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on Econometric Time Series |
| By: | Matteo Iacopini; Luca Rossini |
| Abstract: | Over the last decade, big data have poured into econometrics, demanding new statistical methods for analysing high-dimensional data and complex non-linear relationships. A common approach for addressing dimensionality issues relies on the use of static graphical structures for extracting the most significant dependence interrelationships between the variables of interest. Recently, Bayesian nonparametric techniques have become popular for modelling complex phenomena in a flexible and efficient manner, but only few attempts have been made in econometrics. In this paper, we provide an innovative Bayesian nonparametric (BNP) time-varying graphical framework for making inference in high-dimensional time series. We include a Bayesian nonparametric dependent prior specification on the matrix of coefficients and the covariance matrix by mean of a Time-Series DPP as in Nieto-Barajas et al. (2012). Following Billio et al. (2019), our hierarchical prior overcomes over-parametrization and over-fitting issues by clustering the vector autoregressive (VAR) coefficients into groups and by shrinking the coefficients of each group toward a common location. Our BNP timevarying VAR model is based on a spike-and-slab construction coupled with dependent Dirichlet Process prior (DPP) and allows to: (i) infer time-varying Granger causality networks from time series; (ii) flexibly model and cluster non-zero time-varying coefficients; (iii) accommodate for potential non-linearities. In order to assess the performance of the model, we study the merits of our approach by considering a well-known macroeconomic dataset. Moreover, we check the robustness of the method by comparing two alternative specifications, with Dirac and diffuse spike prior distributions. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1906.02140&r=all |
| By: | Ivan Mendieta-Munoz; Mengheng Li |
| Abstract: | We propose a multivariate simultaneous unobserved components framework to determine the two-sided interactions between structural trend and cycle innovations. We relax the standard assumption in unobserved components models that trends are only driven by permanent shocks and cycles are only driven by transitory shocks by considering the possible spillover effects between structural innovations. The direction of spillover has a structural interpretation, whose identification is achieved via heteroskedasticity. We provide identifiability conditions and develop an efficient Bayesian MCMC procedure for estimation. Empirical implementations for both Okun's law and the Phillips curve show evidence of significant spillovers between trend and cycle components. |
| Keywords: | Unobserved components, Identification via heteroskedasticity, Trends and cycles, Permanent and transitory shocks, State space models, Spillover structural effects. JEL Classification: C11, C32, E31, E32, E52 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:uta:papers:2019_06&r=all |
| By: | Bo Zhang; Jiti Gao; Guangming Pan |
| Abstract: | This paper considers a p–dimensional time series model of the form x(t)-δ(t)=ψ(x(t−1)−δ(t−1))+Σ(1/2)y(t), 1 |
| Keywords: | asymptotic normality, largest eigenvalue, linear process, near unit root test. |
| JEL: | C21 C32 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2019-10&r=all |
| By: | Earo Wang; Dianne Cook; Rob J Hyndman |
| Abstract: | Mining temporal data for information is often inhibited by a multitude of formats: irregular or multiple time intervals, point events that need aggregating, multiple observational units or repeated measurements on multiple individuals, and heterogeneous data types. On the other hand, the software supporting time series modeling and forecasting, makes strict assumptions on the data to be provided, typically requiring a matrix of numeric data with implicit time indexes. Going from raw data to model-ready data is painful. This work presents a cohesive and conceptual framework for organizing and manipulating temporal data, which in turn flows into visualization, modeling and forecasting routines. Tidy data principles are extended to temporal data by: (1) mapping the semantics of a dataset into its physical layout; (2) including an explicitly declared index variable representing time; (3) incorporating a "key" comprising single or multiple variables to uniquely identify units over time. This tidy data representation most naturally supports thinking of operations on the data as building blocks, forming part of a “data pipeline†in time-based contexts. A sound data pipeline facilitates a fluent workflow for analyzing temporal data. The infrastructure of tidy temporal data has been implemented in the R package tsibble. |
| Keywords: | time series, data wrangling, tidy data, R, forecasting, data science, exploratory data analysis, data pipelines |
| JEL: | C88 C81 C82 C22 C32 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2019-12&r=all |
| By: | Li, Z. M.; Laeven, R. J. A.; Vellekoop, M. H. |
| Abstract: | In this paper, we develop econometric tools to analyze the integrated volatility (IV) of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive consistent estimators of the IV, which converge stably to a mixed Gaussian distribution at the optimal rate n1/4. To improve the finite sample performance, we propose a multi-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our multi-step estimators. In an empirical study, we analyze the dependence structures of microstructure noise and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating IV. |
| Keywords: | Dependent microstructure noise, realized volatility, bias correction, integrated volatility, mixing sequences, pre-averaging method |
| JEL: | C13 C14 C58 |
| Date: | 2019–06–14 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1952&r=all |
| By: | Laniado Rodas, Henry; Lillo Rodríguez, Rosa Elvira; Cabana Garceran del Vall, Elisa |
| Abstract: | A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with normal and heavy-tailed errors, the robustness under contamination, the computational times, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socio-economic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression. |
| Keywords: | Environmental Study; Outliers; Shrinkage Estimator; Robust Mahalanobis Distance; Robust Regression |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:28500&r=all |
| By: | David Frazier; Bonsoo Koo |
| Abstract: | We propose the use of indirect inference estimation for inference in locally stationary models. We develop a local indirect inference algorithm and establish the asymptotic properties of the proposed estimator. Due to the nonparametric nature of the model under study, the resulting estimators display nonparametric rates of convergence and behavior. We validate our methodology via simulation studies in the confines of a locally stationary moving average model and a locally stationary multiplicative stochastic volatility model. An application of the methodology gives evidence of non-linear, time-varying volatility for monthly returns on the Fama-French portfolios. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1906.01768&r=all |
| By: | Mohamed Chikhi; Claude Diebolt; Tapas Mishra |
| Abstract: | Stock price forecasting, a popular growth-enhancing exercise for investors, is inherently complex – thanks to the interplay of financial economic drivers which determine both the magnitude of memory and the extent of non-linearity within a system. In this paper, we accommodate both features within a single estimation framework to forecast stock prices and identify the nature of market efficiency commensurate with the proposed model. We combine a class of semiparametric autoregressive fractionally integrated moving average (SEMIFARMA) model with asymmetric exponential generalized autoregressive score (AEGAS) errors to design a SEMIRFARMA-AEGAS framework based on which predictive performance of this model is tested against competing methods. Our conditional variance includes leverage effects, jumps and fat tail-skewness distribution, each of which affects magnitude of memory in a stock price system. A true forecast function is built and new insights into stock price forecasting are presented. We estimate several models using the Skewed Student-t maximum likelihood and find that the informational shocks have permanent effects on returns and the SEMIFARMA-AEGAS is appropriate for capturing volatility clustering for both negative (long Value-at-Risk) and positive returns (short Value-at-Risk). We show that this model has better predictive performance over competing models for both long and/or some short time horizons. The predictions from SEMIRFARMA-AEGAS model beats comfortably the random walk model. Our results have implications for market-efficiency: the weak efficiency assumption of financial markets stands violated for all stock price returns studied over a long period. |
| Keywords: | Stock price forecasting; SEMIFARMA model; AEGAS model; Skewed Student-t maximum likelihood; Asymmetry; Jumps. |
| JEL: | C14 C58 C22 G17 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2019-24&r=all |
| By: | Nathaniel Tomasetti; Catherine Forbes; Anastasios Panagiotelis |
| Abstract: | Variational Bayesian (VB) methods usually produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good parameter estimates and predicted values when a rich class of approximating distributions are considered. In this paper we propose Updating VB (UVB), a recursive algorithm used to update a sequence of VB posterior approximations in an online setting, with the computation of each posterior update requiring only the data observed since the previous update. An extension to the proposed algorithm, named UVB-IS, allows the user to trade accuracy for a substantial increase in computational speed through the use of importance sampling. The two methods and their properties are detailed in two separate simulation studies. Two empirical illustrations of the proposed UVB methods are provided, including one where a Dirichlet Process Mixture model is repeatedly updated in the context of predicting the future behaviour of vehicles on a stretch of the US Highway 101. |
| Keywords: | importance sampling, forecasting, clustering, dirichlet process mixture, variational inference |
| JEL: | C11 G18 G39 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2019-13&r=all |