Skip to main content Accessibility help
×
Home
Hostname: page-component-5c569c448b-ph4cd Total loading time: 0.14 Render date: 2022-07-02T09:44:08.376Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process

Published online by Cambridge University Press:  18 October 2010

Helmut Lütkepohl
Affiliation:
Christian-Albrechts-Universität Kiel

Abstract

The coefficients of the moving average (MA) representation of a vector autoregressive (VAR) process are the dynamic multipliers of the system. These quantities are often used to analyze the relationships between the variables involved. Assuming that the actual data generation process is stationary and has a VAR representation of unknown and possibly infinite order, the asymptotic distribution of the MA coefficients is derived. A computationally simple formula for the asymptotic co variance matrix is obtained.

Type
Articles
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Backus, D.The Canadian-U.S. exchange rate: evidence from a vector autoregression. Review of Economics and Statistics 68 (1986): 628637.CrossRefGoogle Scholar
2.Baillie, R.T.Asymptotic prediction mean squared error for vector autoregressive models. Biometrika 66 (1979): 675678.CrossRefGoogle Scholar
3.Baillie, R.T.Inference in dynamic models containing “surprise” variables. Journal of Econometrics 35 (1987): 101117.CrossRefGoogle Scholar
4.Berk, K.N.Consistent autoregressive spectral estimates. Annals of Statistics 2 (1974): 489502.CrossRefGoogle Scholar
5.Bhansali, R.J.Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics 6 (1978): 224231.CrossRefGoogle Scholar
6.Lewis, R. & Reinsel, G.. Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16 (1985): 393411.CrossRefGoogle Scholar
7.Lütkepohl, H.Forecasting aggregated vector ARMA processes. Berlin: Springer-Verlag, 1987.CrossRefGoogle Scholar
8.Reinsel, G.Asymptotic properties of prediction errors for the multivariate autoregressive model using estimated parameters. Journal of the Royal Statistical Society B 42 (1980): 328333.Google Scholar
9.Said, S.E. & Dickey, D.A.. Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71 (1984): 599607.CrossRefGoogle Scholar
10.Schmidt, P.The asymptotic distribution of dynamic multipliers. Econometrica 41 (1973): 161164.CrossRefGoogle Scholar
11.Sims, C.A. Macroeconomics and reality. Econometrica 48 (1980): 148.CrossRefGoogle Scholar
12.Sims, C.A. An autoregressive index model for the U.S. 1948–1975. In Kmenta, J. & Ramsey, J.B. (eds.), Large-scale macroeconometric models, pp. 283327. Amsterdam: North-Holland, 1981.Google Scholar
13.Yamamoto, T.On the treatment of autocorrelated errors in the multiperiod prediction of dynamic simultaneous equation models. International Economic Review 21 (1980): 735748.CrossRefGoogle Scholar
14.Yamamoto, T.Prediction of multivariate autoregressive-moving average models. Biometrika 68 (1981): 485492.CrossRefGoogle Scholar
17
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *