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Conditional means of time series processes and time series processes for conditional means

Author

Listed:
  • Gabriele Fiorentini

    () (Universidad de Alicante)

  • Enrique Sentana Iváñez

    (CEMFI)

Abstract

We study the processes for the conditional mean and variance given a specification of the process for the observed time series. We derive general results for the conditional mean of univariate and vector linear processes, and then apply it to various models of interest. We also consider the joint process for a subvector and its expected value conditional on the whole information set. In this respect, we derive necessary and sufficient conditions for one of the variables in a bivariate VAR(l) to have a white noise univariate representation while its conditional mean follows an AR(l) with a high autocorrelation coefficient. We also compare the persistence of shocks to the conditional mean relative to the observed variable using mea sures of total and iterim persistence of shocks for stationary processes based on the impulse response function. We apply our results to post-war US monthly real stock market returns and dividend yields. Our findings seem to confirm that stock returns are very close to white noise, while expected returns are well represented by an AR(l) process with a firstorder autocorrelation of .9755. We also find that small unexpected variations in expected returns have a large negative immediate impact on observed returns, which is thereafter compensated by a slowly diminishing positive effect on expected returns.

Suggested Citation

  • Gabriele Fiorentini & Enrique Sentana Iváñez, 1997. "Conditional means of time series processes and time series processes for conditional means," Working Papers. Serie AD 1997-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  • Handle: RePEc:ivi:wpasad:1997-17
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    Cited by:

    1. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    2. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.
    4. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    5. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    6. Bruno Feunou & Jean-Sébastien Fontaine, 2012. "Forecasting Inflation and the Inflation Risk Premiums Using Nominal Yields," Staff Working Papers 12-37, Bank of Canada.
    7. Neil Kellard & Denise Osborn & Jerry Coakley & Christian Conrad & Menelaos Karanasos, 2015. "On the Transmission of Memory in Garch-in-Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 706-720, September.
    8. Bruno Feunou & Jean-Sébastien Fontaine, 2014. "Bond Risk Premia and Gaussian Term Structure Models," Staff Working Papers 14-13, Bank of Canada.
    9. René Garcia & Éric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.

    More about this item

    Keywords

    Time series processes; conditional moments; expected returns; persistence;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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