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Estimating Orthogonal Impulse Responses via Vector Autoregressive Models

Published online by Cambridge University Press:  11 February 2009

Helmut Lütkepohl  and
D.S. Poskitt
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Abstract

Impulse response functions from time series models are standard tools for analyzing the relationship between economic variables. The asymptotic distribution of orthogonalized impulse responses is derived under the assumption that finite order vector autoregressive (VAR) models are fitted to time series generated by possibly infinite order processes. The resulting asymptotic distributions of forecast error variance decompositions are also given.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 4 , December 1991 , pp. 487 - 496
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1.Akaike, H. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19 (1974): 716–723.10.1109/TAC.1974.1100705CrossRefGoogle Scholar
2.Baillie, R.T. Asymptotic tests on moving average representation coefficients with an application to innovations on spot and forward exchange rates. Economics Letters 13 (1983): 201–206.10.1016/0165-1765(83)90086-1CrossRefGoogle Scholar
3.Baillie, R.T. Inference in dynamic models containing “surprise” variables. Journal of Econometrics 35 (1987): 101–117.10.1016/0304-4076(87)90083-2CrossRefGoogle Scholar
4.Baxter, G. A norm inequality for a finite section Wiener-Hopf equation. Illinois Journal of Mathematics 7 (1963): 97–103.10.1215/ijm/1255637484CrossRefGoogle Scholar
5.Berk, K.N. Consistent autoregressive spectral estimates. Annals of Statistics 2 (1974): 489–502.10.1214/aos/1176342709CrossRefGoogle Scholar
6.Bhansali, R.J. Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics 6 (1978): 224–231.10.1214/aos/1176344081CrossRefGoogle Scholar
7.Burbidge, J. & Harrison, A.. Testing for the effects of oil-price rises using vector autoregressions. International Economic Review 25 (1984): 459–484.10.2307/2526209CrossRefGoogle Scholar
8.Hannan, E.T. & Kavalieris, L.. Regression; autoregression models. Journal of Time Series Analysis 7 (1986): 27–49.10.1111/j.1467-9892.1986.tb00484.xCrossRefGoogle Scholar
9.Huber, P.J. Robust regression: Asymptotics, conjectures and Monte Carlo. Annals of Statistics 5 (1973): 799–821.Google Scholar
10.Lewis, R. & Reinsel, G.. Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16 (1985): 393–411.10.1016/0047-259X(85)90027-2CrossRefGoogle Scholar
11.Litterman, R.B. & Weiss, L.. Money, real interest rates, and output: A reinterpretation of postwar U.S. data. Econometrica 53 (1985): 129–156.10.2307/1911728CrossRefGoogle Scholar
12.Lütkepohl, H. Asymptotic distribution of the moving average coefficients of an estimated vector autoregressive process. Econometric Theory 4 (1988): 77–85.10.1017/S0266466600011865CrossRefGoogle Scholar
13.Lütkepohl, H. A note on the asymptotic distribution of impulse response functions of estimated VAR models with orthogonal residuals. Journal of Econometrics 42 (1989): 371–376.10.1016/0304-4076(89)90059-6CrossRefGoogle Scholar
14.Lütkepohl, H. Asymptotic distributions of impulse response functions and forecast error variance decompositions of vector autoregressive models. Review of Economics and Statistics 72 (1990): 116–125.10.2307/2109746CrossRefGoogle Scholar
15.Magnus, J.R. & Neudecker, H.. Matrix Differential Calculus with Applications in Statistics and Econometrics Chichester: Wiley, 1988.Google Scholar
16.Portnoy, S. On the central limit theorem in R p when p → ∞. Probability Theory and Related Fields 73 (1986): 571–583.10.1007/BF00324853CrossRefGoogle Scholar
17.Portnoy, S. Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. Annals of Statistics 16 (1988): 356–366.10.1214/aos/1176350710CrossRefGoogle Scholar
18.Rao, C.R. Linear Statistical Inference and Its Applications New York: Wiley, 1965.Google Scholar
19.Rozanov, Yu A. Stationary Random Processes San Francisco: Holden-Day, 1967.Google Scholar
20.Schmidt, P. The asymptotic distribution of dynamic multipliers. Econometrica 41 (1973): 161–164.10.2307/1913891CrossRefGoogle Scholar
21.Schwarz, G. Estimating the dimension of a model. Annals of Statistics 6 (1978): 461–464.10.1214/aos/1176344136CrossRefGoogle Scholar
22.Shibata, R. Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics 8 (1980): 147–164.10.1214/aos/1176344897CrossRefGoogle Scholar
23.Sims, C.A. Macroeconomics and reality. Econometrica 48 (1980): 1–48.10.2307/1912017CrossRefGoogle Scholar
24.Sims, C.A. An autoregressive index model for the U.S. 1948–1975. In Kmenta, J. & Ramsey, J.B. (eds.), Large-Scale Macro-Econometric Models, pp. 283–327. Amsterdam: North-Holland, 1981.Google Scholar