Significant Variable Selection and Autoregressive Order Determination for Time-Series Partially Linear Models PDF Download
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Author: Degao Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is concerned with the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation (SCAD) penalty for a partially linear model with time-series errors. By combining the profile semi-parametric least squares method and SCAD penalty technique, a new penalized estimation for the regression and autoregressive parameters in the model is proposed. We show that the asymptotic property of the resultant estimator is the same as if the order of autoregressive error structure and non-zero regression coefficients are known in advance, thus achieving the oracle property in the sense of Fan and Li (2001). In addition, based on a prewhitening technique, we construct a two-stage local linear estimator (TSLLE) for the non-parametric component. It is shown that the TSLLE is more asymtotically efficient than the one that ignores the autoregressive time-series error structure. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on electricity usage data is also illustrated.
Author: Degao Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is concerned with the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation (SCAD) penalty for a partially linear model with time-series errors. By combining the profile semi-parametric least squares method and SCAD penalty technique, a new penalized estimation for the regression and autoregressive parameters in the model is proposed. We show that the asymptotic property of the resultant estimator is the same as if the order of autoregressive error structure and non-zero regression coefficients are known in advance, thus achieving the oracle property in the sense of Fan and Li (2001). In addition, based on a prewhitening technique, we construct a two-stage local linear estimator (TSLLE) for the non-parametric component. It is shown that the TSLLE is more asymtotically efficient than the one that ignores the autoregressive time-series error structure. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on electricity usage data is also illustrated.
Author: Henrik Madsen
Publisher: CRC Press
ISBN: 142005967X
Category : Mathematics
Languages : en
Pages : 398
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Book Description
With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explores the connections among stochastic dynamic models. Emphasizing the time domain description, the author presents theorems to highlight the most important results, proofs to clarify some results, and problems to illustrate the use of the results for modeling real-life phenomena. The book first provides the formulas and methods needed to adapt a second-order approach for characterizing random variables as well as introduces regression methods and models, including the general linear model. It subsequently covers linear dynamic deterministic systems, stochastic processes, time domain methods where the autocorrelation function is key to identification, spectral analysis, transfer-function models, and the multivariate linear process. The text also describes state space models and recursive and adaptivemethods. The final chapter examines a host of practical problems, including the predictions of wind power production and the consumption of medicine, a scheduling system for oil delivery, and the adaptive modeling of interest rates. Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems. It will help you understand the relationship between linear dynamic systems and linear stochastic processes.
Author: Wolfgang Härdle
Publisher: Springer Science & Business Media
ISBN: 3642577008
Category : Mathematics
Languages : en
Pages : 210
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Book Description
In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Author:
Publisher: John Wiley & Sons
ISBN: 1394248407
Category :
Languages : en
Pages : 580
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Book Description
Author: Manfred Deistler
Publisher: Springer Nature
ISBN: 3031132130
Category : Mathematics
Languages : en
Pages : 213
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Book Description
This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.
Author: Michael H. Kutner
Publisher: McGraw-Hill/Irwin
ISBN: 9780072386882
Category : Mathematics
Languages : en
Pages : 1396
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Book Description
Linear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
Author: Granville Tunnicliffe Wilson
Publisher: CRC Press
ISBN: 1420011502
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vect
Author: Jan Ulbricht
Publisher:
ISBN: 9783868536317
Category :
Languages : de
Pages : 198
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Book Description
Author: Wayne A. Fuller
Publisher: John Wiley & Sons
ISBN: 9780471552390
Category : Mathematics
Languages : en
Pages : 738
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Book Description
The subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accommodate a wide variety of readers, review material,especially on elementary results in Fourier analysis, large samplestatistics, and difference equations, has been included.
Author: Wayne A. Woodward
Publisher: CRC Press
ISBN: 100055533X
Category : Mathematics
Languages : en
Pages : 529
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Book Description
Data Science students and practitioners want to find a forecast that “works” and don’t want to be constrained to a single forecasting strategy, Time Series for Data Science: Analysis and Forecasting discusses techniques of ensemble modelling for combining information from several strategies. Covering time series regression models, exponential smoothing, Holt-Winters forecasting, and Neural Networks. It places a particular emphasis on classical ARMA and ARIMA models that is often lacking from other textbooks on the subject. This book is an accessible guide that doesn’t require a background in calculus to be engaging but does not shy away from deeper explanations of the techniques discussed. Features: Provides a thorough coverage and comparison of a wide array of time series models and methods: Exponential Smoothing, Holt Winters, ARMA and ARIMA, deep learning models including RNNs, LSTMs, GRUs, and ensemble models composed of combinations of these models. Introduces the factor table representation of ARMA and ARIMA models. This representation is not available in any other book at this level and is extremely useful in both practice and pedagogy. Uses real world examples that can be readily found via web links from sources such as the US Bureau of Statistics, Department of Transportation and the World Bank. There is an accompanying R package that is easy to use and requires little or no previous R experience. The package implements the wide variety of models and methods presented in the book and has tremendous pedagogical use.
