Shumway Stoffer Time_Series_Analysis_and_Its_Applications__With_R_Examples 3rd edition (1)

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Contentsxi7 Statistical Methods in the Frequency Domain . . . . . . . . . . . . . 4057.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4057.2 Spectral Matrices and Likelihood Functions . . . . . . . . . . . . . . . . . 4097.3 Regression for Jointly Stationary Series . . . . . . . . . . . . . . . . . . . . 4107.4 Regression with Deterministic Inputs . . . . . . . . . . . . . . . . . . . . . . 4207.5 Random Coefficient Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 4297.6 Analysis of Designed Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 4347.7 Discrimination and Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . 4507.8 Principal Components and Factor Analysis . . . . . . . . . . . . . . . . . 4687.9 The Spectral Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501Appendix A: Large Sample Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507A.1 Convergence Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507A.2 Central Limit Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515A.3 The Mean and Autocorrelation Functions . . . . . . . . . . . . . . . . . . . 518Appendix B: Time Domain Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527B.1 Hilbert Spaces and the Projection Theorem . . . . . . . . . . . . . . . . . 527B.2 Causal Conditions for ARMA Models . . . . . . . . . . . . . . . . . . . . . . 531B.3 Large Sample Distribution of the AR(p) Conditional LeastSquares Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533B.4 The Wold Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537Appendix C: Spectral Domain Theory . . . . . . . . . . . . . . . . . . . . . . . . . 539C.1 Spectral Representation Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 539C.2 Large Sample Distribution of the DFT and SmoothedPeriodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543C.3 The Complex Multivariate Normal Distribution . . . . . . . . . . . . . 554Appendix R: R Supplement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559R.1 First Things First . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559R.1.1 Included Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560R.1.2 Included Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562R.2 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567R.3 Time Series Primer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
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Page 2: Springer Texts in StatisticsSeries
Page 5 and 6: Prof. Robert H. ShumwayDepartment o
Page 8 and 9: Preface to the Third EditionThe goa
Page 10 and 11: ContentsPreface to the Third Editio
Page 14 and 15: 1Characteristics of Time Series1.1
Page 16 and 17: 1.2 The Nature of Time Series Data
Page 24 and 25: 1.3 Time Series Statistical Models1
Page 26 and 27: 1.3 Time Series Statistical Models
Page 28 and 29: 1.3 Time Series Statistical Models
Page 30 and 31: 1.4Measures of Dependence 17in Exam
Page 32 and 33: 1.4Measures of Dependence 19Example
Page 34 and 35: 1.4Measures of Dependence 21depends
Page 36 and 37: 1.5 Stationary Time Series 23P {x s
Page 38 and 39: 1.5 Stationary Time Series 25⎧39
Page 40 and 41: 1.5 Stationary Time Series 27γ yx
Page 42 and 43: 1.6 Estimation of Correlation 29If
Page 44 and 45: 1.6 Estimation of Correlation 31Tab
Page 46 and 47: 1.7 Vector-Valued and Multidimensio
Page 52 and 53: and its sample estimatorProblems 39
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Page 56 and 57: 1.16 Consider the seriesx t = sin(2
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2.2 Classical Regression in the Tim
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Example 2.3 Regression With Lagged
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2.3 Exploratory Data Analysis 59Fig
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2.3 Exploratory Data Analysis 61One
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varve2.3 Exploratory Data Analysis
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2.3 Exploratory Data Analysis 65soi
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2.3 Exploratory Data Analysis 67Exa
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2.3 Exploratory Data Analysis 69Sca
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2.4 Smoothing in the Time Series Co
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Problems 792.4 Kullback-Leibler Inf
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Problems 81(f) Based on part (e), u
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3ARIMA Models3.1 IntroductionIn Cha
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3.2 Autoregressive Moving Average M
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3.3 Difference Equations 973.3 Diff
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3.3 Difference Equations 99Example
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3.3 Difference Equations 101ar2−5
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3.4 Autocorrelation and Partial Aut
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3.5 Forecasting 109ACF−0.5 0.0 0.
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3.5 Forecasting 111For ARMA models,
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3.5 Forecasting 113An important con
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Example 3.21 Prediction for an MA(1
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3.5 Forecasting 117Noting that the
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3.5 Forecasting 119Fig. 3.6. Twenty
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3.6 Estimation 1213.6 EstimationThr
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3.6 Estimation 123Example 3.27 Yule
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3.6 Estimation 125To find f(x 1 ),
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P t−1t⎧⎡⎨ ∞∑= σw2 ⎣
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3.6 Estimation 1291 rec.mle = ar.ml
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3.6 Estimation 131ACF−0.4 0.0 0.4
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Table 3.2. Gauss-Newton Results for
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Example 3.34 Overfitting Caveat3.6
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3.6 Estimation 137Fig. 3.9. One hun
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P t−1tWhen t = 1, we have= E(x t
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3.7 Integrated Models for Nonstatio
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3.7 Integrated Models for Nonstatio
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3.8 Building ARIMA Models 145where
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3.8 Building ARIMA Models 147diff(g
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3.8 Building ARIMA Models 149(3.151
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3.8 Building ARIMA Models 151Standa
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3.8 Building ARIMA Models 153Fig. 3
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3.9 Multiplicative Seasonal ARIMA M
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Problems 163Fig. 3.26. Forecasts an
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Problems 1653.11 Consider the MA(1)
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Problems 1673.16 Consider the ARMA(
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Problems 169(c) If the time delay
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Problems 171The following problems
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174 4 Spectral Analysis and Filteri
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5Additional Time Domain Topics5.1 I
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5.2 Long Memory ARMA and Fractional
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5.3 Unit Root Testing 277and jointl
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5.3 Unit Root Testing 279The denomi
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5.4 GARCH Models 281y t = x t − x
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5.4 GARCH Models 283Estimation of t
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5.4 GARCH Models 285Standardised Re
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5.4 GARCH Models 287NYSE Returns−
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5.5 Threshold Models 289flu0.2 0.3
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5.5 Threshold Models 291dflu−0.4
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5.6 Regression with Autocorrelated
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5.6 Regression with Autocorrelated
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5.7 Lagged Regression: Transfer Fun
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5.7 Lagged Regression: Transfer Fun
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5.8 Multivariate ARMAX Models 301wh
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5.8 Multivariate ARMAX Models 303se
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5.8 Multivariate ARMAX Models 305Re
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5.8 Multivariate ARMAX Models 307̂
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5.8 Multivariate ARMAX Models 309po
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5.8 Multivariate ARMAX Models 311Pr
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5.8 Multivariate ARMAX Models 313[
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andProblems 315z t = (1, x ′ t−
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Problems 3175.12 Consider the corre
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6State-Space Models6.1 Introduction
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6.1 Introduction 321on three variab
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y t1 = x t + v t1 and y t2 = x t +
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6.2 Filtering, Smoothing, and Forec
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6.3 Maximum Likelihood Estimation 3
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andS 10 =S 00 =6.3 Maximum Likeliho
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6.4 Missing Data Modifications 345S
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6.4 Missing Data Modifications 347I
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6.4 Missing Data Modifications 349
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6.5 Structural Models: Signal Extra
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10 # Initial Parameters6.5 Structur
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6.6 State-Space Models with Correla
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6.6 State-Space Models with Correla
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6.7 Bootstrapping State-Space Model
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6.8 Dynamic Linear Models with Swit
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P n n,n−1 =6.8 Dynamic Linear Mod
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15 phi=matrix(0,nstate,nstate)6.8 D
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6.9 Stochastic Volatility 379Variou
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6.9 Stochastic Volatility 381log(Sq
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6.9 Stochastic Volatility 3830.00 0
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6.9 Stochastic Volatility 385Densit
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6.10 State-Space Models Using Monte
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Problems 399Section 6.26.3 Simulate
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t=1Problems 401n∑n∑[y t − x t
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Problems 403Section 6.46.13 As an e
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7Statistical Methods in the Frequen
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7.1 Introduction 407when the subjec
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7.2 Spectral Matrices and Likelihoo
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7.3 Regression for Jointly Stationa
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[E (y t −7.3 Regression for Joint
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7.4 Regression with Deterministic I
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Tests of Hypotheses7.4 Regression w
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7.5 Random Coefficient Regression 4
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7.6 Analysis of Designed Experiment
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17 for (k in 1:512){7.6 Analysis of
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7.7 Discrimination and Cluster Anal
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d l (x) = g 1 (x) − g 2 (x)7.7 Di
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0<ω k <1/27.7 Discrimination and C
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Cluster Analysis7.7 Discrimination
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7.8 Principal Components and Factor
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and the MLE of D is7.8 Principal Co
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7.9 The Spectral Envelope 485Table
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7.9 The Spectral Envelope 487Sleep
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7.9 The Spectral Envelope 489length
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7.9 The Spectral Envelope 491estima
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7.9 The Spectral Envelope 493Spectr
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7.9 The Spectral Envelope 495The Sp
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7.9 The Spectral Envelope 497their
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7.9 The Spectral Envelope 499Series
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Problems 501g (x)5.0 5.5 6.0 6.5 7.
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( ) ( ) ( ) ( )Y c Xc −X=s Bc V+
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Problems 505Section 7.77.10 The pro
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Appendix ALarge Sample TheoryA.1 Co
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A.1 Convergence Modes 509The output
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A.1 Convergence Modes 511Under this
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∫φ(λ) = E(exp{iλ ′ x}) =A.1
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A.2 Central Limit Theorems 515A.2 C
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A.2 Central Limit Theorems 517varia
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A.3 The Mean and Autocorrelation Fu
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A.3 The Mean and Autocorrelation Fu
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whereA.3 The Mean and Autocorrelati
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=A.3 The Mean and Autocorrelation F
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Appendix BTime Domain TheoryB.1 Hil
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B.1 Hilbert Spaces and the Projecti
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B.2 Causal Conditions for ARMA Mode
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B.3 Large Sample Distribution of AR
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so thatB.3 Large Sample Distributio
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B.4 The Wold Decomposition 537B.4 T
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Appendix CSpectral Domain TheoryC.1
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and, from the right-hand side of th
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C.2 Distribution of the DFT and Per
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andC.2 Distribution of the DFT and
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C.3 The Complex Multivariate Normal
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C.3 The Complex Multivariate Normal
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Appendix RR SupplementR.1 First Thi
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R.1.1 Included Data Sets 561gnp - Q
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acf2(series, max.lag=NULL)R.1.2 Inc
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R.1.2 Included Scripts 565observati
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R.2 Getting Started 567R.2 Getting
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4 x+z # guess[1] 11 22 13 24R.2 Get
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R.3 Time Series Primer 571R.3 Time
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plot(x)R.3 Time Series Primer 573pl
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R.3 Time Series Primer 575trend Q1
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ReferencesAkaike, H. (1969). Fittin
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R.3 Time Series Primer 579Box, G.E.
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R.3 Time Series Primer 581Geweke, J
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R.3 Time Series Primer 583Jones, R.
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R.3 Time Series Primer 585Ogawa, S.
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R.3 Time Series Primer 587Shephard,
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R.3 Time Series Primer 589Wiener, N
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592 Indexlikelihood, 126MLE, 127mul
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594 IndexInfrasound series, 421, 42
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596 Indexwavenumber, 252Spectral di
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Shumway Stoffer Time_Series_Analysis_and_Its_Applications__With_R_Examples 3rd edition (1)

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