Bootstrap and Inference for Some Linear Time Series Models PDF Download
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Author: Michael Raymond Allen
Publisher:
ISBN:
Category :
Languages : en
Pages : 220
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Author: Michael Raymond Allen
Publisher:
ISBN:
Category :
Languages : en
Pages : 220
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Book Description
Author: Tucker S. McElroy
Publisher: CRC Press
ISBN: 1439876525
Category : Mathematics
Languages : en
Pages : 587
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Book Description
Time Series: A First Course with Bootstrap Starter provides an introductory course on time series analysis that satisfies the triptych of (i) mathematical completeness, (ii) computational illustration and implementation, and (iii) conciseness and accessibility to upper-level undergraduate and M.S. students. Basic theoretical results are presented in a mathematically convincing way, and the methods of data analysis are developed through examples and exercises parsed in R. A student with a basic course in mathematical statistics will learn both how to analyze time series and how to interpret the results. The book provides the foundation of time series methods, including linear filters and a geometric approach to prediction. The important paradigm of ARMA models is studied in-depth, as well as frequency domain methods. Entropy and other information theoretic notions are introduced, with applications to time series modeling. The second half of the book focuses on statistical inference, the fitting of time series models, as well as computational facets of forecasting. Many time series of interest are nonlinear in which case classical inference methods can fail, but bootstrap methods may come to the rescue. Distinctive features of the book are the emphasis on geometric notions and the frequency domain, the discussion of entropy maximization, and a thorough treatment of recent computer-intensive methods for time series such as subsampling and the bootstrap. There are more than 600 exercises, half of which involve R coding and/or data analysis. Supplements include a website with 12 key data sets and all R code for the book's examples, as well as the solutions to exercises.
Author: Mikael Gredenhoff
Publisher: Stockholm School of Economics Efi Economic Research Institut
ISBN:
Category : Business & Economics
Languages : en
Pages : 170
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Author: Yicong Lin
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We propose two robust bootstrap-based simultaneous inference methods for time series models featuring time-varying coefficients and conduct an extensive simulation study to assess their performance. Our exploration covers a wide range of scenarios, encompassing serially correlated, heteroscedastic, endogenous, nonlinear, and nonstationary error processes. Additionally, we consider situations where the regressors exhibit unit roots, thus delving into a nonlinear cointegration framework. We find that the proposed moving block bootstrap and sieve wild bootstrap methods show superior, robust small sample performance, in terms of empirical coverage and length, compared to the sieve bootstrap introduced by Friedrich and Lin (2022) for stationary models. We then revisit two empirical studies: herding effects in the Chinese new energy market and consumption behaviors in the U.S. Our findings strongly support the presence of herding behaviors before 2016, aligning with earlier studies. However, we diverge from previous research by finding no substantial herding evidence between around 2018 and 2021. In the second example, we find a time-varying cointegrating relationship between consumption and income in the U.S.
Author: Dimitris N. Politis
Publisher: CRC Press
ISBN: 0429527225
Category : Mathematics
Languages : en
Pages : 427
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Book Description
Time Series: A First Course with Bootstrap Starter provides an introductory course on time series analysis that satisfies the triptych of (i) mathematical completeness, (ii) computational illustration and implementation, and (iii) conciseness and accessibility to upper-level undergraduate and M.S. students. Basic theoretical results are presented in a mathematically convincing way, and the methods of data analysis are developed through examples and exercises parsed in R. A student with a basic course in mathematical statistics will learn both how to analyze time series and how to interpret the results. The book provides the foundation of time series methods, including linear filters and a geometric approach to prediction. The important paradigm of ARMA models is studied in-depth, as well as frequency domain methods. Entropy and other information theoretic notions are introduced, with applications to time series modeling. The second half of the book focuses on statistical inference, the fitting of time series models, as well as computational facets of forecasting. Many time series of interest are nonlinear in which case classical inference methods can fail, but bootstrap methods may come to the rescue. Distinctive features of the book are the emphasis on geometric notions and the frequency domain, the discussion of entropy maximization, and a thorough treatment of recent computer-intensive methods for time series such as subsampling and the bootstrap. There are more than 600 exercises, half of which involve R coding and/or data analysis. Supplements include a website with 12 key data sets and all R code for the book's examples, as well as the solutions to exercises.
Author: Dimitris N. Politis
Publisher: Springer
ISBN: 3319213474
Category : Mathematics
Languages : en
Pages : 256
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Book Description
The Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i.e., going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful. Interestingly, being able to predict a response variable Y associated with a regressor variable X taking on any possible value seems to inadvertently also achieve the main goal of modeling, i.e., trying to describe how Y depends on X. Hence, as prediction can be treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product of being able to perform prediction. In other words, a practitioner can use Model-Free Prediction ideas in order to additionally obtain point estimates and confidence intervals for relevant parameters leading to an alternative, transformation-based approach to statistical inference.
Author: Marc S. Paolella
Publisher: John Wiley & Sons
ISBN: 1119431859
Category : Mathematics
Languages : en
Pages : 900
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Book Description
A comprehensive and timely edition on an emerging new trend in time series Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH sets a strong foundation, in terms of distribution theory, for the linear model (regression and ANOVA), univariate time series analysis (ARMAX and GARCH), and some multivariate models associated primarily with modeling financial asset returns (copula-based structures and the discrete mixed normal and Laplace). It builds on the author's previous book, Fundamental Statistical Inference: A Computational Approach, which introduced the major concepts of statistical inference. Attention is explicitly paid to application and numeric computation, with examples of Matlab code throughout. The code offers a framework for discussion and illustration of numerics, and shows the mapping from theory to computation. The topic of time series analysis is on firm footing, with numerous textbooks and research journals dedicated to it. With respect to the subject/technology, many chapters in Linear Models and Time-Series Analysis cover firmly entrenched topics (regression and ARMA). Several others are dedicated to very modern methods, as used in empirical finance, asset pricing, risk management, and portfolio optimization, in order to address the severe change in performance of many pension funds, and changes in how fund managers work. Covers traditional time series analysis with new guidelines Provides access to cutting edge topics that are at the forefront of financial econometrics and industry Includes latest developments and topics such as financial returns data, notably also in a multivariate context Written by a leading expert in time series analysis Extensively classroom tested Includes a tutorial on SAS Supplemented with a companion website containing numerous Matlab programs Solutions to most exercises are provided in the book Linear Models and Time-Series Analysis: Regression, ANOVA, ARMA and GARCH is suitable for advanced masters students in statistics and quantitative finance, as well as doctoral students in economics and finance. It is also useful for quantitative financial practitioners in large financial institutions and smaller finance outlets.
Author: Yang Li
Publisher:
ISBN: 9781361330562
Category :
Languages : en
Pages :
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Book Description
This dissertation, "Statistical Inference for Some Econometric Time Series Models" by Yang, Li, 李杨, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: With the increasingly economic activities, people have more and more interest in econometric models. There are two mainstream econometric models which are very popular in recent decades. One is quantile autoregressive (QAR) model which allows varying-coefficients in linear time series and greatly promotes the ranges of regression research. The first topic of this thesis is to focus on the modeling of QAR model. We propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to QAR models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the Box-Jenkins three-stage procedure (model identification, model parameter estimation, and model diagnostic checking) from classical autoregressive models to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung- Box test. Moreover, we obtain the bootstrap approximations to the distributions of parameter estimators and proposed measures. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate the usefulness of QAR model. The other important econometric model is autoregressive conditional duration (ACD) model which is developed with the purpose of depicting ultra high frequency (UHF) financial time series data. The second topic of this thesis is designed to incorporate ACD model with one of the extreme value distributions, i.e. Frechet distribution. We apply the maximum likelihood estimation (MLE) to Frechet ACD models and derive its generalized residuals for model adequacy checking. It is noteworthy that simulations show a relative greater sensitiveness in the linear parameters to sampling errors. This phenomenon successfully reflects the skewness of the Frechet distribution and suggests a method to practitioners in proceeding model accuracy. Furthermore, we present the empirical sizes and powers for Box-Pierce, Ljung-Box and modified Box-Pierce statistics as comparisons of the proposed portmanteau statistic. In addition to the Frechet ACD, we also systematically analyze theWeibull ACD, where the Weibull distribution is the other nonnegative extreme value distribution. The last topic of the thesis explains the estimation and diagnostic checking the Weibull ACD model. By investigating the MLE in this model, there exhibits a slight sensitiveness in linear parameters. However, there is an obvious phenomenon on the trade-off between the skewness of Weibull distribution and the sampling error when the simulations are conducted. Moreover, the asymptotic properties are also studied for the generalized residuals and a goodness-of-fit test is employed to obtain a portmanteau statistic. Through the simulation results in size and power, it shows that Weibull ACD is superior to Frechet ACD in specifying the wrong model. This is meaningful in practice. DOI: 10.5353/th_b5153693 Subjects: Econometrics Time-series analysis
Author: Gerhard Dikta
Publisher: Springer Nature
ISBN: 3030734803
Category : Mathematics
Languages : en
Pages : 256
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Book Description
This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
Author: Raquel Prado
Publisher: CRC Press
ISBN: 1420093363
Category : Mathematics
Languages : en
Pages : 375
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Book Description
Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers. The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB® code, and other material are available on the authors’ websites. Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.
