摘要: Abstract In this paper, we give a characterization of the range spectral matrices, which are feasible for bivariate VAR(p) models. addition to marginal spectra and cross-spectrum being ratios trigonometric polynomials, as is also case VARMA(p,q) models, in polynomials involved numerators denominators must fulfil further restrictions. We state these restrictions show that they sufficient matrix belong VAR. demonstrate how may be regained only from coherency. This, turn, used construct visual goodness-of-fit criterion fitting VAR model, yielding indications on necessary order. The phase lags between frequency- λ -components two series discussed detail. Finally, propose methods constructing models with (partially) pre-specified elements. Examples provided illustrating criterion, phase-lag structure above methods.
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sci-hub.se 参考文章(16)
W. Dunsmuir, E. J. Hannan, VECTOR LINEAR TIME SERIES MODELS Advances in Applied Probability. ,vol. 8, pp. 339- 364 ,(1976) , 10.2307/1425908
E. E. Ioannidis, G. A. Chronis, Extreme Spectra of Var Models and Orders of Near-Cointegration Journal of Time Series Analysis. ,vol. 26, pp. 399- 421 ,(2005) , 10.1111/J.1467-9892.2004.00408.X
Santiago Velilla, A GOODNESS-OF-FIT TEST FOR AUTOREGRESSIVE MOVING-AVERAGE MODELS BASED ON THE STANDARDIZED SAMPLE SPECTRAL DISTRIBUTION OF THE RESIDUALS Journal of Time Series Analysis. ,vol. 15, pp. 637- 647 ,(1994) , 10.1111/J.1467-9892.1994.TB00218.X
J. P. Romano, Hui Chen, Bootstrap assisted goodness of fit tests in the frequency domain ,(1996)
T. W. Anderson, Goodness-of-fit tests for autoregressive processes Journal of Time Series Analysis. ,vol. 18, pp. 321- 339 ,(1997) , 10.1111/1467-9892.00053
Rainer Dahlhaus, Empirical spectral processes and their applications to time series analysis Stochastic Processes and their Applications. ,vol. 30, pp. 69- 83 ,(1988) , 10.1016/0304-4149(88)90076-2
Rainer Dahlhaus, Graphical interaction models for multivariate time series 1 Metrika. ,vol. 51, pp. 157- 172 ,(2000) , 10.1007/S001840000055
M. Deistler, E. J. Hannan, The statistical theory of linear systems ,(1988)
T. W. Anderson, Goodness of Fit Tests for Spectral Distributions Annals of Statistics. ,vol. 21, pp. 830- 847 ,(1993) , 10.1214/AOS/1176349153
Peter J. Brockwell, Time Series: Theory and Methods ,(2009)