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Dynamic Time Series Models using R-INLA: An Applied Perspective [Kõva köide]

, (Cogitaas AVA, Mumbai, India), (University of Connecticut, Storrs, USA)
  • Formaat: Hardback, 282 pages, kõrgus x laius: 254x178 mm, kaal: 880 g, 17 Tables, black and white; 68 Line drawings, color; 20 Line drawings, black and white; 68 Illustrations, color; 20 Illustrations, black and white
  • Ilmumisaeg: 10-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 036765427X
  • ISBN-13: 9780367654276
Teised raamatud teemal:
Dynamic Time Series Models using R-INLA: An Applied PerspectiveSuurem pilt
  • Formaat: Hardback, 282 pages, kõrgus x laius: 254x178 mm, kaal: 880 g, 17 Tables, black and white; 68 Line drawings, color; 20 Line drawings, black and white; 68 Illustrations, color; 20 Illustrations, black and white
  • Ilmumisaeg: 10-Aug-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 036765427X
  • ISBN-13: 9780367654276
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367654276.html
Märksõnad:
Dynamic Time Series Models using R-INLA: An Applied Perspective is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework.

The book is an ideal reference for statisticians and scientists who work with time series data. It provides an excellent resource for teaching a course on Bayesian analysis using state space models for time series.

Key Features:





Introduction and overview of R-INLA for time series analysis. Gaussian and non-Gaussian state space models for time series. State space models for time series with exogenous predictors. Hierarchical models for a potentially large set of time series. Dynamic modelling of stochastic volatility and spatio-temporal dependence.

Arvustused

"This book will interest current R-users with a background in time series analyses who would like to expand their knowledge regarding INLA and its application with R-INLA package. This book also provides illustrative examples which can contribute to the understanding of the applications of these methods. This book can also benefit academic researchers who would like to apply these types of approaches in their fields."

Sébastien Bailly, French National Center for Medical Research (INSERM), France, ISCB, May 2023

Preface xi
1 Bayesian Analysis
1(16)
1.1 Introduction
1(1)
1.2 Bayesian framework
2(4)
1.2.1 Bayesian model comparison
3(3)
1.3 Bayesian analysis of time series
6(1)
1.4 Gaussian dynamic linear models (DLMs)
7(6)
1.4.1 Constant level plus noise model
7(2)
1.4.2 Local level model
9(1)
1.4.3 Gaussian DLM framework for univariate time series
10(1)
1.4.4 AR(1) plus noise model
11(1)
1.4.5 DLM for vector-valued time series
11(1)
1.4.6 Kalman filtering and smoothing
12(1)
1.5 Beyond basic Gaussian DLMs
13(4)
2 A Review of INLA
17(12)
2.1 Introduction
17(1)
2.2 Laplace approximation
17(3)
2.2.1 Simplified Laplace approximation
19(1)
2.3 INLA structure for time series
20(2)
2.3.1 INLA steps
21(1)
2.4 Forecasting in INLA
22(1)
2.5 Marginal likelihood computation in INLA
22(1)
2.6 R-INLA package -- some basics
23(6)
3 Details of R-INLA for Time Series
29(50)
3.1 Introduction
29(1)
3.2 Random walk plus noise model
29(13)
3.2.1 R-INLA model formula
30(1)
3.2.2 Model execution
31(4)
3.2.3 Prior specifications for hyperparameters
35(1)
3.2.4 Posterior distributions of hyperparameters
36(2)
3.2.5 Fitted values for latent states and responses
38(3)
3.2.6 Filtering and smoothing in DLM
41(1)
3.3 AR(1) with level plus noise model
42(5)
3.4 Dynamic linear models with higher order AR lags
47(4)
3.5 Random walk with drift plus noise model
51(4)
3.6 Second-order polynomial model
55(6)
3.7 Forecasting states and observations
61(1)
3.8 Model comparisons
62(3)
3.8.1 In-sample model comparisons
63(2)
3.8.2 Out-of-sample comparisons
65(1)
3.9 Non-default prior specifications
65(2)
3.9.1 Custom prior specifications
66(1)
3.9.2 Penalized complexity (PC) priors
67(1)
3.10 Posterior sampling of latent effects and hyperparameters
67(5)
3.11 Posterior predictive samples of unknown observations
72(7)
4 Modeling Univariate Time Series
79(16)
4.1 Introduction
79(1)
4.2 Example: A software engineering example -- Musa data
79(11)
4.2.1 Model
1. AR(1) with level plus noise model
81(3)
4.2.2 Model
2. Random walk plus noise model
84(2)
4.2.3 Model
3. AR(1) with trend plus noise model
86(1)
4.2.4 Model
4. AR(2) with level plus noise model
87(3)
4.3 Forecasting future states and responses
90(2)
4.4 Model comparisons
92(3)
5 Time Series Regression Models
95(16)
5.1 Introduction
95(1)
5.2 Structural models
95(6)
5.2.1 Example: Monthly average cost of nightly hotel stay
96(5)
5.3 Models with exogenous predictors
101(6)
5.3.1 Example: Hourly traffic volumes
102(5)
5.4 Latent AR(1) model with covariates plus noise
107(4)
6 Hierarchical Dynamic Models for Panel Time Series
111(20)
6.1 Introduction
111(1)
6.2 Models with homogenous state evolution
111(6)
6.2.1 Example: Simulated homogeneous panel time series with the same level
112(1)
6.2.2 Example: Simulated homogeneous panel time series with different levels
113(4)
6.3 Example: Ridesourcing in NYC
117(10)
6.3.1 Model H1. Dynamic intercept and exogenous predictors
119(3)
6.3.2 Model H2. Dynamic intercept and Taxi usage
122(4)
6.3.3 Model H3. Taxi usage varies by time and zone
126(1)
6.3.4 Model H4. Fixed intercept, Taxi usage varies over time and zones
126(1)
6.4 Model comparison
127(4)
7 Non-Gaussian Continuous Responses
131(18)
7.1 Introduction
131(1)
7.2 Gamma state space model
131(7)
7.2.1 Example: Volatility index (VIX) time series
132(6)
7.3 Weibull state space model
138(4)
7.3.1 Forecasting from Weibull models
141(1)
7.4 Beta state space model
142(7)
7.4.1 Example: Crest market share
142(7)
8 Modeling Categorical Time Series
149(24)
8.1 Introduction
149(1)
8.2 Binomial response time series
149(7)
8.2.1 Example: Simulated single binomial response series
150(2)
8.2.2 Example: Weekly shopping trips for a single household
152(4)
8.3 Modeling multiple binomial response time series
156(6)
8.3.1 Example: Dynamic aggregated model for multiple binomial response time series
156(3)
8.3.2 Example: Weekly shopping trips for multiple households
159(3)
8.4 Multinomial time series
162(11)
8.4.1 Example: Simulated categorical time series
163(10)
9 Modeling Count Time Series
173(24)
9.1 Introduction
173(1)
9.2 Univariate time series of counts
173(9)
9.2.1 Example: Simulated univariate Poisson counts
173(3)
9.2.2 Example: Modeling crash counts in CT
176(3)
9.2.3 Example: Daily bike rentals in Washington D.C.
179(3)
9.3 Hierarchical modeling of univariate count time series
182(15)
9.3.1 Example: Simulated univariate Poisson counts
182(5)
9.3.2 Example: Modeling daily TNC usage in NYC
187(10)
10 Modeling Stochastic Volatility
197(8)
10.1 Introduction
197(1)
10.2 Univariate SV models
198(7)
10.2.1 Example: Simulated SV data with standard normal errors
198(1)
10.2.2 Example: Simulated SV data with Student-tv errors
199(1)
10.2.3 Example: IBM stock returns
199(4)
10.2.4 Example: NYSE returns
203(2)
11 Spatio-temporal Modeling
205(12)
11.1 Introduction
205(1)
11.2 Spatio-temporal process
206(1)
11.3 Dynamic spatial models for areal data
206(1)
11.4 Example: Monthly TNC usage in NYC taxi zones
207(10)
11.4.1 Model
1. Knorr-Held additive effects model
209(1)
11.4.2 Knorr-Held models with space-time interactions
210(7)
12 Multivariate Gaussian Dynamic Modeling
217(26)
12.1 Introduction
217(1)
12.2 Model with diagonal W and Φ matrices
218(12)
12.2.1 Description of the setup for V
218(1)
12.2.2 Example: Simulated bivariate AR(1) series
218(3)
12.2.3 Example: Ridesourcing data in NYC for a single taxi zone
221(9)
12.3 Model with equicorrelated wt and diagonal Φ
230(4)
12.3.1 Example: Simulated trivariate series
230(4)
12.4 Fitting multivariate models using rgeneric
234(9)
12.4.1 Example: Simulated bivariate VAR(1) series
235(8)
13 Hierarchical Multivariate Time Series
243(18)
13.1 Introduction
243(1)
13.2 Multivariate hierarchical dynamic linear model
243(10)
13.2.1 Example: Analysis of TNC and Taxi as responses
245(8)
13.3 Level correlated models for multivariate time series of counts
253(8)
13.3.1 Example: TNC and Taxi counts based on daily data
254(7)
14 Resources for the User
261(12)
14.1 Introduction
261(1)
14.2 Packages used in the book
261(1)
14.3 Custom functions used in the book
262(7)
14.3.1 rgeneric() function for DLM-VAR model
266(3)
14.4 Often used R--INLA items
269(4)
Bibliography 273(8)
Index 281
Nalini Ravishanker is a professor in the Department of Statistics at the University of Connecticut, Storrs, USA.

Balaji Raman is a statistician at Cogitaas AVA, Mumbai, India.

Refik Soyer is a professor in the Department of Decision Sciences at The George Washington University, Washington D.C., USA.