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Mathematics

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Asymptotically optimal smoothing with ARCH models

Article Abstract:

Nelson (1992) and Nelson and Foster (1994) had demonstrated that a misspecified ARCH model consistently derives the unobserved volatility process through information from the lagged residuals. The efficient derivation of a volatility process through information from lagged and led residuals is demonstrated. The optimal filtering results of Nelson and Foster and Nelson are expanded to filtering error with a random initial condition and to smoothing.

Analysis, Nonlinear functional analysis, Smoothing (Statistics)

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Idiosyncratic volatility, stock market volatility and expected stock returns

Article Abstract:

The value-weighted idiosyncratic stock volatility and aggregate stock market volatility jointly exhibit strong predictive power for excess stock market returns. The stock market risk-return relation is found to be positive as stipulated by the capital asset pricing model however idiosyncratic volatility is negatively related to future stock market returns.

Investment analysis, Securities analysis, Stock markets, Stock market

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Multivariate stochastic volatility via Wishart processes

Article Abstract:

A multivariate stochastic volatility framework for modeling financial data is presented, in which time-varying covariance matrices are driven by Wishart processes.

United Kingdom, Models, Financial analysis

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