Elements of Multivariate Time Series AnalysisThe use of methods of time series analysis in the study of multivariate time series has become of increased interest in recent years. Although the methods are rather well developed and understood for univarjate time series analysis, the situation is not so complete for the multivariate case. This book is designed to introduce the basic concepts and methods that are useful in the analysis and modeling of multivariate time series, with illustrations of these basic ideas. The development includes both traditional topics such as autocovariance and auto correlation matrices of stationary processes, properties of vector ARMA models, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and model checking diagnostics for residuals, as well as topics of more recent interest for vector ARMA models such as reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate unit-root models and cointegration structure, and state-space models and Kalman filtering techniques and applications. This book concentrates on the time-domain analysis of multivariate time series, and the important subject of spectral analysis is not considered here. For that topic, the reader is referred to the excellent books by Jenkins and Watts (1968), Hannan (1970), Priestley (1981), and others. |
Contents
| 1 | |
Review of Multivariate Normal Distribution | 12 |
Some Basic Results on Stochastic Convergence | 18 |
Canonical Structure of Vector ARMA Models | 52 |
Initial Model Building and Least Squares Estimation for Vector | 74 |
Review of the General Multivariate Linear | 105 |
Maximum Likelihood Estimation and Model Checking for Vector | 111 |
ReducedRank and Nonstationary CoIntegrated Models | 144 |
1 | 154 |
StateSpace Models Kalman Filtering and Related Topics | 192 |
Time Series Data Sets | 226 |
Exercises and Problems | 238 |
| 248 | |
| 257 | |
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Common terms and phrases
a₁ approximate AR(p asymptotic distribution autocovariance autoregressive B₁ bivariate canonical correlation analysis coefficient matrices conditional consider correlation matrices covariance matrix denotes Diag diagonal discussed echelon canonical eigenvalues elements equal equations equivalent error covariance example expressed forecast errors given Hannan Hence K₁ Kalman filtering Kronecker indices least squares estimates likelihood function linear combinations MA(q mean squared error ML estimation model representation moving average nonstationary obtained P₁ parameters partial canonical correlations prediction predictor procedure Q₁ rank recursively reduced-rank regression Reinsel relation residual rows S₁ sample canonical Section specification state-space representation stationary process stationary vector structure test statistic tion U₁ unit roots univariate models V₁ values variables vector ARMA model vector ARMA(p,q vector autoregressive vector process W₁ white noise X₁ Y₁ Y₁-j Y₁t Z₁ Σ Θ