Time Series Analysis by State Space MethodsState space time series analysis emerged in the 1960s in engineering, but its applications have spread to other fields. Durbin (statistics, London School of Economics and Political Science) and Koopman (econometrics, Free U., Amsterdam) extol the virtues of such models over the main analytical system currently used for time series data, Box-Jenkins' ARIMA. What distinguishes state space time models is that they separately model components such as trend, seasonal, regression elements and disturbance terms. Part I focuses on traditional and new techniques based on the linear Gaussian model. Part II presents new material extending the state space model to non-Gaussian observations. c. Book News Inc. |
Contents
Chapter 1 Introduction | 1 |
13 NonGaussian and nonlinear models | 3 |
14 Prior knowledge | 4 |
16 Other books on state space methods | 5 |
The linear Gaussian state space model | 7 |
Chapter 2 Local level model | 9 |
22 Filtering | 11 |
23 Forecast errors | 13 |
Chapter 6 Further computational aspects | 121 |
63 Square root filter and smoother | 124 |
64 Univariate treatment of multivariate series | 128 |
65 Filtering and smoothing under linear restrictions | 134 |
Chapter 7 Maximum likelihood estimation | 138 |
73 Parameter estimation | 142 |
74 Goodness of fit | 152 |
Chapter 8 Bayesian analysis | 155 |
24 State smoothing | 16 |
25 Disturbance smoothing | 19 |
26 Simulation | 22 |
27 Missing observations | 23 |
28 Forecasting | 25 |
29 Initialisation | 27 |
210 Parameter estimation | 30 |
211 Steady state | 32 |
212 Diagnostic checking | 33 |
Lemma in multivariate normal regression | 37 |
Chapter 3 Linear Gaussian state space models | 38 |
32 Structural time series models | 39 |
33 ARMA models and ARIMA models | 46 |
34 Exponential smoothing | 49 |
35 State space versus BoxJenkins approaches | 51 |
36 Regression with timevarying coefficients | 54 |
39 Simultaneous modelling of series from different sources | 56 |
310 State space models in continuous time | 57 |
311 Spline smoothing | 61 |
Chapter 4 Filtering smoothing and forecasting | 64 |
42 Filtering | 65 |
43 State smoothing | 70 |
44 Disturbance smoothing | 73 |
45 Covariance matrices of smoothed estimators | 77 |
46 Weight functions | 81 |
47 Simulation smoothing | 83 |
48 Missing observations | 92 |
49 Forecasting | 93 |
410 Dimensionality of observational vector | 94 |
411 General matrix form for filtering and smoothing | 95 |
52 The exact initial Kalman filter | 101 |
53 Exact initial state smoothing | 106 |
54 Exact initial disturbance smoothing | 109 |
55 Exact initial simulation smoothing | 110 |
57 Augmented Kalman filter and smoother | 115 |
83 Markov chain Monte Carlo methods | 159 |
Chapter 9 Illustrations of the use of the linear Gaussian model | 161 |
93 Bivariate structural time series analysis | 167 |
94 BoxJenkins analysis | 169 |
95 Spline smoothing | 172 |
96 Approximate methods for modelling volatility | 175 |
NonGaussian and nonlinear state space models | 177 |
Chapter 10 NonGaussian and nonlinear state space models | 179 |
103 Exponential family models | 180 |
104 Heavytailed distributions | 183 |
105 Nonlinear models | 184 |
106 Financial models | 185 |
Chapter 11 Importance sampling | 189 |
112 Basic ideas of importance sampling | 190 |
113 Linear Gaussian approximating models | 191 |
114 Linearisation based on first two derivatives | 193 |
115 Linearisation based on the first derivative | 195 |
116 Linearisation for nonGaussian state components | 198 |
1 17 Linearisation for nonlinear models | 199 |
118 Estimating the conditional mode | 202 |
119 Computational aspects of importance sampling | 204 |
Chapter 12 Analysis from a classical standpoint | 212 |
123 Estimating conditional densities and distribution functions | 213 |
124 Forecasting and estimating with missing observations | 214 |
125 Parameter estimation | 215 |
Chapter 13 Analysis from a Bayesian standpoint | 222 |
133 Computational aspects of Bayesian analysis | 225 |
134 Posterior analysis of parameter vector | 226 |
135 Markov chain Monte Carlo methods | 228 |
Chapter 14 NonGaussian and nonlinear illustrations | 230 |
outlier in gas consumption in UK | 233 |
pounddollar daily exchange rates | 236 |
OxfordCambridge boat race | 237 |
146 NonGaussian and nonlinear analysis using SsfPack | 238 |
Common terms and phrases
a₁ a₁+1 algorithms antithetic variables approximating model ARIMA models augmented Kalman filter b₁ Box-Jenkins calculated Chapter Cholesky decomposition coefficients components computed consider denote derived discussion disturbance smoothing disturbance vectors Durbin elements equation exact initial Kalman example exponential family F₁ filtering and smoothing forecast errors function Gaussian state space given H₁ Harvey importance density importance sampling initial Kalman filter initial state vector initialisation K₁ Koopman level model linear Gaussian model Linearisation lower triangular matrix maximising maximum likelihood estimate mean square error methods missing observations multivariate N₁ non-Gaussian non-Gaussian and nonlinear observation vector obtain p(aly P₁ parameter estimation parameter vector r₁ random regression seasonal series analysis series models Shephard simulation sample simulation smoother smoothed estimators smoothing recursions space model SsfPack stochastic volatility structural time series t-distribution techniques treatment univariate v₁ values variance matrix y₁ Z₁ zero მს