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Filtering and forecasting with misspecified ARCH models I. Getting the right variance with the wrong model. (English) Zbl 0761.62169
For modelling time-varying conditional variances the financial economists have recently used ARCH (autoregressive conditional heteroscedastic) models to specify market volatility. This paper develops conditions under which a misspecified ARCH model may provide a consistent estimate of the conditional covariance matrix of a stochastic process. For example, if the stochastic process generating prices is approximately a diffusion process, then the paper shows that there may still be so much information on the conditional second moments at high frequencies, that even a misspecified ARCH model can be a consistent filter with a high degree of forecasting power. The paper also shows other cases of ARCH models where consistency properties and robustness fail altogether.

62P20 Applications of statistics to economics
91B84 Economic time series analysis
Full Text: DOI
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