nep-ecm New Economics Papers
on Econometrics
Issue of 2018‒02‒26
27 papers chosen by
Sune Karlsson
Örebro universitet

  1. Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization By Shanika L. Wickramasuriya; George Athanasopoulos; Rob J. Hyndman
  2. Exclusion Restrictions in Dynamic Binary Choice Panel Data Models By Songnian Chen; Shakeeb Khan; Xun Tang
  3. Robust Bayesian exponentially tilted empirical likelihood method By Zhichao Liu; Catherine Forbes; Heather Anderson
  4. Varying-coefficient panel data models with partially observed factor structure By Chaohua Dong; Jiti Gao; Bin Peng
  5. Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions By Akshay Vij; Rico Krueger
  6. Informed Sub-Sampling MCMC: Approximate Bayesian Inference for Large Datasets By Florian Maire; Nial Friel; Pierre ALQUIER
  7. Measuring the Return to Online Advertising: Estimation and Inference of Endogenous Treatment Effects By Shakeeb Khan; Denis Nekipelov; Justin Rao
  8. Approximate Bayesian forecasting By David T. Frazier; Worapree Maneesoonthorn; Gael M. Martin; Brendan P.M. McCabe
  9. Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory By Bodnar, Taras; Mazur, Stepan; Podgórski, Krzysztof; Tyrcha, Joanna
  10. Bayesian inference for the tangent portfolio By Bauder, David; Bodnar, Taras; Mazur, Stepan; Okhrin, Yarema
  11. Randomized Quasi Sequential Markov Chain Monte Carlo2 By Fabian Goessling
  12. A note on the adaptive estimation of the di?erential entropy by wavelet methods By Christophe Chesneau; Fabien Navarro; Oana Silvia Serea
  13. Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise. By Onatski, A.
  14. The analysis and forecasting of ATP tennis matches using a high-dimensional dynamic model By P. Gorgi; Siem Jan (S.J.) Koopman; R. Lit
  15. Mixed frequency models with MA components By Foroni, Claudia; Marcellino, Massimiliano; Stevanović, Dalibor
  16. Testing in High-Dimensional Spiked Models By Johnstone, I. M; Onatski, A.
  17. Nonseparable Sample Selection Models with Censored Selection Rules: An Application to Wage Decompositions By Fernández-Val, Iván; van Vuuren, Aico; Vella, Francis
  18. On the cyclical properties of Hamilton's regression filter By Schüler, Yves S.
  19. Random Effects Models with Deep Neural Network Basis Functions: Methodology and Computation By Kohn, Robert; Nguyen, Nghia; Nott, David; Tran, Minh-Ngoc
  20. Indexed Markov Chains for financial data: testing for the number of states of the index process By Guglielmo D'Amico; Ada Lika; Filippo Petroni
  21. Estimation of Factor Structured Covariance Mixed Logit Models By Jonathan James
  22. Concentration of tempered posteriors and of their variational approximations By Pierre Alquier; James Ridgway
  23. Robustified expected maximum production frontiers By Daouia, Abdelaati; Florens, Jean-Pierre; Simar, Léopold
  24. An approach to increasing forecast-combination accuracy through VAR error modeling By Till Weigt; Bernd Wilfling
  25. Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes By Nicolas Chopin; Mathieu Gerber
  26. Nonparametric estimation of international R&D spillovers By Georgios Gioldasis; Antonio Musolesi; Michel Simioni
  27. Extreme canonical correlations and high-dimensional cointegration analysis By Onatski, A.; Wang, C.

  1. By: Shanika L. Wickramasuriya; George Athanasopoulos; Rob J. Hyndman
    Abstract: Large collections of time series often have aggregation constraints due to product or geographical groupings. The forecasts for the most disaggregated series are usually required to add-up exactly to the forecasts of the aggregated series, a constraint we refer to as "coherence". Forecast reconciliation is the process of adjusting forecasts to make them coherent. The reconciliation algorithm proposed by Hyndman et al. (2011) is based on a generalized least squares estimator that requires an estimate of the covariance matrix of the coherency errors (i.e., the errors that arise due to incoherence). We show that this matrix is impossible to estimate in practice due to identifiability conditions. We propose a new forecast reconciliation approach that incorporates the information from a full covariance matrix of forecast errors in obtaining a set of coherent forecasts. Our approach minimizes the mean squared error of the coherent forecasts across the entire collection of time series under the assumption of unbiasedness. The minimization problem has a closed form solution. We make this solution scalable by providing a computationally efficient representation. We evaluate the performance of the proposed method compared to alternative methods using a series of simulation designs which take into account various features of the collected time series. This is followed by an empirical application using Australian domestic tourism data. The results indicate that the proposed method works well with artificial and real data.
    Keywords: Aggregation, Australian tourism, Coherent forecasts, contemporaneous error correlation, forecast combinations, spatial correlations.
    Date: 2017
  2. By: Songnian Chen (HKUST); Shakeeb Khan (Boston College); Xun Tang (Rice University)
    Abstract: In this note we revisit the use of exclusion restrictions in the semiparametric binary choice panel data model introduced in Honore and Lewbel (2002). We show that in a dynamic panel data setting (where one of the pre-determined explanatory variables is the lagged dependent variable), the exclusion restriction in Honore and Lewbel (2002) implicitly re- quires serial independence condition on an observed regressor, that if violated in the data will result in their procedure being inconsistent. We propose a new identification strategy and estimation procedure for the semiparametric binary panel data model under exclusion restrictions that accommodate the serial correlation of observed regressors in a dynamic setting. The new estimator converges at the parametric rate to a limiting normal distri- bution. This rate is faster than the nonparametric rates of existing alternative estimators for the binary choice panel data model, including the static case in Manski (1987) and the dynamic case in Honore and Kyriazidou (2000).
    Keywords: Panel Data, Dynamic Binary Choice, Exclusion Restriction
    JEL: C14 C23 C25
    Date: 2018–02–12
  3. By: Zhichao Liu; Catherine Forbes; Heather Anderson
    Abstract: This paper proposes a new Bayesian approach for analysing moment condition models in the situation where the data may be contaminated by outliers. The approach builds upon the foundations developed by Schennach (2005) who proposed the Bayesian exponentially tilted empirical likelihood (BETEL) method, justified by the fact that an empirical likelihood (EL) can be interpreted as the nonparametric limit of a Bayesian procedure when the implied probabilities are obtained from maximizing entropy subject to some given moment constraints. Considering the impact that outliers are thought to have on the estimation of population moments, we develop a new robust BETEL (RBETEL) inferential methodology to deal with this potential problem. We show how the BETEL methods are linked to the recent work of Bissiri et al. (2016) who propose a general framework to update prior belief via a loss function. A controlled simulation experiment is conducted to investigate the performance of the RBETEL method. We find that the proposed methodology produces reliable posterior inference for the fundamental relationships that are embedded in the majority of the data, even when outliers are present. The method is also illustrated in an empirical study relating brain weight to body weight using a dataset containing sixty-five different land animal species.
    Keywords: Moment condition models, outliers, misspecification.
    Date: 2017
  4. By: Chaohua Dong; Jiti Gao; Bin Peng
    Abstract: In this paper, we study a varying–coefficient panel data model with nonstationarity, wherein a factor structure is adopted to capture different effects of time invariant variables over time. The methodology employed in this paper fills a gap of dealing with the mixed I(1)/I(0) regressors and factors in the literature. For comparison purposes, we consider the scenarios where the factors are either observable or unobservable, respectively. We propose an estimation method for both the unknown coefficient functions involved and the unknown factors before we establish the corresponding theory. We then evaluate the finite–sample performance of the proposed estimation theory through extensive Monte Carlo simulations. In an empirical study, we use our newly proposed model and method to study the returns to scale of large commercial banks in the U.S.. Some overlooked modelling issues in the literature of production econometrics are addressed.
    Keywords: Asymptotic theory, orthogonal series method, translog cost function, return to scale.
    JEL: C14 C23 D24
    Date: 2018
  5. By: Akshay Vij; Rico Krueger
    Abstract: This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any arbitrary degree of accuracy. The grid with unequal intervals, in particular, offers greater flexibility than existing multivariate nonparametric specifications, while requiring the estimation of a small number of additional parameters. An expectation maximization algorithm is developed for the estimation of these models. Multiple synthetic datasets and a case study on travel mode choice behavior are used to demonstrate the value of the model framework and estimation algorithm. Compared to extant models that incorporate random taste heterogeneity through continuous mixture distributions, the proposed model provides better out-of-sample predictive ability. Findings reveal significant differences in willingness to pay measures between the proposed model and extant specifications. The case study further demonstrates the ability of the proposed model to endogenously recover patterns of attribute non-attendance and choice set formation.
    Date: 2018–02
  6. By: Florian Maire (School of Mathematics and Statistics, University College Dublin; Insight Centre for Data Analytics, University College Dublin); Nial Friel (School of Mathematics and Statistics, University College Dublin; Insight Centre for Data Analytics, University College Dublin); Pierre ALQUIER (CREST-ENSAE)
    Abstract: This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation (ABC) literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and exible approach which, contrarily to existing scalable methodologies, preserves the simplicity of the Metropolis-Hastings algorithm. Even though exactness is lost, i.e the chain distribution approximates the target, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments.
    Keywords: Bayesian inference, Big-data, Approximate Bayesian Computation, noisy Markov chain Monte Carlo
    Date: 2017–06–26
  7. By: Shakeeb Khan (Boston College); Denis Nekipelov (University of Virginia); Justin Rao (Microsoft Research)
    Abstract: In this paper we aim to conduct inference on the “lift” effect generated by an online advertisement display: specifically we want to analyze if the presence of the brand ad among the advertisements on the page increases the overall number of consumer clicks on that page. A distinctive feature of online advertising is that the ad displays are highly targeted- the advertising platform evaluates the (unconditional) probability of each consumer clicking on a given ad which leads to a higher probability of displaying the ads that have a higher a priori estimated probability of click. As a result, inferring the causal effect of the ad display on the page clicks by a given consumer from typical observational data is difficult. To address this we use the large scale of our dataset and propose a multi-step estimator that focuses on the tails of the consumer distribution to estimate the true causal effect of an ad display. This “identification at infinity” (Chamberlain (1986)) approach alleviates the need for independent experimental randomization but results in nonstandard asymptotics. To validate our estimates, we use a set of large scale randomized controlled experiments that Microsoft has run on its advertising platform. Our dataset has a large number of observations and a large number of variables and we employ LASSO to perform variable selection. Our non-experimental estimates turn out to be quite close to the results of the randomized controlled trials.
    Keywords: Endogenous treatment effects, randomized control trials, online advertising, lift effect
    JEL: C14 C31 C90 M37
    Date: 2018–02–01
  8. By: David T. Frazier; Worapree Maneesoonthorn; Gael M. Martin; Brendan P.M. McCabe
    Abstract: Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function. In this paper, we focus on the use of ABC not as a tool for parametric inference, but as a means of generating probabilistic forecasts; or for conducting what we refer to as ‘approximate Bayesian forecasting’. The four key issues explored are: i) the link between the theoretical behavior of the ABC posterior and that of the ABC-based predictive; ii) the use of proper scoring rules to measure the (potential) loss of forecast accuracy when using an approximate rather than an exact predictive; iii) the performance of approximate Bayesian forecasting in state space models; and iv) the use of forecast accuracy to inform the selection of ABC summaries in empirical settings. The primary finding of the paper is that ABC can provide a computationally ecient means of generating probabilistic forecasts that are nearly identical to those produced by the exact predictive, and in a fraction of the time required to produce predictions via an exact method.
    Keywords: Bayesian prediction, likelihood-free methods, predictive merging, proper scoring rules, particle filtering, jump-diffusion models.
    JEL: C11 C53 C58
    Date: 2018
  9. By: Bodnar, Taras (Stockholm University); Mazur, Stepan (Örebro University School of Business); Podgórski, Krzysztof (Lund University); Tyrcha, Joanna (Stockholm University)
    Abstract: In this paper we derive the nite-sample distribution of the esti- mated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency port- folio where the distribution of the test statistic is obtained under both the null and the alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sam- ple size increase to in nity. The theoretical ndings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.
    Keywords: tangency portfolio; singular Wishart distribution; singular covariance matrix; high-dimensional asymptotics; hypothesis testing
    JEL: C10 C44
    Date: 2018–02–01
  10. By: Bauder, David (Humboldt-University of Berlin); Bodnar, Taras (Stockholm University); Mazur, Stepan (Örebro University School of Business); Okhrin, Yarema (University of Augsburg)
    Abstract: In this paper we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For di↵use and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.
    Keywords: asset allocation; tangent portfolio; Bayesian analysis
    JEL: C10 C44
    Date: 2018–02–01
  11. By: Fabian Goessling
    Abstract: Sequential Monte Carlo and Markov Chain Monte Carlo methods are combined into a unifying framework for Bayesian parameter inference in non-linear, non-Gaussian state space models. A variety of tuning approaches are suggested to boost convergence: likelihood tempering, data tempering, adaptive proposals, random blocking, and randomized Quasi Monte Carlo numbers. The methods are illustrated and compared by running eight variants of the algorithm to estimate the parameters of a standard stochastic volatility model.
    Keywords: SMC, MCMC, Bayesian Estimation, Filtering
    JEL: C11 C13 C32
    Date: 2018–02
  12. By: Christophe Chesneau (Université de Caen; LMNO); Fabien Navarro (CREST;ENSAI); Oana Silvia Serea (Université Perpignan; Laboratoire de Mathématiques et Physique)
    Abstract: In this note we consider the estimation of the di?erential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean Lp error, p = 1, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical ?ndings.
    Keywords: Entropy, Wavelet estimation, Rate of convergence, Mean Lp error
    Date: 2017–02–02
  13. By: Onatski, A.
    Abstract: We consider large factor models where factors' explanatory power does not strongly dominate the explanatory power of the idiosyncratic terms asymptotically. We find the first and second order asymptotics of the principal components estimator of such a weak factors as the dimensionality of the data and the number of observations tend to infinity proportionally. The principal components estimator is inconsistent but asymptotically normal.
    Keywords: Large factor models, principal components, phase transition, weak factors, inconsistency, asymptotic distribution, Marčenko-Pastur law
    JEL: C13 C33
    Date: 2018–01–25
  14. By: P. Gorgi (VU Amsterdam, The Netherlands); Siem Jan (S.J.) Koopman (VU Amsterdam, The Netherlands; CREATES Aarhus University, Denmark); R. Lit (VU Amsterdam, The Netherlands)
    Abstract: We propose a basic high-dimensional dynamic model for tennis match results with time varying player-specific abilities for different court surface types. Our statistical model can be treated in a likelihood-based analysis and is capable of handling high-dimensional datasets while the number of parameters remains small. In particular, we analyze 17 years of tennis matches for a panel of over 500 players, which leads to more than 2000 dynamic strength levels. We find that time varying player-specific abilities for different court surfaces are of key importance for analyzing tennis matches. We further consider several other extensions including player-specific explanatory variables and the accountance of specific configurations for Grand Slam tournaments. The estimation results can be used to construct rankings of players for different court surface types. We finally show that our proposed model can also be effective in forecasting. We provide evidence that our model significantly outperforms existing models in the forecasting of tennis match results.
    Keywords: Sports statistics; Score-driven time series models; Rankings; Forecasting.
    JEL: C32 C53
    Date: 2018–01–26
  15. By: Foroni, Claudia; Marcellino, Massimiliano; Stevanović, Dalibor
    Abstract: Temporal aggregation in general introduces a moving average (MA) component in the aggregated model. A similar feature emerges when not all but only a few variables are aggregated, which generates a mixed frequency model. The MA component is generally neglected, likely to preserve the possibility of OLS estimation, but the consequences have never been properly studied in the mixed frequency context. In this paper, we show, analytically, in Monte Carlo simulations and in a forecasting application on U.S. macroeconomic variables, the relevance of considering the MA component in mixed-frequency MIDAS and Unrestricted-MIDAS models (MIDASARMA and UMIDAS-ARMA). Specifically, the simulation results indicate that the short-term forecasting performance of MIDAS-ARMA and UMIDAS-ARMA is better than that of, respectively, MIDAS and UMIDAS. The empirical applications on nowcasting U.S. GDP growth, investment growth and GDP deflator inflation confirm this ranking. Moreover, in both simulation and empirical results, MIDAS-ARMA is better than UMIDAS-ARMA.
    Keywords: temporal aggregation,MIDAS models,ARMA models
    JEL: E37 C53
    Date: 2018
  16. By: Johnstone, I. M; Onatski, A.
    Abstract: We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of {code} where H and E are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of H has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the sub-critical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike.
    Keywords: Likelihood ratio test, hypergeometric function, principal components analysis, canonical correlations, matrix denoising, multiple response regression
    JEL: E20
    Date: 2018–01–25
  17. By: Fernández-Val, Iván (Boston University); van Vuuren, Aico (University of Gothenburg); Vella, Francis (Georgetown University)
    Abstract: We consider identification and estimation of nonseparable sample selection models with censored selection rules. We employ a control function approach and discuss different objects of interest based on (1) local effects conditional on the control function, and (2) global effects obtained from integration over ranges of values of the control function. We provide conditions under which these objects are appropriate for the total population. We also present results regarding the estimation of counterfactual distributions. We derive conditions for identification for these different objects and suggest strategies for estimation. We also provide the associated asymptotic theory. These strategies are illustrated in an empirical investigation of the determinants of female wages and wage growth in the United Kingdom.
    Keywords: sample selection, nonseparable models, control function, quantile and distribution regression
    JEL: C14 C21 C24
    Date: 2018–01
  18. By: Schüler, Yves S.
    Abstract: Hamilton (2017) criticises the Hodrick and Prescott (1981, 1997) filter (HP filter) because of three drawbacks (i. spurious cycles, ii. end-of-sample bias, iii. ad hoc assumptions regarding the smoothing parameter) and proposes a regression filter as an alternative. I demonstrate that Hamilton's regression filter shares some of these drawbacks. For instance, Hamilton's ad hoc formulation of a 2-year regression filter implies a cancellation of two-year cycles and an amplification of cycles longer than typical business cycles. This is at odds with stylised business cycle facts, such as the one-year duration of a typical recession, leading to inconsistencies, for example, with the NBER business cycle chronology. Nonetheless, I show that Hamilton's regression filter should be preferred to the HP filter for constructing a credit-to-GDP gap. The filter extracts the various medium-term frequencies more equally. Due to this property, a regression-filtered credit-to-GDP ratio indicates that imbalances prior to the global financial crisis started earlier than shown by the Basel III creditto-GDP gap.
    Keywords: detrending,spurious cycles,business cycles,financial cycles,Basel III
    JEL: C10 E32 E58 G01
    Date: 2018
  19. By: Kohn, Robert; Nguyen, Nghia; Nott, David; Tran, Minh-Ngoc
    Abstract: Deep neural networks (DNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a deep neural network. The consideration of neural networks with random effects seems little used in the literature, perhaps because of the computational challenges of incorporating subject specific parameters into already complex models. Efficient computational methods for Bayesian inference are developed based on Gaussian variational approximation methods. A parsimonious but flexible factor parametrization of the covariance matrix is used in the Gaussian variational approximation. We implement natural gradient methods for the optimization, exploiting the factor structure of the variational covariance matrix to perform fast matrix vector multiplications in iterative conjugate gradient linear solvers in natural gradient computations. The method can be implemented in high dimensions, and the use of the natural gradient allows faster and more stable convergence of the variational algorithm. In the case of random effects, we compute unbiased estimates of the gradient of the lower bound in the model with the random effects integrated out by making use of Fisher's identity. The proposed methods are illustrated in several examples for DNN random effects models and high-dimensional logistic regression with sparse signal shrinkage priors.
    Keywords: Variational approximation; Stochastic optimization; Reparametrization gradient; Factor models
    Date: 2017
  20. By: Guglielmo D'Amico; Ada Lika; Filippo Petroni
    Abstract: A new branch based on Markov processes is developing in the recent literature of financial time series modeling. In this paper, an Indexed Markov Chain has been used to model high frequency price returns of quoted firms. The peculiarity of this type of model is that through the introduction of an Index process it is possible to consider the market volatility endogenously and two very important stylized facts of financial time series can be taken into account: long memory and volatility clustering. In this paper, first we propose a method for the optimal determination of the state space of the Index process which is based on a change-point approach for Markov chains. Furthermore we provide an explicit formula for the probability distribution function of the first change of state of the index process. Results are illustrated with an application to intra-day prices of a quoted Italian firm from January $1^{st}$, 2007 to December $31^{st}$ 2010.
    Date: 2018–02
  21. By: Jonathan James (Department of Economics, California Polytechnic State University)
    Abstract: Mixed logit models with normally distributed random coefficients are typically estimated under the extreme assumptions that either the random coefficients are completely independent or fully correlated. A factor structured covariance provides a middle ground between these two assumptions. However, because these models are more difficult to estimate, they are not frequently used to model preference heterogeneity. This paper develops a simple expectation maximization algorithm for estimating mixed logit models when preferences are generated from a factor structured covariance. The algorithm is easy to implement for both exploratory and confirmatory factor models. The estimator is applied to stated-preference survey data from residential energy customers (Train, 2007). Comparing the fit across five different models, which differed in their assumptions on the covariance of preferences, the results show that all three factor specifications produced a better fit of the data than the fully correlated model measured by BIC and two out of three performed better in terms of AIC.
    Keywords: Discrete Choice, Mixed Logit, EM Algorithm, Factor Models
    JEL: C02 C13 C25 C35 C38
    Date: 2018
  22. By: Pierre Alquier (CREST-ENSAE, CNRS); James Ridgway (INRIA)
    Abstract: While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the model dimension and the sample size are large. Variational Bayesian methods aim at approximating the posterior by a distribution in a tractable family. Thus, MCMC are replaced by an optimization algorithm which is orders of magnitude faster. VB methods have been applied in such computationally demanding applications as including collaborative filtering, image and video processing, NLP and text processing... However, despite very nice results in practice, the theoretical properties of these approximations are usually not known. In this paper, we propose a general approach to prove the concentration of variational approximations of fractional posteriors. We apply our theory to two examples: matrix completion, and Gaussian VB.
    Date: 2017–06–28
  23. By: Daouia, Abdelaati; Florens, Jean-Pierre; Simar, Léopold
    Abstract: The aim of this paper is to construct a robust nonparametric estimator for the production frontier. We study this problem under a regression model with one-sided errors where the regression function defines the achievable maximum output, for a given level of inputs-usage, and the regression error defines the inefficiency term. The main tool is a concept of partial regression boundary defined as a special probability-weighted moment. This concept motivates a robustified unconditional alternative to the pioneering class of nonparametric conditional expected maximum production functions. We prove that both the resulting benchmark partial frontier and its estimator share the desirable monotonicity of the true full frontier. We derive the asymptotic properties of the partial and full frontier estimators, and unravel their behavior from a robustness theory point of view. We provide numerical illustrations and Monte Carlo evidence that the presented concept of unconditional expected maximum production functions is more efficient and reliable in filtering out noise than the original conditional version. The methodology is very easy and fast to implement. Its usefulness is discussed through two concrete datasets from the sector of Delivery Services, where outliers are likely to affect the traditional conditional approach.
    Keywords: Boundary regression; Expected maximum; Nonparametric estimation; Production function; Robustnes
    Date: 2018–02
  24. By: Till Weigt; Bernd Wilfling
    Abstract: We consider a situation in which the forecaster has available M individual forecasts of a univariate target variable. We propose a 3-step procedure designed to exploit the interrelationships among the M forecast-error series (estimated from a large time-varying parameter VAR model of the errors, using past observations) with the aim of obtaining more accurate predictions of future forecast errors. The refined future forecast-error predictions are then used to obtain M new individual forecasts that are adapted to the information from the estimated VAR. The adapted M individual forecasts are ultimately combined and any potential accuracy gains of the adapted combination forecasts analyzed. We evaluate our approach in an out-of-sample forecasting analysis, using a well-established 7-country data set on output growth. Our 3-step procedure yields substantial accuracy gains (in terms of loss reductions ranging between 6.2% up to 18%) for the simple average and three time-varying-parameter combination forecasts.
    Keywords: Forecast combinations, large time-varying parameter VARs, Bayesian VAR estimation, state-space model, forgetting factors, dynamic model averaging.
    JEL: C53 C32 C11
    Date: 2018–02
  25. By: Nicolas Chopin (CREST; ENSAE); Mathieu Gerber (School of Mathematics, university of Bristol, University Walk, Clifton, Bristol)
    Abstract: SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. [16] introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.
    Date: 2017–06–01
  26. By: Georgios Gioldasis (University of Ferrara); Antonio Musolesi (University of Ferrara); Michel Simioni (Institut National de la Recherche Agronomique (INRA))
    Abstract: In a recent paper, Ertur and Musolesi (Journal of Applied Econometrics 2017; 32: 477-503) employ the Common Correlated Effects (CCE) approach to address the issue of strong cross-sectional dependence while studying international technology diffusion. We carefully revisit this issue by adopting Su and Jin's (Journal of Econometrics 2012; 169: 34-47) method, which extends the CCE approach to nonparametric specifications. Our results indicate that the adoption of a nonparametric approach provides significant benefits in terms of predictive ability. This work also refines previous results by showing threshold effects, nonlinearities and interactions, which are obscured in parametric specifications and which have relevant policy implications.
    Date: 2018–03
  27. By: Onatski, A.; Wang, C.
    Abstract: The simplest version of Johansen's (1988) trace test for cointegration is based on the squared sample canonical correlations between a random walk and its own innovations. Onatski and Wang (2017) show that the empirical distribution of such squared canonical correlations weakly converges to the Wachter distribution as the sample size and the dimensionality of the random walk go to infinity proportionally. In this paper we prove that, in addition, the extreme squared correlations almost surely converge to the upper and lower boundaries of the support of the Wachter distribution. This result yields strong laws of large numbers for the averages of functions of the squared canonical correlations that may be discontinuous or unbounded outside the support of the Wachter distribution. In particular, we establish the a.s. limit of the scaled Johansen's trace statistic, which has a logarithmic singularity at unity. We use this limit to derive a previously unknown analytic expression for the Bartlett-type correction coefficient for Johansen's test in a high-dimensional environment.
    Keywords: High-dimensional random walk, cointegration, extreme canonical correlations, Wachter distribution, trace statistic.
    Date: 2018–01–25

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