Introduction to time series and forecasting /
Brockwell, Peter J.,
Introduction to time series and forecasting / Peter J. Brockwell, Richard A. Davis. - Second edition. - xiv, 434 pages : illustrations ; 24 cm + 1 computer optical laser disc (4 3/4 in.). - Springer texts in statistics . - Springer texts in statistics. .
Includes bibliographical references (pages 423-428) and index.
Cover -- Table of Contents -- Preface -- Chapter 1. Introduction -- 1.1. Examples of Time Series -- 1.2. Objectives of Time Series Analysis -- 1.3. Some Simple Time Series Models -- 1.4. Stationary Models and the Autocorrelation Function -- 1.5. Estimation and Elimination of Trend and Seasonal Components -- 1.6. Testing the Estimated Noise Sequence -- Problems -- Chapter 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 -- 2.5. Forecasting Stationary Time Series -- 2.6. The Wold Decomposition -- Problems -- Chapter 3. ARMA Models -- 3.1. ARMA(p, q) Processes -- 3.2. The ACF and PACF of an ARMA(p, q) Process -- 3.3. Forecasting ARMA Processes -- Problems -- Chapter 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 -- Chapter 5. Modeling and Forecasting with ARMA Processes -- 5.1. Preliminary Estimation -- 5.2. Maximum Likelihood Estimation -- 5.3. Diagnostic Checking -- 5.4. Forecasting -- 5.5. Order Selection -- Problems -- Chapter 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 -- 6.4. Forecasting ARIMA Models -- 6.5. Seasonal ARIMA Models -- 6.6. Regression with ARMA Errors -- Problems -- Chapter 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 -- 7.4. Multivariate ARMA Processes -- 7.5. Best Linear Predictors of Second-Order Random Vectors -- 7.6. Modeling and Forecasting with Multivariate AR Processes -- 7.7. Cointegration -- Problems -- Chapter 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 -- Problems -- Chapter 9. Forecasting Techniques -- 9.1. The ARAR Algorithm -- 9.2. The Holt ... Winters Algorithm -- 9.3. The Holt ... Winters Seasonal Algorithm -- 9.4. Choosing a Forecasting Algorithm -- Problems -- Chapter 10. Further Topics -- 10.1. Transfer Function Models -- 10.2. Intervention Analysis -- 10.3. Nonlinear Models -- 10.4. Continuous-Time Models -- 10.5. Long-Memory Models -- Problems -- Appendix A. Random Variables and Probability Distributions -- A.1. Distribution Functions and Expectation -- A.2. Random Vectors -- A.3. The Multivariate Normal Distribution -- Problems -- Appendix B. Statistical Complements -- B.1. Least Squares Estimation -- B.2. Maximum Likelihood Estimation -- B.3. Confidence Intervals -- B.4. Hypothesis Testing -- Appendix C. Mean Square Convergence -- C.1. The Cauchy Criterion.
9798181284043 8181284046 0387953515
Time-series analysis.
MATHEMATICS--Probability & Statistics--Time Series.
Time-series analysis.
519.55 / B.P.I.
Introduction to time series and forecasting / Peter J. Brockwell, Richard A. Davis. - Second edition. - xiv, 434 pages : illustrations ; 24 cm + 1 computer optical laser disc (4 3/4 in.). - Springer texts in statistics . - Springer texts in statistics. .
Includes bibliographical references (pages 423-428) and index.
Cover -- Table of Contents -- Preface -- Chapter 1. Introduction -- 1.1. Examples of Time Series -- 1.2. Objectives of Time Series Analysis -- 1.3. Some Simple Time Series Models -- 1.4. Stationary Models and the Autocorrelation Function -- 1.5. Estimation and Elimination of Trend and Seasonal Components -- 1.6. Testing the Estimated Noise Sequence -- Problems -- Chapter 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 -- 2.5. Forecasting Stationary Time Series -- 2.6. The Wold Decomposition -- Problems -- Chapter 3. ARMA Models -- 3.1. ARMA(p, q) Processes -- 3.2. The ACF and PACF of an ARMA(p, q) Process -- 3.3. Forecasting ARMA Processes -- Problems -- Chapter 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 -- Chapter 5. Modeling and Forecasting with ARMA Processes -- 5.1. Preliminary Estimation -- 5.2. Maximum Likelihood Estimation -- 5.3. Diagnostic Checking -- 5.4. Forecasting -- 5.5. Order Selection -- Problems -- Chapter 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 -- 6.4. Forecasting ARIMA Models -- 6.5. Seasonal ARIMA Models -- 6.6. Regression with ARMA Errors -- Problems -- Chapter 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 -- 7.4. Multivariate ARMA Processes -- 7.5. Best Linear Predictors of Second-Order Random Vectors -- 7.6. Modeling and Forecasting with Multivariate AR Processes -- 7.7. Cointegration -- Problems -- Chapter 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 -- Problems -- Chapter 9. Forecasting Techniques -- 9.1. The ARAR Algorithm -- 9.2. The Holt ... Winters Algorithm -- 9.3. The Holt ... Winters Seasonal Algorithm -- 9.4. Choosing a Forecasting Algorithm -- Problems -- Chapter 10. Further Topics -- 10.1. Transfer Function Models -- 10.2. Intervention Analysis -- 10.3. Nonlinear Models -- 10.4. Continuous-Time Models -- 10.5. Long-Memory Models -- Problems -- Appendix A. Random Variables and Probability Distributions -- A.1. Distribution Functions and Expectation -- A.2. Random Vectors -- A.3. The Multivariate Normal Distribution -- Problems -- Appendix B. Statistical Complements -- B.1. Least Squares Estimation -- B.2. Maximum Likelihood Estimation -- B.3. Confidence Intervals -- B.4. Hypothesis Testing -- Appendix C. Mean Square Convergence -- C.1. The Cauchy Criterion.
9798181284043 8181284046 0387953515
Time-series analysis.
MATHEMATICS--Probability & Statistics--Time Series.
Time-series analysis.
519.55 / B.P.I.