Asymptotic Filtering Theory for Multivariate ARCH Models
AbstractARCH models are widely used to estimate conditional variances and covariances in financial time series models. How successfully can ARCH models carry out this estimation when they are misspecified? How can ARCH models be optimally constructed? Nelson and Foster (1994) employed continuous record asymptotics to answer these questions in the univariate case. This paper considers the general multivariate case. Our results allow us, for example, to construct an asymptotically optimal ARCH model for estimating the conditional variance or conditional beta of a stock return given lagged returns on the stock, volume, market returns, implicit volatility from options contracts, and other relevant data. We also allow for time-varying shapes of conditional densities (e.g., `heteroskewticity` and `heterokurticity'). Examples are provided.
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Bibliographic InfoPaper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0162.
Date of creation: Aug 1994
Date of revision:
Publication status: published as Nelson, Daniel B. "Asymptotic Filtering Theory For Multivariate ARCH Models," Journal of Econometrics, 1996, v71(1&2,Mar/Apr), 1-47.
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Find related papers by 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
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