2 model being incorrectly specified. More importantly, the MUE procedure that they implement spuriously amplifies the estimate of $\lambda _{z}$. Using a simulation experiment, I show that their MUE procedure generates excessively large estimates of $\lambda _{z}$ when applied to data simulated from a model where the true $\lambda _{z}$ is equal to zero. Correcting their Stage 2 MUE procedure leads to a substantially smaller estimate of $\lambda _{z}$, and a more subdued downward trending influence of `other factor' $z_{t}$ on the natural rate. This correction is quantitatively important. With everything else remaining the same in the model, the natural rate of interest is estimated to be 1.5% at the end of 2019:Q2; that is, three times the 0.5% estimate obtained from Holston et al.'s (2017) original Stage 2 MUE implementation. I also discuss various other issues that arise in their model of the natural rate that make it unsuitable for policy analysis. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.11583&r=all 
By:  Giulia Carallo; Roberto Casarin; Christian P. Robert 
Abstract:  This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and exploit the thinning representation to derive stationarity conditions and the stationary distribution of the process. We provide a Bayesian inference method and an efficient posterior approximation procedure based on Monte Carlo. Numerical illustrations on both simulated and real data show the effectiveness of the proposed inference. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.04470&r=all 
By:  Yong Song; Tomasz Wo\'zniak 
Abstract:  Markov switching models are a popular family of models that introduces timevariation in the parameters in the form of their state or regimespecific values. Importantly, this timevariation is governed by a discretevalued latent stochastic process with limited memory. More specifically, the current value of the state indicator is determined only by the value of the state indicator from the previous period, thus the Markov property, and the transition matrix. The latter characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period, given the state in the current period. This setup decides on the two main advantages of the Markov switching models. Namely, the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the statespecific parameters. These two features open the possibility for improved interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities, as well as for improved forecasting performance based on persistent regimes and parameters characterizing them. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.03598&r=all 
By:  Oscar Espinosa; Fabio Nieto 
Abstract:  This research shows that under certain mathematical conditions, a threshold autoregressive model (TAR) can represent the leverage effect based on its conditional variance function. Furthermore, the analytical expressions for the third and fourth moment of the TAR model are obtained when it is weakly stationary. 
Date:  2020–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2002.05319&r=all 
By:  Adam Elbourne (CPB Netherlands Bureau for Economic Policy Analysis); Kan Ji (CPB Netherlands Bureau for Economic Policy Analysis) 
Abstract:  This research reexamines the findings of the existing literature on the effects of unconventional monetary policy. It concludes that the existing estimates based on vector autoregressions in combination with zero and sign restrictions do not successfully isolate unconventional monetary policy shocks from other shocks impacting the euro area economy. In our research, we show that altering existing published studies by making the incorrect assumption that expansionary monetary shocks shrink the ECB’s balance sheet or even ignoring all information about the stance of monetary policy results in the same shocks and, therefore, the same estimated responses of output and prices. As a consequence, it is implausible that the shocks previously identified in the literature are true unconventional monetary policy shocks. Since correctly isolating unconventional monetary policy shocks is a prerequisite for subsequently estimating the effects of unconventional monetary policy shocks, the conclusions from previous vector autoregression models are unwarranted. We show this lack of identification for different specifications of the vector autoregression models and different sample periods. 
JEL:  C32 E52 
Date:  2019–02 
URL:  http://d.repec.org/n?u=RePEc:cpb:discus:391.rdf&r=all 