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

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Author Info

  • 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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1997-17.pdf
File Function: Fisrt version / Primera version, 1997
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1997-17.

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Length: 48 pages
Date of creation: Jun 1997
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1997-17

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Related research

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

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Cited by:
  1. René Garcia & Richard Luger & Éric Renault, 2001. "Asymmetric Smiles, Leverage Effects and Structural Parameters," CIRANO Working Papers 2001s-01, CIRANO.
  2. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO.
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series 2046, CESifo Group Munich.
  4. GARCIA, René & RENAULT, Éric, 2000. "Latent Variable Models for Stochastic Discount Factors," Cahiers de recherche 2000-01, Universite de Montreal, Departement de sciences economiques.
  5. Bruno Feunou & Jean-Sébastien Fontaine, 2012. "Forecasting Inflation and the Inflation Risk Premiums Using Nominal Yields," Working Papers 12-37, Bank of Canada.

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