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Course in Time Series Analysis

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ISBN-10: 047136164X

ISBN-13: 9780471361640

Edition: 2001

Authors: Daniel Pe�a, George C. Tiao, Ruey S. Tsay, Daniel Pe�a

List price: $255.95
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Description:

This text derives from a number of presentations at the European Advance Course in Statistics (ECAS) in 1997. It aims to shed light on future directions of research in time series, and is written by many researchers in the fields of statistics and econometrics.
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Book details

List price: $255.95
Copyright year: 2001
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/4/2000
Binding: Hardcover
Pages: 496
Size: 6.34" wide x 9.57" long x 1.11" tall
Weight: 1.804
Language: English

Daniel Pe�a is a Pushcart Prize-winning writer and Assistant Professor in the Department of English at the University of Houston-Downtown. Formerly, he was based out of the UNAM in Mexico City where he worked as a writer, blogger, book reviewer and journalist. He is a Fulbright-Garcia Robles Scholar and a graduate of Cornell University. His fiction has appeared in Ploughshares, The Rumpus, the Kenyon Review Online, Callaloo, and Huizache among other venues. He's currently a regular contributor to the Guardian and the Ploughshares blog. BANG! is his debut novel. He lives in beautiful Houston, Texas.

Preface
About ECAS
Contributors
Introduction
Examples of time series problems
Stationary series
Nonstationary series
Seasonal series
Level shifts and outliers in time series
Variance changes
Asymmetric time series
Unidirectional-feedback relation between series
Comovement and cointegration
Overview of the book
Further reading
Basic Concepts in Univariate Time Series
Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, and State-Space Model
Linear time series models
The autocorrelation function
Lagged prediction and the partial autocorrelation function
Transformations to stationarity
Cycles and the periodogram
The spectrum
Further interpretation of time series acf, pacf, and spectrum
State-space models and the Kalman Filter
Univariate Autoregressive Moving-Average Models
Introduction
Univariate ARMA models
Outline of the chapter
Some basic properties of univariate ARMA models
The [phi] and [pi] weights
Stationarity condition and autocovariance structure of z[subscript t]
The autocorrelation function
The partial autocorrelation function
The extended autocorrelation function
Model specification strategy
Tentative specification
Tentative model specification via SEACF
Examples
Model Fitting and Checking, and the Kalman Filter
Prediction error and the estimation criterion
The likelihood of ARMA models
Likelihoods calculated using orthogonal errors
Properties of estimates and problems in estimation
Checking the fitted model
Estimation by fitting to the sample spectrum
Estimation of structural models by the Kalman filter
Prediction and Model Selection
Introduction
Properties of minimum mean-square error prediction
Prediction by the conditional expectation
Linear predictions
The computation of ARIMA forecasts
Interpreting the forecasts from ARIMA models
Nonseasonal models
Seasonal models
Prediction confidence intervals
Known parameter values
Unknown parameter values
Forecast updating
Computing updated forecasts
Testing model stability
The combination of forecasts
Model selection criteria
The FPE and AIC criteria
The Schwarz criterion
Conclusions
Outliers, Influential Observations, and Missing Data
Introduction
Types of outliers in time series
Additive outliers
Innovative outliers
Level shifts
Outliers and intervention analysis
Procedures for outlier identification and estimation
Estimation of outlier effects
Testing for outliers
Influential observations
Influence on time series
Influential observations and outliers
Multiple outliers
Masking effects
Procedures for multiple outlier identification
Missing-value estimation
Optimal interpolation and inverse autocorrelation function
Estimation of missing values
Forecasting with outliers
Other approaches
Appendix
Automatic Modeling Methods for Univariate Series
Classical model identification methods
Subjectivity of the classical methods
The difficulties with mixed ARMA models
Automatic model identification methods
Unit root testing
Penalty function methods
Pattern identification methods
Uniqueness of the solution and the purpose of modeling
Tools for automatic model identification
Test for the log-level specification
Regression techniques for estimating unit roots
The Hannan--Rissanen method
Liu's filtering method
Automatic modeling methods in the presence of outliers
Algorithms for automatic outlier detection and correction
Estimation and filtering techniques to speed up the algorithms
The need to robustify automatic modeling methods
An algorithm for automatic model identification in the presence of outliers
An automatic procedure for the general regression--ARIMA model in the presence of outlierw, special effects, and, possibly, missing observations
Missing observations
Trading day and Easter effects
Intervention and regression effects
Examples
Tabular summary
Seasonal Adjustment and Signal Extraction Time Series
Introduction
Some remarks on the evolution of seasonal adjustment methods
Evolution of the methodologic approach
The situation at present
The need for preadjustment
Model specification
Estimation of the components
Stationary case
Nonstationary series
Historical or final estimator
Properties of final estimator
Component versus estimator
Covariance between estimators
Estimators for recent periods
Revisions in the estimator
Structure of the revision
Optimality of the revisions
Inference
Optical Forecasts of the Components
Estimation error
Growth rate precision
The gain from concurrent adjustment
Innovations in the components (pseudoinnovations)
An example
Relation with fixed filters
Short-versus long-term trends; measuring economic cycles
Advanced Topics in Univariate Time Series
Heteroscedastic Models
The ARCH model
Some simple properties of ARCH models
Weaknesses of ARCH models
Building ARCH models
An illustrative example
The GARCH Model
An illustrative example
Remarks
The exponential GARCH model
An illustrative example
The CHARMA model
Random coefficient autoregressive (RCA) model
Stochastic volatility model
Long-memory stochastic volatility model
Nonlinear Time Series Models: Testing and Applications
Introduction
Nonlinearity tests
The test
Comparison and application
The Tar model
U.S. real GNP
Postsample forecasts and discussion
Concluding remarks
Bayesian Time Series Analysis
Introduction
A general univariate time series model
Estimation
Gibbs sampling
Griddy Gibbs
An illustrative example
Model discrimination
A mixed model with switching
Implementation
Examples
Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression, and Quantile Regression
Introduction
Nonparametric regression
Kernel estimation in time series
Problems of simple kernel estimation and restricted approaches
Locally weighted regression
Applications of locally weighted regression to time series
Parameter selection
Time series decomposition with locally weighted regression
Neural Network Models
Introduction
The multilayer perceptron
Autoregressive neural network models
Example: Sunspot series
The recurrent perceptron
Examples of recurrent neural network models
A unifying view
Multivariate Time Series
Vector ARMA Models
Introduction
Transfer function or unidirectional models
The vector ARMA model
Some simple examples
Relationship to transfer function model
Cross-covariance and correlation matrices
The partial autoregression matrices
Model building strategy for multiple time series
Tentative specification
Estimation
Diagnostic checking
Analyses of three examples
The SCC data
The gas furnace data
The census housing data
Structural analysis of multivariate time series
A canonical analysis of multiple time series
Scalar component models in multiple time series
Scalar component models
Exchangeable models and overparameterization
Model specification via canonical correlation analysis
An illustrative example
Some further remarks
Cointegration in the VAR Model
Introduction
Basic definitions
Solving autoregressive equations
Some examples
An inversion theorem for matrix polynomials
Granger's representation
Prediction
The statistical model for I(1) variables
Hypotheses on cointegrating relations
Estimation of cointegrating vectors and calculation of test statistics
Estimation of [beta] under restrictions
Asymptotic theory
Asymptotic results
Test for cointegrating rank
Asymptotic distribution of [beta] and test for restrictions on [beta]
Various applications of the cointegration model
Rational expectations
Arbitrage pricing theory
Seasonal cointegration
Identification of Linear Dynamic Multiinput/Multioutput Systems
Introduction and problem statement
Representations of linear systems
Input/output representations
Solutions of linear vector difference equations (VDEs)
ARMA and state-space representations
The structure of state-space systems
The structure of ARMA systems
The realization of state-space systems
General structure
Echelon forms
The realization of ARMA systems
Parametrization
Estimation of real-valued parameters
Dynamic specification
Index
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