Continuous Record Asymptotics for Rolling Sample Variance Estimators
Dean P. Foster,Daniel B. Nelson +1 more
TL;DR: In this article, the authors developed continuous record asymptotic approximations for the measurement error in conditional variances and covariances when using two-sided rolling regressions and a one-sided weighted rolling regression.
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Abstract: It is widely known that conditional covariances of asset returns change over time. Researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity. Among the popular strategies are: (a) chopping the available data into short blocks of time and assuming homoskedasticity within the blocks, (b) performing one-sided rolling regressions, in which only data from, say, the preceding five year period is used to estimate the conditional covariance of returns at a given date, and (c) performing two-sided rolling regressions, in which covariances are estimated for each date using, say, five years of lags and five years of leads. Another model-GARCH-amounts to a one-sided weighted rolling regression. We develop continuous record asymptotic approximations for the measurement error in conditional variances and covariances when using these methods. We derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions. As an empirical example, we estimate volatility on the S&P 500 stock index using daily data from 1928 to 1990.
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References
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
TL;DR: In this article, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced, which are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances.
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Generalized autoregressive conditional heteroskedasticity
Tim Bollerslev,Tim Bollerslev +1 more
TL;DR: In this paper, a natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in 1982 to allow for past conditional variances in the current conditional variance equation is proposed.
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Risk, Return, and Equilibrium: Empirical Tests
Eugene F. Fama,James D. MacBeth +1 more
TL;DR: In this article, the relationship between average return and risk for New York Stock Exchange common stocks was tested using a two-parameter portfolio model and models of market equilibrium derived from the two parameter portfolio model.
Expected stock returns and volatility
TL;DR: In this article, the authors examined the relation between stock returns and stock market volatility and found that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns.
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ARCH modeling in finance: A review of the theory and empirical evidence
TL;DR: An overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data can be found in this paper, where several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and pricing of derivative assets, are also discussed.
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