Introduction to time series and forecasting / Peter J. Brockwell and Richard A. Davis.
Series Springer texts in statisticsEditor: New York : Springer, c1996Descripción: xiii, 420 p. : ill. ; 25 cm. + 1 computer disk (3 1/2 in.)ISBN: 0387947191 (hard : alk. paper)Tema(s): Time-series analysisOtra clasificación: *CODIGO*Preface vii --
1. Introduction [1] --
1.1. Examples of Time Series [1] --
1.2. Objectives of Time Series Analysis [5] --
1.3. Some Simple Time Series Models [6] --
1.3.1. Some Zero-Mean Models [7] --
1.3.2. Models with Trend and Seasonality [9] --
1.3.3. A General Approach to Time Series Modelling [13] --
1.4. Stationary Models and the Autocorrelation Function [14] --
1.4.1. The Sample Autocorrelation Function [17] --
1.4.2. A Model for the Lake Huron Data [20] --
1.5. Estimation and Elimination of Trend and Seasonal Components [22] --
1.5.1. Estimation and Elimination of Trend in the Absence of Seasonality [23] --
1.5.2. Estimation and Elimination of Both Trend and Seasonality [30] --
1.6. Testing the Estimated Noise Sequence [34] --
Problems [38] --
2. Stationary Processes [43] --
2.1. Basic Properties [43] --
2.2. Linear Processes [49] --
2.3. Introduction to ARMA Processes [53] --
2.4. Properties of the Sample Mean and Autocorrelation Function [56] --
2.4.1. Estimation of n [56] --
2.4.2. Estimation of y( ) and p(-) [57] --
2.5. Forecasting Stationary Time Series [62] --
2.5.1. The Durbin-Levinson Algorithm [67] --
2.5.2. The Innovations Algorithm [70] --
2.5.3. Prediction of a Stationary Process in Terms of Infinitely Many Past Values [73] --
2.6. The Wold Decomposition [75] --
Problems [77] --
3. ARMA Models [81] --
3.1. ARMA(p. q) Processes [81] --
3.2. The ACF and PACF of an ARMA(p.q) Process [86] --
3.2.1. Calculation of the AC VF [86] --
3.2.2. The Autocorrelation Function [92] --
3-23. The Partial Autocorrelation Function [92] --
3.2.4. Examples [94] --
3.3. Forecasting ARMA Processes [98] --
Problems [106] --
4. Spectral Analysis [109] --
4.1. Spectral Densities [110] --
4.2. The Periodogram [120] --
4.3. Time-Invariant Linear Filters [126] --
4.4. The Spectral Density of an ARMA Process [130] --
Problems [132] --
5. Modelling and Forecasting with ARMA Processes [135] --
5.1. Preliminary Estimation [136] --
5.1.1. Yule-Walker Estimation [137] --
5.1.2. Burg’s Algorithm [145] --
5.1.3. The Innovations Algorithm [148] --
5.1.4. The Hannan-Rissanen Algorithm [154] --
5.2. Maximum Likelihood Estimation [156] --
5.3. Diagnostic Checking [162] --
5.3.1. The Graph of {R,,r = 1, ...,n) [162] --
5.3.2. The Sample ACF of the Residuals [163] --
5.3.3. Tests for Randomness of the Residuals [164] --
5.4. Forecasting [165] --
5.5. Order Selection [167] --
5.5.1. The FPE Criterion [167] --
5.5.2. The AICC Criterion [169] --
Problems [172] --
6. Nonstationary and Seasonal Time Series Models [177] --
6.1. ARIMA Models for Nonstationary Time Series [178] --
6.2. Identification Techniques [186] --
6.3. Unit Roots in Time Series Models [192] --
6.3.1. Unit Roots in Autoregressions [192] --
6.3.2. Unit Roots in Moving Averages [195] --
6.4. Forecasting ARIMA Models [197] --
6.4.1. The Forecast Function [199] --
6.5. Seasonal ARIMA Models [201] --
6.5.1. Forecasting SARIM A Processes [206] --
6.6. Regression with ARMA Errors [208] --
Problems [213] --
7. Multivariate Time Series [217] --
7.1. Examples [218] --
7.2. Second-Order Properties of Multivariate Time Series [223] --
7.3. Estimation of the Mean and Covariance Function [227] --
7.3.1. Estimation of p [227] --
7.3.2. Estimation of I" (A) [229] --
7.3.3. Testing for Independence of Two Stationary Time Series [230] --
7.3.4. Bartlett’s Formula [232] --
7.4. Multivariate ARMA Processes [234] --
7.4.1. The Covariance Matrix Function of a Causal ARMA Process [237] --
7.5. Best Linear Predictors of Second-Order Random Vectors [237] --
7.6. Modelling and Forecasting with Multivariate AR Processes [239] --
7.6.1. Estimation for Autoregressive Processes Using Whittle’s Algorithm [240] --
7.6.2. Forecasting Multivariate Autoregressive Processes [242] --
7.7. Cointegration [247] --
Problems [248] --
8. State-Space Models [251] --
8.1. State-Space Representations [252] --
8.2. The Basic Structural Model [255] --
8.3. State-Space Representation of ARIMA Models [259] --
8.4. The Kalman Recursions [263] --
8.5. Estimation For State-Space Models [269] --
8.6. State-Space Models with Missing Observations [275] --
8.7. The EM Algorithm [281] --
8.8. Generalized State-Space Models [284] --
8.8.1. Parameter-Driven Models [284] --
8.8.2. Observation-Driven Models [291] --
Problems [303] --
9. Forecasting Techniques [309] --
9.1. The ARAR Algorithm [310] --
9.1.1. Memory Shortening [310] --
9.1.2. Fitting a Subset Autoregression [311] --
9.1.3. Forecasting 3 [12] --
9.1.4. Running the Program ARAR [313] --
9.2. The Holt-Winters Algorithm [315] --
9.3. The Holt-Winters Seasonal Algorithm [318] --
9.4. Choosing a Forecasting Algorithm [320] --
Problems [322] --
10. Further Topics [323] --
10.1. Transfer Function Models [323] --
10.1.1. Prediction Based on a Transfer-Function Model [328] --
10.2. Intervention Analysis [332] --
10.3. Nonlinear Models [335] --
10.3.1. Deviations from Linearity [335] --
10.3.2. Chaotic Deterministic Sequences [337] --
10.3.3. Distinguishing Between White Noise and IID Sequences [333] --
10.3.4. Three Useful Classes of Nonlinear Models [340] --
10.3.5. Modelling Volatility [341] --
10.4. Continuous-Time Models [344] --
10.5. Long-Memory Models [343] --
Problems [352] --
A. Random Variables and Probability Distributions [355] --
A. 1. Distribution Functions and Expectation [355] --
A.2. Random Vectors [350] --
A. 3. The Multivariate Normal Distribution [353] --
Problems [355] --
B. Statistical Complements [359] --
B. l. Least Squares Estimation [359] --
B. 1.1. The Gauss-Markov Theorem [371] --
B. 1.2. Generalized Least Squares [371] --
B.2. Maximum Likelihood Estimation [372] --
B.2.1. Properties of Maximum Likelihood Estimators [373] --
B.3. Confidence Intervals [373] --
B.3.1. Large-Sample Confidence Regions [374] --
B.4. Hypothesis Testing [375] --
B.4.1. Error Probabilities [375] --
B.4.2. Large-Sample Tests Based on Confidence Regions [376] --
C. Mean Square Convergence [379] --
C. 1. The Cauchy Criterion [379] --
D. An ITSM Tutorial [381] --
D. l. Getting Started [381] --
D.1.1. Running PEST [381] --
D.2. Preparing Your Data for Modelling [382] --
D.2.1. Entering Data [383] --
D.2.2. Filing Data [383] --
D.2.3. Plotting Data [383] --
D.2.4. Transforming Data [384] --
D.3. Finding a Model for Your Data [388] --
D.3.1. The Sample ACF and PACF [388] --
D.3.2. Entering a Model [389] --
D.3.3. Preliminary Estimation [391] --
D.3.4. The AICC Statistic [393] --
D.3.5. Changing Your Model [394] --
D.3.6. Maximum Likelihood Estimation [394] --
D.3.7. Optimization Results [395] --
D.4. Testing Your Model [396] --
D.4.1. Plotting the Residuals [397] --
D.4.2. ACF/PACF of the Residuals [397] --
D.4.3. Testing for Randomness of the Residuals [399] --
D.5. Prediction [400] --
D.5.1. Forecast Criteria [400] --
D.5.2. Forecast Results [400] --
D.5.3. Inverting Transformations [401] --
D.6. Model Properties [402] --
D.6.1. ARMA Models [403] --
D.6.2. Model ACF, PACF [403] --
D.6.3. Model Representations [405] --
D.6.4. Generating Realizations of a Random Series [406] --
D.6.5. Spectral Properties [407] --
Bibliography [409] --
Index [415] --| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 B864i (Browse shelf) | Available | A-9359 |
Includes bibliographical references (p. [409]-414) and index.
Preface vii --
1. Introduction [1] --
1.1. Examples of Time Series [1] --
1.2. Objectives of Time Series Analysis [5] --
1.3. Some Simple Time Series Models [6] --
1.3.1. Some Zero-Mean Models [7] --
1.3.2. Models with Trend and Seasonality [9] --
1.3.3. A General Approach to Time Series Modelling [13] --
1.4. Stationary Models and the Autocorrelation Function [14] --
1.4.1. The Sample Autocorrelation Function [17] --
1.4.2. A Model for the Lake Huron Data [20] --
1.5. Estimation and Elimination of Trend and Seasonal Components [22] --
1.5.1. Estimation and Elimination of Trend in the Absence of Seasonality [23] --
1.5.2. Estimation and Elimination of Both Trend and Seasonality [30] --
1.6. Testing the Estimated Noise Sequence [34] --
Problems [38] --
2. Stationary Processes [43] --
2.1. Basic Properties [43] --
2.2. Linear Processes [49] --
2.3. Introduction to ARMA Processes [53] --
2.4. Properties of the Sample Mean and Autocorrelation Function [56] --
2.4.1. Estimation of n [56] --
2.4.2. Estimation of y( ) and p(-) [57] --
2.5. Forecasting Stationary Time Series [62] --
2.5.1. The Durbin-Levinson Algorithm [67] --
2.5.2. The Innovations Algorithm [70] --
2.5.3. Prediction of a Stationary Process in Terms of Infinitely Many Past Values [73] --
2.6. The Wold Decomposition [75] --
Problems [77] --
3. ARMA Models [81] --
3.1. ARMA(p. q) Processes [81] --
3.2. The ACF and PACF of an ARMA(p.q) Process [86] --
3.2.1. Calculation of the AC VF [86] --
3.2.2. The Autocorrelation Function [92] --
3-23. The Partial Autocorrelation Function [92] --
3.2.4. Examples [94] --
3.3. Forecasting ARMA Processes [98] --
Problems [106] --
4. Spectral Analysis [109] --
4.1. Spectral Densities [110] --
4.2. The Periodogram [120] --
4.3. Time-Invariant Linear Filters [126] --
4.4. The Spectral Density of an ARMA Process [130] --
Problems [132] --
5. Modelling and Forecasting with ARMA Processes [135] --
5.1. Preliminary Estimation [136] --
5.1.1. Yule-Walker Estimation [137] --
5.1.2. Burg’s Algorithm [145] --
5.1.3. The Innovations Algorithm [148] --
5.1.4. The Hannan-Rissanen Algorithm [154] --
5.2. Maximum Likelihood Estimation [156] --
5.3. Diagnostic Checking [162] --
5.3.1. The Graph of {R,,r = 1, ...,n) [162] --
5.3.2. The Sample ACF of the Residuals [163] --
5.3.3. Tests for Randomness of the Residuals [164] --
5.4. Forecasting [165] --
5.5. Order Selection [167] --
5.5.1. The FPE Criterion [167] --
5.5.2. The AICC Criterion [169] --
Problems [172] --
6. Nonstationary and Seasonal Time Series Models [177] --
6.1. ARIMA Models for Nonstationary Time Series [178] --
6.2. Identification Techniques [186] --
6.3. Unit Roots in Time Series Models [192] --
6.3.1. Unit Roots in Autoregressions [192] --
6.3.2. Unit Roots in Moving Averages [195] --
6.4. Forecasting ARIMA Models [197] --
6.4.1. The Forecast Function [199] --
6.5. Seasonal ARIMA Models [201] --
6.5.1. Forecasting SARIM A Processes [206] --
6.6. Regression with ARMA Errors [208] --
Problems [213] --
7. Multivariate Time Series [217] --
7.1. Examples [218] --
7.2. Second-Order Properties of Multivariate Time Series [223] --
7.3. Estimation of the Mean and Covariance Function [227] --
7.3.1. Estimation of p [227] --
7.3.2. Estimation of I" (A) [229] --
7.3.3. Testing for Independence of Two Stationary Time Series [230] --
7.3.4. Bartlett’s Formula [232] --
7.4. Multivariate ARMA Processes [234] --
7.4.1. The Covariance Matrix Function of a Causal ARMA Process [237] --
7.5. Best Linear Predictors of Second-Order Random Vectors [237] --
7.6. Modelling and Forecasting with Multivariate AR Processes [239] --
7.6.1. Estimation for Autoregressive Processes Using Whittle’s Algorithm [240] --
7.6.2. Forecasting Multivariate Autoregressive Processes [242] --
7.7. Cointegration [247] --
Problems [248] --
8. State-Space Models [251] --
8.1. State-Space Representations [252] --
8.2. The Basic Structural Model [255] --
8.3. State-Space Representation of ARIMA Models [259] --
8.4. The Kalman Recursions [263] --
8.5. Estimation For State-Space Models [269] --
8.6. State-Space Models with Missing Observations [275] --
8.7. The EM Algorithm [281] --
8.8. Generalized State-Space Models [284] --
8.8.1. Parameter-Driven Models [284] --
8.8.2. Observation-Driven Models [291] --
Problems [303] --
9. Forecasting Techniques [309] --
9.1. The ARAR Algorithm [310] --
9.1.1. Memory Shortening [310] --
9.1.2. Fitting a Subset Autoregression [311] --
9.1.3. Forecasting 3 [12] --
9.1.4. Running the Program ARAR [313] --
9.2. The Holt-Winters Algorithm [315] --
9.3. The Holt-Winters Seasonal Algorithm [318] --
9.4. Choosing a Forecasting Algorithm [320] --
Problems [322] --
10. Further Topics [323] --
10.1. Transfer Function Models [323] --
10.1.1. Prediction Based on a Transfer-Function Model [328] --
10.2. Intervention Analysis [332] --
10.3. Nonlinear Models [335] --
10.3.1. Deviations from Linearity [335] --
10.3.2. Chaotic Deterministic Sequences [337] --
10.3.3. Distinguishing Between White Noise and IID Sequences [333] --
10.3.4. Three Useful Classes of Nonlinear Models [340] --
10.3.5. Modelling Volatility [341] --
10.4. Continuous-Time Models [344] --
10.5. Long-Memory Models [343] --
Problems [352] --
A. Random Variables and Probability Distributions [355] --
A. 1. Distribution Functions and Expectation [355] --
A.2. Random Vectors [350] --
A. 3. The Multivariate Normal Distribution [353] --
Problems [355] --
B. Statistical Complements [359] --
B. l. Least Squares Estimation [359] --
B. 1.1. The Gauss-Markov Theorem [371] --
B. 1.2. Generalized Least Squares [371] --
B.2. Maximum Likelihood Estimation [372] --
B.2.1. Properties of Maximum Likelihood Estimators [373] --
B.3. Confidence Intervals [373] --
B.3.1. Large-Sample Confidence Regions [374] --
B.4. Hypothesis Testing [375] --
B.4.1. Error Probabilities [375] --
B.4.2. Large-Sample Tests Based on Confidence Regions [376] --
C. Mean Square Convergence [379] --
C. 1. The Cauchy Criterion [379] --
D. An ITSM Tutorial [381] --
D. l. Getting Started [381] --
D.1.1. Running PEST [381] --
D.2. Preparing Your Data for Modelling [382] --
D.2.1. Entering Data [383] --
D.2.2. Filing Data [383] --
D.2.3. Plotting Data [383] --
D.2.4. Transforming Data [384] --
D.3. Finding a Model for Your Data [388] --
D.3.1. The Sample ACF and PACF [388] --
D.3.2. Entering a Model [389] --
D.3.3. Preliminary Estimation [391] --
D.3.4. The AICC Statistic [393] --
D.3.5. Changing Your Model [394] --
D.3.6. Maximum Likelihood Estimation [394] --
D.3.7. Optimization Results [395] --
D.4. Testing Your Model [396] --
D.4.1. Plotting the Residuals [397] --
D.4.2. ACF/PACF of the Residuals [397] --
D.4.3. Testing for Randomness of the Residuals [399] --
D.5. Prediction [400] --
D.5.1. Forecast Criteria [400] --
D.5.2. Forecast Results [400] --
D.5.3. Inverting Transformations [401] --
D.6. Model Properties [402] --
D.6.1. ARMA Models [403] --
D.6.2. Model ACF, PACF [403] --
D.6.3. Model Representations [405] --
D.6.4. Generating Realizations of a Random Series [406] --
D.6.5. Spectral Properties [407] --
Bibliography [409] --
Index [415] --
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