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316 Chapter 8 State-Space Models a. Show that the observation equation with state variable transformed by the logit transformation Wt ln(Xt/(1 − Xt)) follows an exponential family p(yt|wt) exp{ytwt − b(wt) + c(yt)}. Determine the functions b(·) and c(·). b. Suppose that the state Xt has the beta density where p(xt+1|y (t) ) f(xt+1; αt+1|t,λt+1|t), f(x; α, λ) [B(α, λ)] −1 x α−1 (1 − x) λ−1 , 0
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Introduction to Time Series and For
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Peter J. Brockwell Richard A. Davis
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viii Preface Since the upgrade to I
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x Contents 2.6. The Wold Decomposit
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xii Contents 8.8.2. Observation-Dri
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xiv Contents D.6. Model Properties
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2 Chapter 1 Introduction Figure 1-1
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4 Chapter 1 Introduction Figure 1-3
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6 Chapter 1 Introduction 3.5% of th
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8 Chapter 1 Introduction Example 1.
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10 Chapter 1 Introduction where mt
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12 Chapter 1 Introduction Figure 1-
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14 Chapter 1 Introduction n/12 6,
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16 Chapter 1 Introduction variable,
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18 Chapter 1 Introduction at once t
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20 Chapter 1 Introduction Example 1
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22 Chapter 1 Introduction ACF -0.2
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28 Chapter 1 Introduction can be co
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30 Chapter 1 Introduction If the op
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32 Chapter 1 Introduction The reest
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36 Chapter 1 Introduction (a) The s
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38 Chapter 1 Introduction It can al
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40 Chapter 1 Introduction Problems
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42 Chapter 1 Introduction 1.8. Let
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44 Chapter 1 Introduction At this p
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46 Chapter 2 Stationary Processes T
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48 Chapter 2 Stationary Processes T
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50 Chapter 2 Stationary Processes i
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52 Chapter 2 Stationary Processes P
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54 Chapter 2 Stationary Processes I
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56 Chapter 2 Stationary Processes A
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58 Chapter 2 Stationary Processes 2
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60 Chapter 2 Stationary Processes w
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62 Chapter 2 Stationary Processes A
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70 Chapter 2 Stationary Processes
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74 Chapter 2 Stationary Processes a
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76 Chapter 2 Stationary Processes t
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80 Chapter 2 Stationary Processes 2
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84 Chapter 3 ARMA Models The proces
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86 Chapter 3 ARMA Models where θ0
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88 Chapter 3 ARMA Models The AR pol
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90 Chapter 3 ARMA Models moving ave
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92 Chapter 3 ARMA Models ACF -0.2 0
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94 Chapter 3 ARMA Models can be fou
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96 Chapter 3 ARMA Models Example 3.
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98 Chapter 3 ARMA Models is entirel
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100 Chapter 3 ARMA Models 3.3 Forec
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102 Chapter 3 ARMA Models and rn
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104 Chapter 3 ARMA Models and 2 E
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106 Chapter 3 ARMA Models where the
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108 Chapter 3 ARMA Models Problems
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110 Chapter 3 ARMA Models 3.10. By
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112 Chapter 4 Spectral Analysis 4.1
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114 Chapter 4 Spectral Analysis (ii
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116 Chapter 4 Spectral Analysis Not
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118 Chapter 4 Spectral Analysis Exa
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120 Chapter 4 Spectral Analysis Fig
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124 Chapter 4 Spectral Analysis The
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126 Chapter 4 Spectral Analysis fac
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130 Chapter 4 Spectral Analysis Sin
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134 Chapter 4 Spectral Analysis Pro
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136 Chapter 4 Spectral Analysis 4.9
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138 Chapter 5 Modeling and Forecast
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180 Chapter 6 Nonstationary and Sea
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224 Chapter 7 Multivariate Time Ser
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260 Chapter 8 State-Space Models li
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262 Chapter 8 State-Space Models In
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264 Chapter 8 State-Space Models Fi
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266 Chapter 8 State-Space Models To
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272 Chapter 8 State-Space Models De
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286 Chapter 8 State-Space Models an
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288 Chapter 8 State-Space Models We
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Page 662: 9 Forecasting Techniques 9.1 The AR
Page 666: 9.1 The ARAR Algorithm 319 and choo
Page 670: 9.1 The ARAR Algorithm 321 9.1.4 Ap
Page 674: 9.2 The Holt-Winters Algorithm 323
Page 678: Figure 9-2 The data set DEATHS.TSM
Page 682: Figure 9-3 The data set DEATHS.TSM
Page 686: Figure 9-4 The first 132 values of
Page 690: 10Further Topics 10.1 Transfer Func
Page 694: 10.1 Transfer Function Models 333 1
Page 698: 10.1 Transfer Function Models 335 (
Page 702: Figure 10-2 The sample correlation
Page 706: 10.1 Transfer Function Models 339 I
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10.2 Intervention Analysis 341 form
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10.3 Nonlinear Models 10.3 Nonlinea
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Figure 10-5 A sequence generated by
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10.3 Nonlinear Models 347 lation at
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10.3 Nonlinear Models 349 is a part
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Figure 10-7 A realization of the p
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10.3 Nonlinear Models 353 process {
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10.3 Nonlinear Models 355 Compariso
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10.4 Continuous-Time Models 357 whe
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10.4 Continuous-Time Models 359 i
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10.5 Long-Memory Models 361 and Cov
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10.5 Long-Memory Models 363 The spe
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Problems Figure 10-13 The minimum a
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Problems 367 c. For p ≥ 1, show t
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A Random Variables and Probability
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A.1 Distribution Functions and Expe
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A.1 Distribution Functions and Expe
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A.2 Random Vectors 375 The probabil
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A.3 The Multivariate Normal Distrib
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A.3 The Multivariate Normal Distrib
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Problems Problems 381 A.1. Let X ha
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B Statistical B.1 Least Squares Est
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B.1 Least Squares Estimation 385 Th
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B.2 Maximum Likelihood Estimation 3
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B.4 Hypothesis Testing 389 Example
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B.4 Hypothesis Testing 391 B.3.1, w
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C Mean C.1 The Cauchy Criterion Squ
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D An ITSM Tutorial D.1 Getting Star
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D.2 Preparing Your Data for Modelin
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D.2 Preparing Your Data for Modelin
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Figure D-2 The logged AIRPASS.TSM s
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D.3 Finding a Model for Your Data 4
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Figure D-4 The sample ACF of the tr
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D.4 Testing Your Model D.4 Testing
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D.4 Testing Your Model 413 frequenc
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D.5 Prediction D.5 Prediction 415 t
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D.6 Model Properties 417 of differe
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Figure D-12 The PACF of the model i
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D.7 Multivariate Time Series 421 us
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References Akaike, H. (1969), Fitti
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References 425 Dempster, A.P., Lair
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References 427 Mood, A.M., Graybill
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A accidental deaths (DEATHS.TSM), 3
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estimation of missing values in an
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polynomial fitting, 28 population o
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