book

Multivariate Time Series Analysis and Applications

March 2019

Intermediate to advanced

680 pages

13h 56m

English

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1.1 Introduction1.2 Fundamental conceptsProjectsReferences
2.1 Vector moving average processes2.2 Vector autoregressive processes2.3 Vector autoregressive moving average processes2.4 Nonstationary vector autoregressive moving average processes2.5 Vector time series model building2.6 Seasonal vector time series model2.7 Multivariate time series outliers2.8 Empirical examplesSoftware codeProjectsReferences
3.1 Introduction3.2 Multivariate multiple time series regression models3.3 Estimation of the multivariate multiple time series regression model3.4 Vector time series regression models3.5 Empirical Example III – Total mortality and air pollution in CaliforniaSoftware codeProjectsReferences
4.1 Introduction4.2 Population PCA4.3 Implications of PCA4.4 Sample principle components4.5 Empirical examplesSoftware codeProjectsReferences
5.1 Introduction5.2 The orthogonal factor model5.3 Estimation of the factor model5.4 Factor rotation5.5 Factor scores5.6 Factor models with observable factors5.7 Another empirical example – Yearly U.S. sexually transmitted diseases (STD)5.8 Concluding remarksSoftware codeProjectsReferences
6.1 Introduction6.2 Representations of multivariate GARCH models6.3 O‐GARCH and GO‐GARCH models6.4 Estimation of GO‐GARCH models6.5 Properties of the weighted scatter estimator6.6 Empirical examplesSoftware codeProjectsReferences

7.1 Introduction7.2 Multivariate analysis of variance7.3 Models utilizing time series structure7.4 Nested random effects model7.5 Further generalization and remarks7.6 Another empirical example – the oral condition of neck cancer patientsSoftware codeProjectsReferences
8.1 Introduction8.2 Space–time autoregressive integrated moving average (STARIMA) models8.3 Generalized space–time autoregressive integrated moving average (GSTARIMA) models8.4 Iterative model building of STARMA and GSTARMA models8.5 Empirical examplesSoftware codeProjectsReferences
9.1 Introduction9.2 Spectral representations of multivariate time series processes9.3 The estimation of the spectral density matrix9.4 Empirical examples of stationary vector time series9.5 Spectrum analysis of a nonstationary vector time series9.6 Empirical spectrum example of nonstationary vector time seriesSoftware codeProjectsReferences
10.1 Introduction10.2 Existing methods10.3 The proposed method for high‐dimension reduction10.4 Simulation studies10.5 Empirical examples10.6 Further discussions and remarks10.A Appendix: Parameter estimation results of various proceduresSoftware codeProjectsReferences

Subject index

Absolutely summable, 8, 12, 302, 304, 305
Adjoint matrix, 12, 29
Aggregation
- contemporal aggregation, 437, 466
- spatial aggregation, 281, 285, 286, 506
- temporal aggregation, 103, 467, 506
Air pollution, 120–137
Amplitude spectrum, 307
ARCH models, 203
Autoregressive representation of vector processes, 7–9

Cauchy–Schwarz inequality, 4
Cholesky decomposition, 315, 317, 318, 333, 334, 337
Clustering
- hierarchical clustering, 460, 463
- model‐based cluster approach, 443
- nonhierarchical clustering, 460, 463
- partitioning around mediods (PAM), 463, 465
- total within sum of square (TWSS), 461, 463
Cointegration, 25
Cointegration in vector time series
- error‐correction representation, 25
- the trace test, 25
Conditional covariance matrix, 204, 207
Correlation matrix function
- partial, 3–7, 24
- sample, 24, 32
Co‐spectrum, 306, 311
Covariance matrix function, 12, 23, 304, 320
Cross‐spectrum, 306, 312