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ARIMA Processes with ARIMA Parameters

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  • Grillenzoni, Carlo

Abstract

This article introduces a general class of nonlinear and nonstationary time-series models whose basic scheme is an autoregressive integrated moving average (ARIMA). The main feature i s that the parameters are assumed to behave like a vector ARIMAx model in which the exogenous (x) component is represented by the regressors o f the observable process. For this class, a general algorithm of identification-estimation is outlined based on the sampling information alone. The initial estimation, in particular, consists o f an iterative procedure of nonlinear regressions on recursive paramet er estimates generated with the extended Kalman filter.

Suggested Citation

  • Grillenzoni, Carlo, 1993. "ARIMA Processes with ARIMA Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 235-250, April.
  • Handle: RePEc:bes:jnlbes:v:11:y:1993:i:2:p:235-50
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    References listed on IDEAS

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    1. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    2. Gregory, Allan W, 1994. "Testing for Cointegration in Linear Quadratic Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 347-360, July.
    3. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    4. Engle, R. F. & Granger, C. W. J. (ed.), 1991. "Long-Run Economic Relationships: Readings in Cointegration," OUP Catalogue, Oxford University Press, number 9780198283393.
    5. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
    6. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
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    Cited by:

    1. Ammermann, Peter A. & Patterson, Douglas M., 2003. "The cross-sectional and cross-temporal universality of nonlinear serial dependencies: Evidence from world stock indices and the Taiwan Stock Exchange," Pacific-Basin Finance Journal, Elsevier, vol. 11(2), pages 175-195, April.
    2. Levent Ozbek & Umit Ozlale & Fikri Ozturk, 2003. "Employing Extended Kalman Filter in a Simple Macroeconomic Model," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 3(1), pages 53-65.
    3. Carlo Grillenzoni, 2008. "Performance of adaptive estimators in slowly varying parameter models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(4), pages 471-482, October.
    4. Ozbek, Levent & Ozlale, Umit, 2005. "Employing the extended Kalman filter in measuring the output gap," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1611-1622, September.
    5. Carlo Grillenzoni, 2000. "Time-Varying Parameters Prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 108-122, March.
    6. Franses, Philip Hans & Paap, Richard & Vroomen, Bjorn, 2004. "Forecasting unemployment using an autoregression with censored latent effects parameters," International Journal of Forecasting, Elsevier, vol. 20(2), pages 255-271.
    7. Franses, Ph.H.B.F. & Paap, R., 1998. "Modelling asymmetric persistence over the business cycle," Econometric Institute Research Papers EI 9852, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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