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Speed of Adjustment in Cointegrated Systems

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  • Fanelli, Luca
  • Paruolo, Paolo

Abstract

This paper considers the speed of adjustment to long-run equilibria, in the context of cointegrated Vector Autoregressive Processes (VAR). We discuss the definition of multivariate p-lives for any indicator of predictive ability, concentrating on cumulated interim multipliers which converge to impact factor for increasing forecasting horizon. Interim multipliers are related to autoregressive Granger-causality coefficients, structural or generalized cumulative impulse responses. We discuss the relation of the present definition of multivariate p-lives with existing definitions for univariate time series and for nonlinear multivariate stationary processes. For multivariate (possibly cointegrated) VAR systems, p-lives are functions of the dynamics of the system only,and do not depend on the history path on which the forecast is based. Hence one can discuss inference on p-lives as (discrete) functions of parameters in the VAR model. We discuss a likelihood-based approach, both for point estimation and for confidence regions. An illustrative application to adjustment to purchasing-power parity (PPP) is presented.

Suggested Citation

  • Fanelli, Luca & Paruolo, Paolo, 2007. "Speed of Adjustment in Cointegrated Systems," MPRA Paper 9174, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:9174
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    3. Giovanni Angelini & Emanuele Bacchiocchi & Giovanni Caggiano & Luca Fanelli, 2019. "Uncertainty across volatility regimes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 437-455, April.
    4. Paolo Paruolo & Ben Murphy & Greet Janssens-Maenhout, 2011. "Do emissions and income have a common trend? A country-specific, time-series, global analysis, 1970-2008," Economics and Quantitative Methods qf1113, Department of Economics, University of Insubria.
    5. Luca Fanelli & Marco M. Sorge, 2015. "Indeterminacy, Misspecification and Forecastability: Good Luck in Bad Policy?," CSEF Working Papers 402, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Camarero, Mariam & D'Adamo, Gaetano & Tamarit, Cecilio, 2014. "Wage leadership models: A country-by-country analysis of the EMU," Economic Modelling, Elsevier, vol. 44(S1), pages 2-11.
    7. Machava, Agostinho, 2017. "The Macroeconomic Determinants of the Pass-Through from the Market Interest Rate to the Bank Lending Rate in Mozambique," Umeå Economic Studies 954, Umeå University, Department of Economics.
    8. M. Castellani & L. Fanelli & M. Savioli, 2015. "Government fiscal efforts vs. labour union strikes. Strategic substitutes or complements?," Working Papers wp1013, Dipartimento Scienze Economiche, Universita' di Bologna.
    9. Chaboud, Alain & Hjalmarsson, Erik & Zikes, Filip, 2021. "The evolution of price discovery in an electronic market," Journal of Banking & Finance, Elsevier, vol. 130(C).
    10. Berta, P. & Lovaglio, P.G. & Paruolo, P. & Verzillo, S., 2020. "Real Time Forecasting of Covid-19 Intensive Care Units demand," Health, Econometrics and Data Group (HEDG) Working Papers 20/16, HEDG, c/o Department of Economics, University of York.
    11. Matteo Barigozzi & Antonio M. Conti, 2018. "On the Stability of Euro Area Money Demand and Its Implications for Monetary Policy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(4), pages 755-787, August.
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    13. Fanelli, Luca & Sorge, Marco M., 2017. "Indeterminate forecast accuracy under indeterminacy," Journal of Macroeconomics, Elsevier, vol. 53(C), pages 57-70.
    14. Giovanni Angelini & Emanuele Bacchiocchi & Giovanni Caggiano & Luca Fanelli, 2019. "Uncertainty across volatility regimes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 437-455, April.
    15. Abadir, Karim M. & Luati, Alessandra & Paruolo, Paolo, 2023. "GARCH density and functional forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 470-483.
    16. Girardi, Riccardo & Paruolo, Paolo, 2013. "Wages and prices in Europe before and after the onset of the Monetary Union," Economic Modelling, Elsevier, vol. 35(C), pages 643-653.

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    More about this item

    Keywords

    p-life; speed of adjustment; impact factors; vector equilibrium correction; shock absorption;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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