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Variable Selection And Forecasting In High Dimensional Linear Regressions With Structural Breaks
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Book Synopsis Variable Selection and Forecasting in High Dimensional Linear Regressions with Structural Breaks by : Alexander Chudik
Download or read book Variable Selection and Forecasting in High Dimensional Linear Regressions with Structural Breaks written by Alexander Chudik and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with problem of variable selection and forecasting in the presence of parameter instability. There are a number of approaches proposed for forecasting in the presence of breaks, including the use of rolling windows or exponential down-weighting. However, these studies start with a given model specification and do not consider the problem of variable selection. It is clear that, in the absence of breaks, researchers should weigh the observations equally at both variable selection and forecasting stages. In this study, we investigate whether or not we should use weighted observations at the variable selection stage in the presence of structural breaks, particularly when the number of potential covariates is large. Amongst the extant variable selection approaches we focus on the recently developed One Covariate at a time Multiple Testing (OCMT) method that allows a natural distinction between the selection and forecasting stages, and provide theoretical justification for using the full (not down-weighted) sample in the selection stage of OCMT and down-weighting of observations only at the forecasting stage (if needed). The benefits of the proposed method are illustrated by empirical applications to forecasting output growths and stock market returns.
Book Synopsis Dynamic Variable Selection in High-Dimensional Predictive Regressions by : Daniele Bianchi
Download or read book Dynamic Variable Selection in High-Dimensional Predictive Regressions written by Daniele Bianchi and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop methodology and theory for a general Bayesian approach towards dynamic variable selection in high-dimensional regression models with time-varying parameters. Specifically, we propose a variational inference scheme which features dynamic sparsity-inducing properties so that different subsets of "active'' predictors can be identified over different time periods. We compare our modeling framework against established static and dynamic variable selection methods both in simulation and within the context of two common problems in macroeconomics and finance: inflation forecasting and equity returns predictability. The results show that our approach helps to tease out more accurately the dynamic impact of different predictors over time. This translates into significant gains in terms of out-of-sample point and density forecasting accuracy. We believe our results highlight the importance of taking a dynamic approach towards variable selection for economic modeling and forecasting.
Book Synopsis Boosting Methods for Variable Selection in High Dimensional Sparse Models by :
Download or read book Boosting Methods for Variable Selection in High Dimensional Sparse Models written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Firstly, we propose new variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work better for an extremely sparse high dimensional linear regression model. We exploit the fact that the LASSO, adaptive LASSO and elastic net have closed form solutions when the predictor is one-dimensional. The explicit formula is then repeatedly used in an iterative fashion until convergence occurs. By carefully considering the relationship between estimators at successive stages, we develop fast algorithms to compute our estimators. The performance of our new estimators is compared with commonly used estimators in terms of predictive accuracy and errors in variable selection. It is observed that our approach has better prediction performance for highly sparse high dimensional linear regression models. Secondly, we propose a new variable selection technique for binary classification in high dimensional models based on a forward selection version of the Squared Support Vector Machines or one-norm Support Vector Machines, to be called as forward iterative selection and classification algorithm (FISCAL). This methods seem to work better for a highly sparse high dimensional binary classification model. We suggest the squared support vector machines using 1-norm and 2-norm simultaneously. The squared support vector machines are convex and differentiable except at zero when the predictor is one-dimensional. Then an iterative forward selection approach is applied along with the squared support vector machines until a stopping rule is satisfied. Also, we develop a recursive algorithm for the FISCAL to save computational burdens. We apply the processes to the original onenorm Support Vector Machines. We compare the FISCAL with other widely used.
Book Synopsis Variable Selection in Linear Regressions with Many Highly Correlated Covariates by : Mahrad Sharifvaghefi
Download or read book Variable Selection in Linear Regressions with Many Highly Correlated Covariates written by Mahrad Sharifvaghefi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with variable selection in linear high-dimensional frameworks when the covariates under consideration are highly correlated. Existing methods in the literature generally require that the degree of correlation among covariates be weak, yet, often in applied research, covariates can be strongly cross correlated due to common factors. This paper generalizes the One Covariate at a Time Multiple Testing procedure proposed by Chudik et al. (2018) to allow the set of covariates under consideration to be highly correlated. We exploit ideas from the latent factor and multiple testing literature to control the probability of selecting the approximating model. We also establish the asymptotic behavior of the post GOCMT selected model estimated by the least squares method. Our results show that the estimation error of the coecients converges to zero at the limit. Moreover, the mean square error and the mean square forecast error of the estimated model approach their corresponding optimal values asymptotically. The proposed method is shown to be valid under general assumptions and is computationally very fast. Our Monte Carlo experiments indicate that the newly suggested method has appealing finite-sample performance relative to competing methods under many different settings. The benefits of the proposed method are also illustrated by an empirical application to the selection of risk factors in the asset pricing literature.
Book Synopsis Variable Selection in Panel Models with Breaks by : Simon Smith
Download or read book Variable Selection in Panel Models with Breaks written by Simon Smith and published by . This book was released on 2018 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a Bayesian approach that performs variable selection in panel regression models that are subject to breaks. Our variable selection approach enables deactivation of pervasive regressors and activation of weak regressors for short periods. Allowing the coefficients on individual variables to change at each break point introduces a high-dimensional search problem even in settings with modest numbers of cross-sectional units and time-series observations. Our methodology is demonstrated on simulated data and in an empirical application to firms' choice of capital structure. We find that ignoring breaks to the data generating process typically results in overestimating the number of relevant regressors, but also leads to a failure to activate regressors that are only informative for short periods.
Book Synopsis Forecasting with Exponential Smoothing by : Rob Hyndman
Download or read book Forecasting with Exponential Smoothing written by Rob Hyndman and published by Springer Science & Business Media. This book was released on 2008-06-19 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic models, likelihood calculation, prediction intervals and procedures for model selection, was not developed until recently. This book brings together all of the important new results on the state space framework for exponential smoothing. It will be of interest to people wanting to apply the methods in their own area of interest as well as for researchers wanting to take the ideas in new directions. Part 1 provides an introduction to exponential smoothing and the underlying models. The essential details are given in Part 2, which also provide links to the most important papers in the literature. More advanced topics are covered in Part 3, including the mathematical properties of the models and extensions of the models for specific problems. Applications to particular domains are discussed in Part 4.
Book Synopsis A One-Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models by : Alexander Chudik
Download or read book A One-Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models written by Alexander Chudik and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear predictive regression framework by : Lukasz Prochownik
Download or read book Linear predictive regression framework written by Lukasz Prochownik and published by GRIN Verlag. This book was released on 2011-11-22 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master's Thesis from the year 2011 in the subject Economics - Macro-economics, general, grade: 81 %, University of Southampton, course: Econometrics, language: English, abstract: The concept of predictive regressions has been studied for over the past 20 years and its application is particularly present in applied economics, finance and econometrics. The basic set-up in the predictive regression framework associates the noisy explained variable with the lagged persistent regressor, which can be characterized as a process close to the unit root process. In my work I describe the relevance and implications of an adoption of the linear predictive regressions in forecasting the volatile stock return using the lagged variable, dividend-price ratio, which is highly persistent. Subsequently, I aim to answer questions whether the excess stock returns are predictable using dividend yields and whether the predictability is stable over time. The analysis I conduct, based on financial data, aim to detect the hypothetical presence of structural breaks in the model. In order to search for the structural instability of coefficients I construct a Wald test for each possible structural break location and investigate the accuracy of the SupWald statistic and its tabulated critical values in the framework described. Having obtained the test statistic for each of the possible break-points, I describe predictive power of explanatory variable and provide economic rationale to support some of the statistical outcomes.
Book Synopsis Essays in Honor of Cheng Hsiao by : Dek Terrell
Download or read book Essays in Honor of Cheng Hsiao written by Dek Terrell and published by Emerald Group Publishing. This book was released on 2020-04-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including contributions spanning a variety of theoretical and applied topics in econometrics, this volume of Advances in Econometrics is published in honour of Cheng Hsiao.
Book Synopsis Forward Variable Selection for Ultra-high Dimensional Quantile Regression Models by : Toshio Honda
Download or read book Forward Variable Selection for Ultra-high Dimensional Quantile Regression Models written by Toshio Honda and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variable Selection and Dimension Reduction in High-dimensional Regression by : Tao Wang
Download or read book Variable Selection and Dimension Reduction in High-dimensional Regression written by Tao Wang and published by . This book was released on 2013 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Break Point Estimation and Variable Selection in Quantile Regressions by : Ming Zhong
Download or read book Break Point Estimation and Variable Selection in Quantile Regressions written by Ming Zhong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In both statistics and econometrics, there is a large amount of research literature on issues related to structural breaks. Since checking model stability is a long-standing problem in regression (or autoregression) models, it is desirable to develop methodsto test the presence of break points, and estimate their locations if they exist. By doing so a data series may be segmented into several subseries, which are commonly assumed to have the same functional form but dierent parameters. Another important issue in multiple regressions involves determining which covariates are to be included in the final model. In practice, it is often the case that many covariates are collected and a large parametric model is built at the initial stage. However, the inclusion of irrelevant variables may reduce model performance and stability, aggravate computational burden, and make the resultant model difficult to interpret. Thus, how to efficiently select a subset of significant covariates upon which the response variable depends is of key importance when building multiple regressionmodels. The goal of our research focuses on the above-mentioned two questions: break point detection and variable selection. In Chapter 2, we jointly address both issues in a quantile regression setting. We then elaborate on the problem of break point detection for nonstationary time series in Chapter 3. For both investigations, we emphasize the importance of utilizing quantile related models, and develop methodologies based on them. In Chapter 1, we first introduce the quantile regression model. Distinct from classical regressions in which parameter estimates are derived based on the conditional mean of the response variable given certain values of the predictor variables, quantile regressions aim at estimating either at the conditional median or other quantiles of the response variable. As time series counterpart, the quantile autoregression model is then presented, and shown to be a member of the class of random coefficient autoregressions, often used in time series analysis. We further introduce the problem of break point detection and variable selection in detail, and conduct a literature review on these two topics. As the goal is to nd the best model (either with correctly identified break points, or with appropriately selected variables, or both), the estimation criterion (based on the Minimum Description Length Principle) and the optimization algorithm (based on a Genetic Algorithm) are illustrated. In the second chapter, we propose a new procedure for simultaneously estimating the number and locations of structural breaks and conducting variable selection at conditional quantile(s). In particular, with piecewise quantile regression structure, the estimated segments with selected variables are expected to minimize a convex objective function, and a genetic algorithm is implemented to solve this optimization problem. To incorporate possibly skewed and heavy-tailed innovations into the model building process, we propose the use of Asymmetric Laplace innovations as a substitute of Gaussian innovations. We develop large sample properties and theoretical justifications for the consistency of this method. Numerical results from simulations and data applications show that the proposed approach turns out to be competitive with and often superior to a number of existing methods. The third chapter presents the approach for estimating the number and locations of break points in nonstationary time series via quantile autoregression models. The methodology and its implementation details are linked to those in Chapter 2. Asymptotic properties and theoretical justifications for the consistency of this method are derived, and several simulations as well as data applications are employed to illustrate that our method consistently estimates the number and locations of the breaks.
Book Synopsis Large-dimensional Panel Data Econometrics: Testing, Estimation And Structural Changes by : Feng Qu
Download or read book Large-dimensional Panel Data Econometrics: Testing, Estimation And Structural Changes written by Feng Qu and published by World Scientific. This book was released on 2020-08-24 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to fill the gap between panel data econometrics textbooks, and the latest development on 'big data', especially large-dimensional panel data econometrics. It introduces important research questions in large panels, including testing for cross-sectional dependence, estimation of factor-augmented panel data models, structural breaks in panels and group patterns in panels. To tackle these high dimensional issues, some techniques used in Machine Learning approaches are also illustrated. Moreover, the Monte Carlo experiments, and empirical examples are also utilised to show how to implement these new inference methods. Large-Dimensional Panel Data Econometrics: Testing, Estimation and Structural Changes also introduces new research questions and results in recent literature in this field.
Book Synopsis High-dimensional Variable Selection for Spatial Regression and Covariance Estimation by : Siddhartha Nandy
Download or read book High-dimensional Variable Selection for Spatial Regression and Covariance Estimation written by Siddhartha Nandy and published by . This book was released on 2016 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Consistent Bi-level Variable Selection Via Composite Group Bridge Penalized Regression by : Indu Seetharaman
Download or read book Consistent Bi-level Variable Selection Via Composite Group Bridge Penalized Regression written by Indu Seetharaman and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the composite group bridge penalized regression methods for conducting bilevel variable selection in high dimensional linear regression models with a diverging number of predictors. The proposed method combines the ideas of bridge regression (Huang et al., 2008a) and group bridge regression (Huang et al., 2009), to achieve variable selection consistency in both individual and group levels simultaneously, i.e., the important groups and the important individual variables within each group can both be correctly identi ed with probability approaching to one as the sample size increases to in nity. The method takes full advantage of the prior grouping information, and the established bi-level oracle properties ensure that the method is immune to possible group misidenti cation. A related adaptive group bridge estimator, which uses adaptive penalization for improving bi-level selection, is also investigated. Simulation studies show that the proposed methods have superior performance in comparison to many existing methods.
Book Synopsis Penalized Regressions for Variable Selection Model, Single Index Model and an Analysis of Mass Spectrometry Data by : Yubing Wan
Download or read book Penalized Regressions for Variable Selection Model, Single Index Model and an Analysis of Mass Spectrometry Data written by Yubing Wan and published by . This book was released on 2014 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this dissertation is to develop statistical methods, under the framework of penalized regressions, to handle three different problems. The first research topic is to address missing data problem for variable selection models including elastic net (ENet) method and sparse partial least squares (SPLS). I proposed a multiple imputation (MI) based weighted ENet (MI-WENet) method based on the stacked MI data and a weighting scheme for each observation. Numerical simulations were implemented to examine the performance of the MIWENet method, and compare it with competing alternatives. I then applied the MI-WENet method to examine the predictors for the endothelial function characterized by median effective dose and maximum effect in an ex-vivo experiment. The second topic is to develop monotonic single-index models for assessing drug interactions. In single-index models, the link function f is unnecessary monotonic. However, in combination drug studies, it is desired to have a monotonic link function f . I proposed to estimate f by using penalized splines with I-spline basis. An algorithm for estimating f and the parameter a in the index was developed. Simulation studies were conducted to examine the performance of the proposed models in term of accuracy in estimating f and a. Moreover, I applied the proposed method to examine the drug interaction of two drugs in a real case study. The third topic was focused on the SPLS and ENet based accelerated failure time (AFT) models for predicting patient survival time with mass spectrometry (MS) data. A typical MS data set contains limited number of spectra, while each spectrum contains tens of thousands of intensity measurements representing an unknown number of peptide peaks as the key features of interest. Due to the high dimension and high correlations among features, traditional linear regression modeling is not applicable. Semi-parametric AFT model with an unspecified error distribution is a well-accepted approach in survival analysis. To reduce the bias caused in denoising step, we proposed a nonparametric imputation approach based on Kaplan-Meier estimator. Numerical simulations and a real case study were conducted under the proposed method.
Book Synopsis Ultra High Dimension Variable Selection with Threshold Partial Correlations by : Yiheng Liu
Download or read book Ultra High Dimension Variable Selection with Threshold Partial Correlations written by Yiheng Liu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With respect to variable selection in linear regression, partial correlation for normal models (Buhlmann, Kalisch and Maathuis, 2010), was a powerful alternative method to penalized least squares approaches (LASSO, SCAD, etc.). The method was improved by Li, Liu, Lou (2015) with the concept of threshold partial correlation (TPC) and extension to elliptical contoured dis- tributions. The TPC procedure is endowed with its dominant advantages over the simple partial correlation in high or ultrahigh dimensional cases (where the dimension of predictors increases in an exponential rate of the sample size). However, the convergence rate for TPC is not very satis- fying since it usually takes substantial amount of time for the procedure to reach the final solution, especially in high or even ultrahigh dimensional scenarios. Besides, the model assumptions on the TPC are too strong, which suggest the approach might not be conveniently used in practice. To address these two important issues, this dissertation puts forward an innovative model selection al- gorithm. It starts with an alternative definition of elliptical contoured distributions, which restricts the impact of the marginal kurtosis. This posts a relatively weaker condition for the validity of the model selection algorithm. Based on the simulation results, the new approach demonstrates not only competitive outcomes with established methods such as LASSO and SCAD, but also advan- tages in terms of computing efficiency. The idea of the algorithm is extended to survival data and nonparametric inference by exploring various measurements on correlations between the response variable and predictors.
