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Author: Juanjuan Kong Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
A kernel distribution estimator (KDE) is proposed for multi-step-ahead prediction error distribution of autoregressive time series, based on prediction residuals. Under general assumptions, the KDE is proved to be oracally efficient as the infeasible KDE and the empirical cumulative distribution function (cdf) based on unobserved prediction errors. Quantile estimator is obtained from the oracally efficient KDE, and prediction interval for multi-step-ahead future observation is constructed using the estimated quantiles and shown to achieve asymptotically the nominal confidence levels. Simulation examples corroborate the asymptotic theory.
Author: Juanjuan Kong Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
A kernel distribution estimator (KDE) is proposed for multi-step-ahead prediction error distribution of autoregressive time series, based on prediction residuals. Under general assumptions, the KDE is proved to be oracally efficient as the infeasible KDE and the empirical cumulative distribution function (cdf) based on unobserved prediction errors. Quantile estimator is obtained from the oracally efficient KDE, and prediction interval for multi-step-ahead future observation is constructed using the estimated quantiles and shown to achieve asymptotically the nominal confidence levels. Simulation examples corroborate the asymptotic theory.
Author: Sa-aat Niwitpong Publisher: ISBN: Category : Gaussian processes Languages : en Pages : 324
Book Description
The thesis deals with three topics. The first topic concerns a comparison of the estimators in an unknown mean Gaussian AR(l) process via the mean, the median, the interquartile range and their distributions and also via the scaled prediction mean square error (PMSE) for a one-step-ahead predictor based on the estimator. The second topic concerns the relative efficiency of one-step-ahead prediction intervals in an unknown mean Gaussian AR(1) process. The third topic concerns the computation of a class of conditional expectations. Chapter 2 compares the estimators of an unknown mean Gaussian AR(1) process via their distributions. In Chapter 3, we compare eight different estimators of (o,p) in an unknown mean Gaussian AR(1) process via the scaled PMSE. Chapter 4 considers the relative efficiency of two estimators (o,p) using scaled PMSEs. One of these estimators is obtained after a preliminary unit root test in an unknown mean Gaussian AR(1) process.
Author: Yan Liu Publisher: Springer ISBN: 9811001529 Category : Mathematics Languages : en Pages : 136
Book Description
This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.
Author: Cagdas Hakan Aladag Publisher: Bentham Science Publishers ISBN: 1608053733 Category : Mathematics Languages : en Pages : 143
Book Description
"Time series analysis is applicable in a variety of disciplines such as business administration, economics, public finances, engineering, statistics, econometrics, mathematics and actuarial sciences. Forecasting the future assists in critical organizationa"
Author: Wayne A. Woodward Publisher: CRC Press ISBN: 100055533X Category : Mathematics Languages : en Pages : 529
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.
Author: C ̆alin Vamos ̧ Publisher: Springer Science & Business Media ISBN: 9400748248 Category : Science Languages : en Pages : 136
Book Description
Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.
Author: Khreshna I.A. Syuhada Publisher: ISBN: Category : Prediction theory Languages : en Pages : 390
Book Description
A very informative way of specifying the accuracy of a time series prediction is to use a prediction interval. This present thesis is concerned with prediction intervals in the context of models such as the autoregressive (AR) and the autoregressive conditional heteroscedastic (ARCH), commonly used for financial time series. Specifically, we aim to obtain improved prediction intervals and show that their coverage probability properties outperform those of estimative prediction intervals. To achieve this aim, we use analytical approaches as well as a new simulation-based approach. Finding the improved prediction interval analytically is carried out by employing the methods based on (a) Taylor expansion of the conditional distribution of a future observation and (b) the predictive density. These methods require the calculation of the expected information matrix and the asymptotic conditional bias of the parameter estimators.
Author: Juanjuan Kong
Author: Juanjuan Kong
Author: Sa-aat Niwitpong
Author: Yan Liu
Author: Cagdas Hakan Aladag
Author: Wayne A. Woodward
Author: R. D. Snyder
Author: W.Allen Spivey and William W. Wecker
Author: Shuwen Zhao
Author: C ̆alin Vamos ̧
Author: Khreshna I.A. Syuhada