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Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series
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Book Synopsis Sieve Bootstrap Based Prediction Intervals and Unit Root Tests for Time Series by : Maduka Nilanga Rupasinghe
Download or read book Sieve Bootstrap Based Prediction Intervals and Unit Root Tests for Time Series written by Maduka Nilanga Rupasinghe and published by . This book was released on 2012 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for such processes are established, and the finite sample properties are examined by employing Monte Carlo simulations. The Monte Carlo simulation study shows that the proposed method works well for both ARIMA and FARIMA processes. Following the existing sieve bootstrap frame-work for testing unit roots for nonseasonal processes, we propose new bootstrap-based unit root tests for seasonal time series. In this procedure, the bootstrap distributions of the well known Dickey-Hasza-Fuller (DHF) seasonal test statistics are obtained and utilized to determine the critical points for the test. The asymptotic properties of the proposed method are established and a Monte Carlo simulation study is employed to demonstrate that the proposed unit root tests yield higher powers compared to the DHF test. Also, a sieve bootstrap method is implemented to obtaining prediction intervals for time series with seasonal unit roots. The asymptotic properties of the proposed prediction intervals are established and a Monte Carlo simulation study is carried out to examine the finite sample validity. Finally, we derive expressions for the asymptotic distributions of the Dickey-Fuller (DHF) type test statistics, under weakly dependent errors and show that they can be expressed as functional of the standard Brownian motions. Currently, the asymptotic results are available only for non-seasonal time series"--Abstract, leaf v.
Book Synopsis Sieve Bootstrap-based Prediction Intervals for GARCH Processes by : Garrett Tresch
Download or read book Sieve Bootstrap-based Prediction Intervals for GARCH Processes written by Garrett Tresch and published by . This book was released on 2015 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time Series deals with observing a variable--interest rates, exchange rates, rainfall, etc.--at regular intervals of time. The main objectives of Time Series analysis are to understand the underlying processes and effects of external variables in order to predict future values. Time Series methodologies have wide applications in the fields of business where mathematics is necessary. The Generalized Autoregressive Conditional Heteroscedasic (GARCH) models are extensively used in finance and econometrics to model empirical time series in which the current variation, known as volatility, of an observation is depending upon the past observations and past variations. Various drawbacks of the existing methods for obtaining prediction intervals include: the assumption that the orders associated with the GARCH process are known; and the heavy computational time involved in fitting numerous GARCH processes. This paper proposes a novel and computationally efficient method for the creation of future prediction intervals using the Sieve Bootstrap, a promising resampling procedure for Autoregressive Moving Average (ARMA) processes. This bootstrapping technique remains efficient when computing future prediction intervals for the returns as well as the volatilities of GARCH processes and avoids extensive computation and parameter estimation. Both the included Monte Carlo simulation study and the exchange rate application demonstrate that the proposed method works very well under normal distributed errors.
Book Synopsis A Modified Approach for Obtaining Sieve Bootstrap Prediction Intervals for Time Series by : Purna Mukhopadhyay
Download or read book A Modified Approach for Obtaining Sieve Bootstrap Prediction Intervals for Time Series written by Purna Mukhopadhyay and published by . This book was released on 2008 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The traditional Box-Jenkins approach to obtaining prediction intervals for stationary time seres assumes that the underlying distribution of the innovations is Gaussian. It is well known that deviations from this assumption can lead to prediction intervals with poor coverage. Nonparametric bootstrap-based procedures for obtaining prediction intervals overcome this handicap, but many early versions of such intervals for autoregressive moving average (ARMA) processes assume that the autoregressive and moving average orders, p, q respectively, are known, The sieve bootstrap, first introduced by Bühlmann in 1997, sidesteps this assumption for invertible time series by approximating the ARMA process by a finite autoregressive model whose order is estimated by using a model procedure such as the AICC. Existing sieve bootstrap methods in general, however, produces liberal prediction intervals due to several factors, including the use of residuals that underestimate the actual variance of the innovations and the failure of the methods to capture variations due to sampling error of some parameter estimates. In this dissertation, a modified sieve bootstrap approach, that corrects these deficiencies, is implemented to obtain prediction intervals for both univariate and multivariate time series. Monte Carlo simulations results show that the modifications provide prediction intervals that achieve nominal or near nominal coverage probabilities. Asymptotic results for the univariate series also establish the validity of the modified approach"--Abstract, leaf iii.
Book Synopsis Prediction Intervals for Fractionally Integrated Time Series and Volatility Models by : Ekanayake Mudiyanselage Rukman Sumedha Bandara Ekanayake
Download or read book Prediction Intervals for Fractionally Integrated Time Series and Volatility Models written by Ekanayake Mudiyanselage Rukman Sumedha Bandara Ekanayake and published by . This book was released on 2021 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The two of the main formulations for modeling long range dependence in volatilities associated with financial time series are fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) and hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models. The traditional methods of constructing prediction intervals for volatility models, either employ a Gaussian error assumption or are based on asymptotic theory. However, many empirical studies show that the distribution of errors exhibit leptokurtic behavior. Therefore, the traditional prediction intervals developed for conditional volatility models yield poor coverage. An alternative is to employ residual bootstrap-based prediction intervals. One goal of this dissertation research is to develop methods for constructing such prediction intervals for both returns and volatilities under FIGARCH and HYGARCH model formulations. In addition, this methodology is extended to obtain prediction intervals for autoregressive moving average (ARMA) and fractionally integrated autoregressive moving average (FARIMA) models with a FIGARCH error structure. The residual resampling is done via a sieve bootstrap approach, which approximates the ARMA and FARIMA portions of the models with an AR component. AIC criteria is used to find order of the finite AR approximation on the conditional mean process. The advantage of the sieve bootstrap method is that it does not require any knowledge of the order of the conditional mean process. However, we assume that the order of the FIGARCH part is known. Monte-Carlo simulation studies show that the proposed methods provide coverages closed to the nominal values"--Abstract, page iv.
Book Synopsis Unit Root Tests in Time Series Volume 1 by : K. Patterson
Download or read book Unit Root Tests in Time Series Volume 1 written by K. Patterson and published by Springer. This book was released on 2011-02-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Testing for a unit root is now an essential part of time series analysis. This volume provides a critical overview and assessment of tests for a unit root in time series, developing the concepts necessary to understand the key theoretical and practical models in unit root testing.
Book Synopsis Unit Root Tests in Time Series Volume 2 by : K. Patterson
Download or read book Unit Root Tests in Time Series Volume 2 written by K. Patterson and published by Springer. This book was released on 2012-07-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Testing for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.
Book Synopsis Bootstrap Prediction Intervals for Multivariate Time Series by : Florian Sebastian Rueck
Download or read book Bootstrap Prediction Intervals for Multivariate Time Series written by Florian Sebastian Rueck and published by . This book was released on 2005 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The theory and methodology of obtaining bootstrap prediction intervals for univariate time series using the forward representation of the series is extended to vector autoregressive (VAR) models. Kim has shown that simultaneous prediction intervals based on the Bonferroni method and the backward representation of the time series achieve coverage close to nominal when the parameter estimates are corrected for small sample bias. To utilize his method, it is necessary to assume that the innovations are normally distributed to maintain independence of the innovations associated with the backward representation of the time series. This assumption is not necessary if the forward representation is used. Bootstrap prediction intervals based on the forward representation of the time series, are less restrictive and thus can also be adapted for time series that do not have a backward representation. The asymptotic validity of the proposed bootstrap method is established and small sample properties are studied using Monte Carlo simulation"--Abstract, leaf iii.
Book Synopsis Sieve Bootstrap Unit Root Tests by : Patrick Richard
Download or read book Sieve Bootstrap Unit Root Tests written by Patrick Richard and published by . This book was released on 2007 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We consider the use of a sieve bootstrap based on moving average (MA) and autoregressive moving average (ARMA) approximations to test the unit root hypothesis when the true Data Generating Process (DGP) is a general linear process. We provide invariance principles for these bootstrap DGPs and we prove that the resulting ADF tests are asymptotically valid. Our simulations indicate that these tests sometimes outperform those based on the usual autoregressive (AR) sieve bootstrap. We study the reasons for the failure of the AR sieve bootstrap tests and propose some solutions, including a modified version of the fast double bootstrap." --
Book Synopsis Bootstrap Prediction Intervals for Time Series by : Li Pan
Download or read book Bootstrap Prediction Intervals for Time Series written by Li Pan and published by . This book was released on 2013 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct bootstrap prediction intervals for linear autoregressions, nonlinear autoregressions, nonparametric autoregressions and Markov processes. Several forward and backward bootstrap methods using predictive residuals and fitted residuals are introduced and applied to those time series. We describe exact algorithms for these different models and show that the bootstrap intervals properly estimate the distribution of the future values. In simulations using standard time series models, we compare the prediction intervals of different methods with regards to coverage level and length of interval.
Book Synopsis A Hybrid Bootstrap Approach to Unit Root Tests by : Chenlei Leng
Download or read book A Hybrid Bootstrap Approach to Unit Root Tests written by Chenlei Leng and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article proposes a hybrid bootstrap approach to approximate the augmented Dickey-Fuller test by perturbing both the residual sequence and the minimand of the objective function. Since innovations can be dependent, this allows the inclusion of conditional heteroscedasticity models. The new bootstrap method is also applied to least absolute deviation-based unit root test statistics, which are efficient in handling heavy-tailed time-series data. The asymptotic distributions of resulting bootstrap tests are presented, and Monte Carlo studies demonstrate the usefulness of the proposed tests.
Book Synopsis An Introduction to Bootstrap Methods with Applications to R by : Michael R. Chernick
Download or read book An Introduction to Bootstrap Methods with Applications to R written by Michael R. Chernick and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to bootstrap methods in the R programming environment Bootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. An Introduction to Bootstrap Methods with Applications to R explores the practicality of this approach and successfully utilizes R to illustrate applications for the bootstrap and other resampling methods. This book provides a modern introduction to bootstrap methods for readers who do not have an extensive background in advanced mathematics. Emphasis throughout is on the use of bootstrap methods as an exploratory tool, including its value in variable selection and other modeling environments. The authors begin with a description of bootstrap methods and its relationship to other resampling methods, along with an overview of the wide variety of applications of the approach. Subsequent chapters offer coverage of improved confidence set estimation, estimation of error rates in discriminant analysis, and applications to a wide variety of hypothesis testing and estimation problems, including pharmaceutical, genomics, and economics. To inform readers on the limitations of the method, the book also exhibits counterexamples to the consistency of bootstrap methods. An introduction to R programming provides the needed preparation to work with the numerous exercises and applications presented throughout the book. A related website houses the book's R subroutines, and an extensive listing of references provides resources for further study. Discussing the topic at a remarkably practical and accessible level, An Introduction to Bootstrap Methods with Applications to R is an excellent book for introductory courses on bootstrap and resampling methods at the upper-undergraduate and graduate levels. It also serves as an insightful reference for practitioners working with data in engineering, medicine, and the social sciences who would like to acquire a basic understanding of bootstrap methods.
Book Synopsis Bootstrap Prediction Intervals in State-Space Models by : Esther Ruiz
Download or read book Bootstrap Prediction Intervals in State-Space Models written by Esther Ruiz and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prediction intervals in state-space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, with the true parameters substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty caused by parameter estimation. Second, the Gaussianity of future innovations assumption may be inaccurate. To overcome these drawbacks, Wall and Stoffer [Journal of Time Series Analysis (2002) Vol. 23, pp. 733-751] propose a bootstrap procedure for evaluating conditional forecast errors that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. In this article, we propose a bootstrap procedure for constructing prediction intervals directly for the observations, which does not need the backward representation of the model. Consequently, its application is much simpler, without losing the good behaviour of bootstrap prediction intervals. We study its finite-sample properties and compare them with those of the standard and the Wall and Stoffer procedures for the local level model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.
Book Synopsis Unit Root Tests in Time Series and Stochastic Volatility Models by :
Download or read book Unit Root Tests in Time Series and Stochastic Volatility Models written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing appropriate forecasts of time series data into the future depends crucially on whether the time series under consideration is non-stationary (i.e. has a unit root) or stationary. In the context of a Stochastic Volatility Model (SVM), the presence of a unit root in financial data has important implications for the pricing of various financial instruments. We propose a unit root test for the volatility process based on the Simulation-Extrapolation (SIMEX) approach. We express the SVM as a measurement error model and propose a Simulation-Extrapolation (SIMEX)-based approach to test for the unit root hypothesis. The asymptotic theory of the Ordinary Least Squares (OLS) and Weighted Symmetric (WS) estimators are exploited to obtain SIMEX-based tests and simulation studies are provided to demonstrate that the SIMEX-based test compares favorably with some of the well known unit root tests already available in the literature. We also propose a unit root test based on the maximum order statistic in a simple autoregressive (AR) model of order 1. The asymptotic distribution of the test statistic under the null hypothesis is derived and the approximate percentiles are also provided. Through simulation studies, the proposed test is compared with the Dickey-Fuller (DF) test under various specifications for the error distributions. In the final chapter of this dissertation, we propose a procedure to test the null hypothesis of stationarity in AR (1) models. The procedure is based on the Intersection-Union tests used in Bio-Equivalence studies. The performance of the test based on finite sample percentiles as well as asymptotic percentiles is assessed using simulation studies.
Book Synopsis Analysis of Integrated and Cointegrated Time Series with R by : Bernhard Pfaff
Download or read book Analysis of Integrated and Cointegrated Time Series with R written by Bernhard Pfaff and published by Springer Science & Business Media. This book was released on 2008-09-03 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for self study. The reader can apply the theoretical concepts directly within R by following the examples.
Book Synopsis On Bootstrap Prediction Intervals for Gaussian Time Series by : Paul Kabaila
Download or read book On Bootstrap Prediction Intervals for Gaussian Time Series written by Paul Kabaila and published by . This book was released on 1998 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essays on Unit Root Testing in Time Series by : Xiao Zhong
Download or read book Essays on Unit Root Testing in Time Series written by Xiao Zhong and published by . This book was released on 2015 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Unit root tests are frequently employed by applied time series analysts to determine if the underlying model that generates an empirical process has a component that can be well-described by a random walk. More specifically, when the time series can be modeled using an autoregressive moving average (ARMA) process, such tests aim to determine if the autoregressive (AR) polynomial has one or more unit roots. The effect of economic shocks do not diminish with time when there is one or more unit roots in the AR polynomial, whereas the contribution of shocks decay geometrically when all the roots are outside the unit circle. This is one major reason for economists' interest in unit root tests. Unit roots processes are also useful in modeling seasonal time series, where the autoregressive polynomial has a factor of the form (1-[zeta][superscript s]), and s is the period of the season. Such roots are called seasonal unit roots. Techniques for testing the unit roots have been developed by many researchers since late 1970s. Most such tests assume that the errors (shocks) are independent or weakly dependent. Only a few tests allow conditionally heteroskedastic error structures, such as Generalized Autoregressive Conditionally Heteroskedastic (GARCH) error. And only a single test is available for testing multiple unit roots. In this dissertation, three papers are presented. Paper I deals with developing bootstrap-based tests for multiple unit roots; Paper II extends a bootstrap-based unit root test to higher order autoregressive process with conditionally heteroscedastic error; and Paper III extends a currently available seasonal unit root test to a bootstrap-based one while at the same time relaxing the assumption of weakly dependent shocks to include conditional heteroscedasticity in the error structure"--Abstract, page iv.
Book Synopsis Local Block Bootstrap Based Inference for Nonstationary Time Series by : Arif Dowla
Download or read book Local Block Bootstrap Based Inference for Nonstationary Time Series written by Arif Dowla and published by . This book was released on 2002 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
