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利用 ARCH 模型进行渐近最优平滑AI 解读

Suppose an observed time series is generated by a stochastic volatility model. As shown by D. B. Nelson (1992) and D. B. Nelson and D. P. Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In…

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ARCH 与随机波动率模型中的标准化误差AI 解读

It is well-known that conditional heteroskedasticity thickens the tails of the unconditional distribution of an error term relative to its conditional distribution. To what extent do imperfect forecasts of the conditional variance undo this tail thickening? This note considers the effect of changing the quality of the information embodied in a forecast of a conditional variance. Adding noise of a certain form thickens the tails of the normalized errors, but decreasing the…

误设 ARCH 模型的滤波与预测：第二篇AI 解读

A companion paper (Nelson, 1992) showed that in data observed at high frequencies, an ARCH model may perform well in estimating the conditional variance of a process, even when the ARCH model is severely misspecified. While such models may perform reasonably well at filtering (i.e., at estimating unobserved instantaneous conditional variances), they may perform disastrously at medium- and long-term forecasting of the process and its volatility. In this paper, we develop…

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单变量 ARCH 模型的渐近滤波理论AI 解读

Researchers often employ ARCH models to estimate conditional variances and covariances. How successfully can misspecified ARCH models carry out this estimation? This paper employs continuous record asymptotics to approximate the distribution of the measurement error. This allows the authors to (1) compare the efficiency of various ARCH models, (2) characterize the impact of different kinds of misspecification on efficiency, and (3) characterize asymptotically optimal ARCH…

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单变量 GARCH 模型中的不等式约束AI 解读

To keep the conditional variances generated by the generalized autoregressive conditional heteroscedastic (p, q) model nonnegative, T. Bollerslev imposed nonnegativity constraints on the parameters of the process. The authors show that these constraints can be substantially weakened and so should not be imposed in estimation. They also provide empirical examples illustrating the importance of relaxing these constraints.

资产收益的条件异方差：一种新方法AI 解读

This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and…

GARCH(1,1) 模型的平稳性与持续性AI 解读

This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition…

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