Empirical vector autoregressive modeling
The main subject of this book is empirical application of multivariate linear time series model on quarterly or month- ly economic data to discoverand describe important dynamic relationships between the variables of interest. The book stresses "real-life" application and the selection of data analytic tools. Simple numerical examples and some more al- gebraicexercises are used to illustrate major points. Rele- vant old and recent results from over 400 authors and refe- rences from econometrics, mathematical statistics, time se- ries analysis, economics and descriptve statistics are dis- cussed. Appropriate use of multivariate time series models requires an intimate knowledge of relevant characteristics of thedata.One can obtain this using a method that combines influence analysis (which data points contain the major part of the information?) and diagnostic checking (does the model describe the interesting part of the information well enough?). For economic time series these issuses are (the type of) nonstationarity of the trend and seasonal compo- nent, be it of the (fractional) "unit root" type or of the changing parameter type (structural breaks), both in a unva- riate and a multivariate context. The book introduces new graphical and statistical methodes to improve the understan- ding of seasonality, outliers, structural breaks, pushing trends and pulling equilibria in aparticular data set.
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The Unrestricted VAR and its components
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additive outlier alternative appendix applied assumption asymptotic autocovariance autoregressive backforecasts canonical correlation changes coefficients cointegrating vectors computed consumption correlation covariance matrix denote derived deterministic discussed dynamic econometric effect eigenvalues eigenvector empirical equation example Figure filter finite sample French data growth rates hypothesis identified impulse responses influence analysis influence measures innovation outlier integration interest interpretation investment level-shift linear LM tests long run macroeconomic matrix inversion lemma method multivariate null null hypothesis number of observations number of unit OLS estimate optimal outcomes p-values parameter stability Perron polynomial prediction procedure real business cycle regression regressors residuals restrictions robust seasonal adjustment seasonal component seasonal frequencies series plots shocks specific specific tests spectrum stationary stochastic studentized residual subsets terms of trade test statistics Tiao transient outlier trend Tsay unit circle unit root nonstationarity unit root tests univariate variance decompositions VECM zero frequency