000			11341nam a2200325 i 4500
008			110628s2012 lau b 001 0 eng
010			_a2011025090
020			_a9781439818374
040			_aDLC _cDLC
049			_aBAUN_MERKEZ
050	0	4	_aQA280 _b.W66 2012
082	0	0	_223
100	1		_aWoodward, Wayne A
245	1	0	_aApplied time series analysis / _cWayne A Woodward, Henry L. Gray, and Alan C. Elliott
264		1	_aBoca Raton : _bChapman and Hall/CRC, _c2012.
300			_axxiii, 540 pages : _billustrations, _c25 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	0		_aStatistics: textbooks and monographs
504			_aIncludes bibliographical references and index
505	0	0	_tContents _t Preface _t Acknowledgments _t1. Stationary Time Series _t1.1. Time Series _t1.2. Stationary Time Series _t1.3. Autocovariance and Autocorrelation Functions for Stationary Time Series _t1.4. Estimation of the Mean, Autocovariance, and Autocorrelation for Stationary Time Series _t1.4.1. Estimation of μ _t1.4.1.1. Ergodicity of X _t1.4.1.2. Variance of X _t1.4.2. Estimation of γk _t1.4.3. Estimation of ρk _t1.5. Power Spectrum _t1.6. Estimating the Power Spectrum and Spectral Density for Discrete Time Series _t1.7. Time Series Examples _t1.7.1. Simulated Data _t1.7.2. Real Data _t1.A. Appendix _t Exercises _t2. Linear Filters _t2.1. Introduction to Linear Filters _t2.1.1. Relationship between the Spectra of the Input and Output of a Linear Filter _t2.2. Stationary General Linear Processes _t2.2.1. Spectrum and Spectral Density for a General Linear Process _t2.3. Wold Decomposition Theorem _t2.4. Filtering Applications _t2.4.1. Butterworth Filters _t2.A. Appendix _t Exercises _t3. ARMA Time Series Models _t3.1. Moving Average Processes _t3.1.1. MA(1) Model _t3.1.2. MA(2) Model _t3.2. Autoregressive Processes _t3.2.1. Inverting the Operator _t3.2.2. AR(1) Model _t3.2.3. AR(p) Model for p [≥] 1 _t3.2.4. Autocorrelations of an AR(p) Model _t3.2.5. Linear Difference Equations _t3.2.6. Spectral Density of an AR(p) Model _t3.2.7. AR(2) Model _t3.2.7.1. Autocorrelations of an AR(2) Model _t3.2.7.2. Spectral Density of an AR(2) _t3.2.7.3. Stationary/Causal Region of an AR(2) _t3.2.7.4. ψ-Weights of an AR(2) Model _t3.2.8. Summary of AR(1) and AR(2) Behavior _t3.2.9. AR(p) Model _t3.2.10. AR(1) and AR(2) Building Blocks of an AR(p) Model _t3.2.11. Factor Tables _t3.2.12. Invertibility/Infinite-Order Autoregressive Processes _t3.2.13. Two Reasons for Imposing Invertibility _t3.3. Autoregressive-Moving Average Processes _t3.3.1. Stationarity and Invertibility Conditions for an ARMA(p,q) Model _t3.3.2. Spectral Density of an ARMA(p,q) Model _t3.3.3. Factor Tables and ARMA(p,q) Models _t3.3.4. Autocorrelations of an ARMA(p,q) Model _t3.3.5. ψ-Weights of an ARMA(p,q) _t3.3.6. Approximating ARMA(p,q) Processes Using High-Order AR(p) Models _t3.4. Visualizing Autoregressive Components _t3.5. Seasonal ARMA(p,q) x (PsrQs)s Models _t3.6. Generating Realizations from ARMA(p,q) Processes _t3.6.1. MA(q) Model _t3.6.2. AR(2) Model _t3.6.3. General Procedure _t3.7. Transformations _t3.7.1. Memoryless Transformations _t3.7.2. Autoregressive Transformations _t3.A. Appendix: Proofs of Theorems _t Exercises _t4. Other Stationary Time Series Models _t4.1. Stationary Harmonic Models _t4.1.1. Pure Harmonic Models _t4.1.2. Harmonic Signal-plus-Noise Models _t4.1.3. ARMA Approximation to the Harmonic Signal-plus-Noise Model _t4.2. ARCH and GARCH Processes _t4.2.1. ARCH Processes _t4.2.1.1. The ARCH(1) Model _t4.2.1.2. The ARCH(90) Model _t4.2.2. The GARCH(po,qo) Process _t4.2.3. AR Processes with ARCH or GARCH Noise _t Exercises _t5. Nonstationary Time Series Models _t5.1. Deterministic Signal-plus-Noise Models _t5.1.1. Trend-Component Models _t5.1.2. Harmonic Component Models _t5.2. ARIMA(p,d,q) and ARUMA(p,d,q) Processes _t5.2.1. Extended Autocorrelations of an ARUMA(p,d,q) Process _t5.2.2. Cyclical Models _t5.3. Multiplicative Seasonal ARUMA(p,d,q) x (PsrDsrQs)s Process _t5.3.1. Factor Tables for Seasonal Models of the Form (5.17) with s = 4 and s = 12 _t5.4. Random Walk Models _t5.4.1. Random Walk _t5.4.2. Random Walk with Drift _t5.5. G-Stationary Models for Data with Time-Varying Frequencies _t Exercises _t6. Forecasting _t6.1. Mean Square Prediction Background _t6.2. Box-Jenkins Forecasting for ARMA(p,q) Models _t6.3. Properties of the Best Forecast Zto(l) _t6.4. π-Weight Form of the Forecast Function _t6.5. Forecasting Based on the Difference Equation _t6.6. Eventual Forecast Function _t6.7. Probability Limits for Forecasts _t6.8. Forecasts Using ARUMA(p,d,q) Models _t6.9. Forecasts Using Multiplicative Seasonal ARUMA Models _t6.10. Forecasts Based on Signal-plus-Noise Models _t6.A. Appendix _t Exercises _t7. Parameter Estimation _t7.1. Introduction _t7.2. Preliminary Estimates _t7.2.1. Preliminary Estimates for AR(p) Models _t7.2.1.1. Yule-Walker Estimates _t7.2.1.2. Least Squares Estimation _t7.2.1.3. Burg Estimates _t7.2.2. Preliminary Estimates for MA(q) Models _t7.2.2.1. Method-of-Moment Estimation for an MA(q) _t7.2.2.2. MA(q) Estimation Using the Innovations Algorithm _t7.2.3. Preliminary Estimates for ARMA(p,q) Models _t7.2.3.1. Extended Yule-Walker Estimates of the Autoregressive Parameters _t7.2.3.2. Tsay-Tiao (TT) Estimates of the Autoregressive Parameters _t7.2.3.3. Estimating the Moving Average Parameters _t7.3. Maximum Likelihood Estimation of ARMA(p,q) Parameters _t7.3.1. Conditional and Unconditional Maximum Likelihood Estimation _t7.3.2. ML Estimation Using the Innovations Algorithm _t7.4. Backcasting and Estimating σ2a _t7.5. Asymptotic Properties of Estimators _t7.5.1. Autoregressive Case _t7.5.1.1. Confidence Intervals: Autoregressive Case _t7.5.2. ARMA(p,q) Case _t7.5.2.1. Confidence Intervals for ARMA(p,q) Parameters _t7.5.3. Asymptotic Comparisons of Estimators for an MA(1) _t7.6. Estimation Examples Using Data _t7.7. ARMA Spectral Estimation _t7.8. ARUMA Spectral Estimation _t Exercises _t8. Model Identification _t8.1. Preliminary Check for White Noise _t8.2. Model Identification for Stationary ARMA Models _t8.2.1. Model Identification Based on AIC and Related Measures _t8.3. Model Identification for Nonstationary ARUMA(p,d,q) Models _t8.3.1. Including a Nonstationary Factor in the Model _t8.3.2. Identifying Nonstationary Component(s) in a Model _t8.3.3. Decision between a Stationary or a Nonstationary Model _t8.3.4. Deriving a Final ARUMA Model _t8.3.5. More on the Identification of Nonstationary Components _t8.3.5.1. Including a Factor (1 - B)d in the Model _t8.3.5.2. Testing for a Unit Root _t8.3.5.3. Including a Seasonal Factor (1 - Bs) in the Model _t8.A. Appendix: Model Identification Based on Pattern Recognition _t Exercises _t9. Model Building _t9.1. Residual Analysis _t9.1.1. Check Sample Autocorrelations of Residuals versus 95% Limit Lines _t9.1.2. Ljung-Box Test _t9.1.3. Other Tests for Randomness _t9.1.4. Testing Residuals for Normality _t9.2. Stationarity versus Nonstationarity _t9.3. Signal-plus-Noise versus Purely Autocorrelation-Driven Models _t9.3.1. Cochrane Orcutt, ML, and Frequency Domain Method _t9.3.2. A Bootstrapping Approach _t9.3.3. Other Methods for Trend Testing _t9.4. Checking Realization Characteristics _t9.5. Comprehensive Analysis of Time Series Data: A Summary _t Exercises _t10. Vector-Valued (Multivariate) Time Series _t10.1. Multivariate Time Series Basics _t10.2. Stationary Multivariate Time Series _t10.2.1. Estimating the Mean and Covariance for Stationary Multivariate Processes _t10.2.1.1. Estimating μ _t10.2.1.2. Estimating π(k) _t10.3. Multivariate (Vector) ARMA Processes _t10.3.1. Forecasting Using VAR(p) Models _t10.3.2. Spectrum of a VAR(p) Model _t10.3.3. Estimating the Coefficients of a VAR(p) Model _t10.3.3.1. Yule-Walker Estimation _t10.3.3.2. Least Squares and Conditional Maximum Likelihood Estimation _t10.3.3.3. Burg-Type Estimation _t10.3.4. Calculating the Residuals and Estimating πa _t10.3.5. VAR(p) Spectral Density Estimation _t10.3.6. Fitting a VAR(p) Model to Data _t10.3.6.1. Model Selection _t10.3.6.2. Estimating the Parameters _t10.3.6.3. Testing the Residuals for White Noise _t10.4. Nonstationary VARMA Processes _t10.5. Testing for Association between Time Series _t10.5.1. Testing for Independence of Two Stationary Time Series _t10.5.2. Testing for Cointegration between Nonstationary Time Series _t10.6. State-Space Models _t10.6.1. State Equation _t10.6.2. Observation Equation _t10.6.3. Goals of State-Space Modeling _t10.6.4. Kalman Filter _t10.6.4.1. Prediction (Forecasting) _t10.6.4.2. Filtering _t10.6.4.3. Smoothing Using the Kalman
505	0	0	_t Filter _t10.6.4.4. H-Step Ahead Predictions _t10.6.5. Kalman Filter and Missing Data _t10.6.6. Parameter Estimation _t10.6.7. Using State-Space Methods to Find Additive Components of a Univariate Autoregressive Realization _t10.6.7.1. Revised State-Space Model _t10.6.7.2. ψ Real _t10.6.7.3. ψ Complex _t10.A. Appendix: Derivation of State-Space Results _t Exercises _t11. Long-Memory Processes _t11.1. Long Memory _t11.2. Fractional Difference and FARMA Processes _t11.3. Gegenbauer and GARMA Processes _t11.3.1. Gegenbauer Polynomials _t11.3.2. Gegenbauer Process _t11.3.3. GARMA Process _t11.4. K-Factor Gegenbauer And Garma Processes _t11.4.1. Calculating Autocovariances _t11.4.2. Generating Realizations _t11.5. Parameter Estimation and Model Identification _t11.6. Forecasting Based on the k-Factor GARMA Model _t11.7. Modeling Atmospheric CO2 Data Using Long-Memory Models _t Exercises _t12. Wavelets _t12.1. Shortcomings of Traditional Spectral Analysis for TVF Data _t12.2. Window-Based Methods That Localize the "Spectrum" in Time _t12.2.1. Gabor Spectrogram _t12.2.2. Wigner-Ville Spectrum _t12.3. Wavelet Analysis _t12.3.1. Fourier Series Background _t12.3.2. Wavelet Analysis Introduction _t12.3.3. Fundamental Wavelet Approximation Result _t12.3.4. Discrete Wavelet Transform for Data Sets of Finite Length _t12.3.5. Pyramid Algorithm _t12.3.6. Multiresolution Analysis _t12.3.7. Wavelet Shrinkage _t12.3.8. Scalogram: Time-Scale Plot _t12.3.9. Wavelet Packets _t12.3.10. Two-Dimensional Wavelets _t12.5. Concluding Remarks on Wavelets _t12.A. Appendix: Mathematical Preliminaries for This Chapter _t Exercises _t13. G-Stationary Processes _t13.1. Generalized-Stationary Processes _t13.1.1. General Strategy for Analyzing G-Stationary Processes _t13.2. M-Stationary Processes _t13.2.1. Continuous M-Stationary Process _t13.2.2. Discrete M-Stationary Process _t13.2.3. Discrete Euler(p) Model _t13.2.4. Time Transformation and Sampling _t13.3. G(λ)-Stationary Processes _t13.3.1. Continuous G(p;λ) Model _t13.3.2. Sampling the Continuous G(λ)-Stationary Processes _t13.3.2.1. Equally Spaced Sampling from G(p;λ) Processes _t13.3.3. Analyzing TVF Data Using the G(p;λ) Model _t13.3.3.1. G(p;λ) Spectral Density _t13.4. Linear Chirp Processes _t13.4.1. Models for Generalized Linear Chirps _t13.5. Concluding Remarks _t13.A. Appendix _t Exercises _t References _t Index
650		0	_aTime-series analysis
700	1		_aGray, Henry L
700	1		_aElliott, Alan C., _d1952-
900			_a34755
900			_bsatın
942			_2lcc _cKT
999			_c31966 _d31966