IDEAS home Printed from https://ideas.repec.org/p/ivi/wpasad/1997-17.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1997-17.pdf
    File Function: Fisrt version / Primera version, 1997
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    2. 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.
    3. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Ángel León & Enrique Sentana, 1997. "Pricing Options on Assets with Predictable White Noise Returns," Working Papers wp1997_9704, CEMFI.
    5. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    6. Chin, Kuo-Hsuan & Li, Xue, 2019. "Bayesian forecast combination in VAR-DSGE models," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 278-298.
    7. 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.
    8. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time‐Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, January.
    9. 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.
    10. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    11. Antonis Demos & Sofia Parissi, 1998. "Testing Asset Pricing Models: The Case of Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 2(3), pages 189-223, September.
    12. Alessandra Canepa, & Karanasos, Menelaos & Paraskevopoulos, Athanasios & Chini, Emilio Zanetti, 2022. "Forecasting Ination: A GARCH-in-Mean-Level Model with Time Varying Predictability," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202212, University of Turin.
    13. Bruno Feunou & Jean-Sébastien Fontaine, 2012. "Forecasting Inflation and the Inflation Risk Premiums Using Nominal Yields," Staff Working Papers 12-37, Bank of Canada.
    14. Bruno Feunou & Jean-Sébastien Fontaine, 2018. "Bond Risk Premia and Gaussian Term Structure Models," Management Science, INFORMS, vol. 64(3), pages 1413-1439, March.
    15. 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.
    16. René Garcia & Eric Renault, 1999. "Latent Variable Models for Stochastic Discount Factors," CIRANO Working Papers 99s-47, CIRANO.
    17. Alessandra Canepa, & Menelaos G. Karanasos & Alexandros G. Paraskevopoulos,, 2019. "Second Order Time Dependent Inflation Persistence in the United States: a GARCH-in-Mean Model with Time Varying Coefficients," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201911, University of Turin.

    More about this item

    Keywords

    Time series processes; conditional moments; expected returns; persistence;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ivi:wpasad:1997-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Departamento de Edición (email available below). General contact details of provider: https://edirc.repec.org/data/ievages.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.