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The Estimation of a Lagged Regression Relation
E. J. Hannan
Vol. 54, No. 3/4 (Dec., 1967), pp. 409-418
Stable URL: http://www.jstor.org/stable/2335033
Page Count: 10
You can always find the topics here!Topics: Matrices, Covariance, Fourier series, Absolute convergence, Least squares, Time series, Central limit theorem, Arithmetic mean, Time series analysis, Statistical estimation
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The paper discusses a technique for estimating the matrices of coefficients, B(j), in a regression relation relating a vector time series, z(n), to lagged values, y(n - j), - p ⩽ j ⩽ q, of a second vector time series. The technique depends upon calculation of spectra and cross-spectra. Once these are computed the estimates B̂(j) are obtained successively without recalculation when an additional lag is introduced. When the residuals from the regression are generated by a linear process independent of y(n) it is shown that under some additional regularity conditions the estimates are asymptotically jointly normal, the variances and covariances of the elements of $\hat\beta(j)$ being independent of j and of p and q. The method of estimation is not efficient unless the spectra of the y process and the residual process are the same. Some idea of the magnitude of B̂(k) for lags for which computations have not been done can be obtained without doing these computations.
Biometrika © 1967 Biometrika Trust