Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks

Abstract

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Generalized dynamic factor models and volatilities: estimation and forecasting

“…16 The results are unaffected if we estimate the model using the various versions of Kalman filter proposed by Diebold and Nerlove (1989), Harvey et al (1992), and Sentana et al (2008). 17 Results are very similar when we assume homoskedastic idiosyncratic components.…”

“…However, being parametric, those models all suffer of the "curse of dimensionality": estimation, even panels of moderate size, rapidly becomes unfeasible. In order to overcome this problem, and in agreement with the Capital Asset Pricing Model (CAPM) idea of a market shock affecting all components of a financial index, factor structures on the returns have been developed jointly with GARCH modelling for the latent factors: see, for instance, Ng et al (1992), Harvey et al (1992), Diebold and Nerlove (1989), Van der Weide (2002), Connor et al (2006), Sentana et al (2008), or Rangel and Engle (2012). All those factor models, however, are static, and mainly of the exact type (strictly no idiosyncratic cross-correlations); thus, they do not fully exploit the time series nature of the data.…”

Simulation-Based Bias Correction Methods for Complex Models

“…For example, Diebold and Nerlove (1989) used it in multivariate autoregressive conditional heteroskedasticity (ARCH) time-series. Sentana et al (2008) proposed to use indirect inference to allow the estimation of any state space model with generalized autoregressive conditional heteroskedasticity (GARCH) disturbances, using the model proposed by Harvey et al (1992) as auxiliary model.…”

Generalized dynamic factor models and volatilities: recovering the market volatility shocks

“…Recently, Fan et al (2015) improved this model by relaxing the assumptions and allowing for the presence of idiosyncratic variances, which are modelled as a sparse matrix. Finally, the papers most related to our work are those proposing a factor structure on the returns and then assuming a GARCH model for the latent factors, such as, for example, Ng et al (1992), Harvey et al (1992), Diebold and Nerlove (1989), Van der Weide (2002), Connor et al (2006) and Sentana et al (2008), among others; see also Jurado et al (2013) for an application to macroeconomic data. All those factor models, however, are static, and of the exact type (strictly no idiosyncratic cross-correlations); thus, they neither exploit the serial correlation in the data nor are able to account for idiosyncratic cross-sectional dependences, which are very likely to exist in large data sets.…”