Introduction to time series and forecasting /
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| Author / Creator: | Brockwell, Peter J. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | New York : Springer, c2002. |
| Description: | xiv, 434 p. : ill. ; 25 cm. + 1 computer optical disk (4 3/4 in.). |
| Language: | English |
| Series: | Springer texts in statistics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4621703 |
Table of Contents:
- Preface
- 1.. Introduction
- 1.1.. Examples of Time Series
- 1.2.. Objectives of Time Series Analysis
- 1.3.. Some Simple Time Series Models
- 1.3.1.. Some Zero-Mean Models
- 1.3.2.. Models with Trend and Seasonality
- 1.3.3.. A General Approach to Time Series Modeling
- 1.4.. Stationary Models and the Autocorrelation Function
- 1.4.1.. The Sample Autocorrelation Function
- 1.4.2.. A Model for the Lake Huron Data
- 1.5.. Estimation and Elimination of Trend and Seasonal Components
- 1.5.1.. Estimation and Elimination of Trend in the Absence of Seasonality
- 1.5.2.. Estimation and Elimination of Both Trend and Seasonality
- 1.6.. Testing the Estimated Noise Sequence
- Problems
- 2.. Stationary Processes
- 2.1.. Basic Properties
- 2.2.. Linear Processes
- 2.3.. Introduction to ARMA Processes
- 2.4.. Properties of the Sample Mean and Autocorrelation Function
- 2.4.1.. Estimation of [mu]
- 2.4.2.. Estimation of [gamma]([middle dot]) and [rho]([middle dot])
- 2.5.. Forecasting Stationary Time Series
- 2.5.1.. The Durbin-Levinson Algorithm
- 2.5.2.. The Innovations Algorithm
- 2.5.3.. Prediction of a Stationary Process in Terms of Infinitely Many Past Values
- 2.6.. The Wold Decomposition
- Problems
- 3.. ARMA Models
- 3.1.. ARMA(p, q) Processes
- 3.2.. The ACF and PACF of an ARMA(p, q) Process
- 3.2.1.. Calculation of the ACVF
- 3.2.2.. The Autocorrelation Function
- 3.2.3.. The Partial Autocorrelation Function
- 3.2.4.. Examples
- 3.3.. Forecasting ARMA Processes
- Problems
- 4.. Spectral Analysis
- 4.1.. Spectral Densities
- 4.2.. The Periodogram
- 4.3.. Time-Invariant Linear Filters
- 4.4.. The Spectral Density of an ARMA Process
- Problems
- 5.. Modeling and Forecasting with ARMA Processes
- 5.1.. Preliminary Estimation
- 5.1.1.. Yule-Walker Estimation
- 5.1.2.. Burg's Algorithm
- 5.1.3.. The Innovations Algorithm
- 5.1.4.. The Hannan-Rissanen Algorithm
- 5.2.. Maximum Likelihood Estimation
- 5.3.. Diagnostic Checking
- 5.3.1.. The Graph of {{R[subscript t], t = 1, ..., n{{
- 5.3.2.. The Sample ACF of the Residuals
- 5.3.3.. Tests for Randomness of the Residuals
- 5.4.. Forecasting
- 5.5.. Order Selection
- 5.5.1.. The FPE Criterion
- 5.5.2.. The AICC Criterion
- Problems
- 6.. Nonstationary and Seasonal Time Series Models
- 6.1.. ARIMA Models for Nonstationary Time Series
- 6.2.. Identification Techniques
- 6.3.. Unit Roots in Time Series Models
- 6.3.1.. Unit Roots in Autoregressions
- 6.3.2.. Unit Roots in Moving Averages
- 6.4.. Forecasting ARIMA Models
- 6.4.1.. The Forecast Function
- 6.5.. Seasonal ARIMA Models
- 6.5.1.. Forecasting SARIMA Processes
- 6.6.. Regression with ARMA Errors
- 6.6.1.. OLS and GLS Estimation
- 6.6.2.. ML Estimation
- Problems
- 7.. Multivariate Time Series
- 7.1.. Examples
- 7.2.. Second-Order Properties of Multivariate Time Series
- 7.3.. Estimation of the Mean and Covariance Function
- 7.3.1.. Estimation of [mu]
- 7.3.2.. Estimation of [Gamma](h)
- 7.3.3.. Testing for Independence of Two Stationary Time Series
- 7.3.4.. Bartlett's Formula
- 7.4.. Multivariate ARMA Processes
- 7.4.1.. The Covariance Matrix Function of a Causal ARMA Process
- 7.5.. Best Linear Predictors of Second-Order Random Vectors
- 7.6.. Modeling and Forecasting with Multivariate AR Processes
- 7.6.1.. Estimation for Autoregressive Processes Using Whittle's Algorithm
- 7.6.2.. Forecasting Multivariate Autoregressive Processes
- 7.7.. Cointegration
- Problems
- 8.. State-Space Models
- 8.1.. State-Space Representations
- 8.2.. The Basic Structural Model
- 8.3.. State-Space Representation of ARIMA Models
- 8.4.. The Kalman Recursions
- 8.5.. Estimation For State-Space Models
- 8.6.. State-Space Models with Missing Observations
- 8.7.. The EM Algorithm
- 8.8.. Generalized State-Space Models
- 8.8.1.. Parameter-Driven Models
- 8.8.2.. Observation-Driven Models
- Problems
- 9.. Forecasting Techniques
- 9.1.. The ARAR Algorithm
- 9.1.1.. Memory Shortening
- 9.1.2.. Fitting a Subset Autoregression
- 9.1.3.. Forecasting
- 9.1.4.. Application of the ARAR Algorithm
- 9.2.. The Holt-Winters Algorithm
- 9.2.1.. The Algorithm
- 9.2.2.. Holt-Winters and ARIMA Forecasting
- 9.3.. The Holt-Winters Seasonal Algorithm
- 9.3.1.. The Algorithm
- 9.3.2.. Holt-Winters Seasonal and ARIMA Forecasting
- 9.4.. Choosing a Forecasting Algorithm
- Problems
- 10.. Further Topics
- 10.1.. Transfer Function Models
- 10.1.1.. Prediction Based on a Transfer Function Model
- 10.2.. Intervention Analysis
- 10.3.. Nonlinear Models
- 10.3.1.. Deviations from Linearity
- 10.3.2.. Chaotic Deterministic Sequences
- 10.3.3.. Distinguishing Between White Noise and iid Sequences
- 10.3.4.. Three Useful Classes of Nonlinear Models
- 10.3.5.. Modeling Volatility
- 10.4.. Continuous-Time Models
- 10.5.. Long-Memory Models
- Problems
- A.. Random Variables and Probability Distributions
- A.1.. Distribution Functions and Expectation
- A.2.. Random Vectors
- A.3.. The Multivariate Normal Distribution
- Problems
- B.. Statistical Complements
- B.1.. Least Squares Estimation
- B.1.1.. The Gauss-Markov Theorem
- B.1.2.. Generalized Least Squares
- B.2.. Maximum Likelihood Estimation
- B.2.1.. Properties of Maximum Likelihood Estimators
- B.3.. Confidence Intervals
- B.3.1.. Large-Sample Confidence Regions
- B.4.. Hypothesis Testing
- B.4.1.. Error Probabilities
- B.4.2.. Large-Sample Tests Based on Confidence Regions
- C.. Mean Square Convergence
- C.1.. The Cauchy Criterion
- D.. An ITSM Tutorial
- D.1.. Getting Started
- D.1.1.. Running ITSM
- D.2.. Preparing Your Data for Modeling
- D.2.1.. Entering Data
- D.2.2.. Information
- D.2.3.. Filing Data
- D.2.4.. Plotting Data
- D.2.5.. Transforming Data
- D.3.. Finding a Model for Your Data
- D.3.1.. Autofit
- D.3.2.. The Sample ACF and PACF
- D.3.3.. Entering a Model
- D.3.4.. Preliminary Estimation
- D.3.5.. The AICC Statistic
- D.3.6.. Changing Your Model
- D.3.7.. Maximum Likelihood Estimation
- D.3.8.. Optimization Results
- D.4.. Testing Your Model
- D.4.1.. Plotting the Residuals
- D.4.2.. ACF/PACF of the Residuals
- D.4.3.. Testing for Randomness of the Residuals
- D.5.. Prediction
- D.5.1.. Forecast Criteria
- D.5.2.. Forecast Results
- D.6.. Model Properties
- D.6.1.. ARMA Models
- D.6.2.. Model ACF, PACF
- D.6.3.. Model Representations
- D.6.4.. Generating Realizations of a Random Series
- D.6.5.. Spectral Properties
- D.7.. Multivariate Time Series
- References
- Index
