Multivariate Analysis in Vector Time Series

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Pena and Box (1987) and Pena and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.

[1]  S. Kullback,et al.  Information Theory and Statistics , 1959 .

[2]  You-yen. Yang.  Classification into two multivariate normal distributions with different covariance matrices , 1965 .

[3]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .

[4]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .

[5]  H. Akaike.  A new look at the statistical model identification , 1974 .

[6]  R. Shumway,et al.  Linear Discriminant Functions for Stationary Time Series , 1974 .

[7]  G. C. Tiao,et al.  A canonical analysis of multiple time series , 1977 .

[8]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[9]  H. Akaike.  A Bayesian extension of the minimum AIC procedure of autoregressive model fitting , 1979 .

[10]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[11]  W Gersch,et al.  Automatic classification of electroencephalograms: Kullback-Leibler nearest neighbor rules. , 1979, Science.

[12]  John Geweke,et al.  Maximum Likelihood "Confirmatory" Factor Analysis of Economic Time Series , 1981 .

[13]  R. Engle,et al.  A One-Factor Multivariate Time Series Model of Metropolitan Wage Rates , 1981 .

[14]  P. Laycock,et al.  SPECTRAL RATIO DISCRIMINANTS AND INFORMATION THEORY , 1981 .

[15]  E. Slud,et al.  Time Series Discrimination by Higher Order Crossings , 1982 .

[16]  R. H. Shumway,et al.  1 Discriminant analysis for time series , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[17]  Peter C. M. Molenaar,et al.  A dynamic factor model for the analysis of multivariate time series , 1985 .

[18]  G. C. Tiao,et al.  Use of canonical analysis in time series model identification , 1985 .

[19]  J. Rissanen.  Stochastic Complexity and Modeling , 1986 .

[20]  Gregory C. Reinsel,et al.  Reduced rank models for multiple time series , 1986 .

[21]  Lyle D. Bromeling,et al.  The classification problem with autoregressive process , 1987 .

[22]  George E. P. Box,et al.  Identifying a Simplifying Structure in Time Series , 1987 .

[23]  Gregory C. Reinsel,et al.  Nested Reduced-Rank Autoregressive Models for Multiple Time Series , 1988 .

[24]  E. Hannan,et al.  The statistical theory of linear systems , 1989 .

[25]  Dean M. Young,et al.  Predictive discrimination for autoregressive processes , 1988, Pattern Recognit. Lett..

[26]  G. C. Tiao,et al.  Model Specification in Multivariate Time Series , 1989 .

[27]  J. Alagón.  SPECTRAL DISCRIMINATION FOR TWO GROUPS OF TIME SERIES , 1989 .

[28]  R. Martin,et al.  Leave‐K‐Out Diagnostics for Time Series , 1989 .

[29]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[30]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[31]  Daniel Peña,et al.  Interpolation, Outliers and Inverse Autocorrelations , 1990 .

[32]  D. Piccolo.  A DISTANCE MEASURE FOR CLASSIFYING ARIMA MODELS , 1990 .

[33]  G. Chaudhuri,et al.  Bhattacharyya distance based linear discriminant function for stationary time series , 1991 .

[34]  Paul S. P. Cowpertwait,et al.  Clustering population means under heterogeneity of variance with an application to a rainfall time series problem , 1992 .

[35]  Linear discriminant function for complex normal time series , 1992 .

[36]  G. R. Dargahi-Noubary,et al.  Disoominkfrcn between gaussian time series based on their spectral differences , 1992 .

[37]  V. Solo.  The Statistical Theory of Linear Systems E. J. Hannan and Manfred Deistler John Wiley & Sons, 1988 , 1992, Econometric Theory.

[38]  Peter C. M. Molenaar,et al.  Dynamic factor analysis of nonstationary multivariate time series , 1992 .

[39]  R. Bhansali.  Order selection for linear time series models: a review , 1993 .

[40]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[41]  C. Gantert.  Classification of Trends Via the Linear State Space Model , 1994 .

[42]  Daniel Peña,et al.  COINTEGRATION AND COMMON FACTORS , 1994 .

[43]  Andrew T. Walden,et al.  Spatial clustering: using simple summaries of seismic data to find the edge of an oil-field , 1994 .

[44]  Genshiro Kitagawa,et al.  State Space Modeling of Time Series , 1994 .

[45]  Maria Macchiato,et al.  Time modelling and spatial clustering of daily ambient temperature: An application in Southern Italy , 1995 .

[46]  Ta-Hsin Li,et al.  Discrimination of Time Series by Parametric Filtering , 1996 .

[47]  J. Cavanaugh,et al.  A BOOTSTRAP VARIANT OF AIC FOR STATE-SPACE MODEL SELECTION , 1997 .

[48]  Tze Leung Lai,et al.  INFORMATION AND PREDICTION CRITERIA FOR MODEL SELECTION IN STOCHASTIC REGRESSION AND ARMA MODELS , 1997 .

[49]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .