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分数整合广义自回归条件异方差模型AI 解读

The new class of Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic (FIGARCH) processes is introduced. The conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations. Unlike I(d) processes for the mean, Maximum Likelihood Estimates (MLE) of the FIGARCH parameters are argued to be T^(1/2)-consistent. The small-sample behavior of an approximate MLE procedure is assessed through a…

股票市场波动率与商业周期AI 解读

This paper investigates the joint time series behavior of monthly stock returns and growth in industrial production. We find that stock returns are well characterized by year-long episodes of high volatility, separated by longer quiet periods. Real output growth, on the other hand, is subject to abrupt changes in the mean associated with economic recessions. We study a bivariate model in which these two changes are driven by related unobserved variables, and conclude that…

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股票市场波动率长记忆的建模与定价AI 解读

A new class of fractionally integrated GARCH and EGARCH models for characterizing financial market volatility is discussed. Monte Carlo simulations illustrate the reliability of quasi maximum likelihood estimation methods, standard model selection criteria, and residual-based portmanteau diagnostic tests in this context. New empirical evidence suggests that the apparent long-run dependence in U.S. stock market volatility is best described by a mean-reverting fractionally…

若干 GMM 估计量的有限样本性质AI 解读

The authors investigate the small sample properties of three alternative generalized method of moments estimators of asset pricing models. The estimators that they consider include ones in which the weighting matrix is iterated to convergence and ones in which the weighting matrix is changed with each choice of the parameters. Particular attention is devoted to assessing the performance of the asymptotic theory for making inferences based directly on the deterioration of GMM…

随机波动率模型的 GMM 估计：蒙特卡洛研究AI 解读

We examine alternative generalized method of moments procedures for estimation of a stochastic autoregressive volatility model by Monte Carlo methods. We document the existence of a tradeoff between the number of moments, or information, included in estimation and the quality, or precision, of the objective function used for estimation. Furthermore, an approximation to the optimal weighting matrix is used to explore the impact of the weighting matrix for estimation,…

解析导数与 GARCH 估计的计算AI 解读

In the context of univariate GARCH models we show how analytic first and second derivatives of the log-likelihood can be successfully employed for estimation purposes. Maximum likelihood GARCH estimation usually relies on the numerical approximation to the log-likelihood derivatives, on the grounds that an exact analytic differentiation is much too burdensome. We argue that this is not the case and that the computational benefit of using the analytic derivatives (first and…

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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…

利率衍生证券的非参数定价AI 解读

The author proposes a nonparametric estimation procedure for continuous-time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, he leaves the volatility function unrestricted and estimates it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous-time model by some discrete approximation. Instead, the drift and…

IGARCH(1,1)与协方差平稳GARCH(1,1)模型中准极大似然估计的一致性与渐近正态性AI 解读

This paper provides a proof of the consistency and asymptotic normality of the quasi-maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models. In contrast to the case of a unit root in the conditional mean, the presence of a 'unit root' in the conditional variance does not affect the limiting distribution of the estimators; in both models, estimators are normally distributed. In addition, a consistent estimator of the covariance matrix is available, enabling the use…

以区制转换检验汇率投机泡沫AI 解读

This paper develops a new test for speculative bubbles, which is applied to data for the Japanese yen, the German mark and the Canadian dollar exchange rates from 1977 to 1991. The test assumes that bubbles display a particular kind of regime-switching behaviour, which is shown to imply coefficient restrictions on a simple switching-regression model of exchange rate innovations. Test results are sensitive to the specification of exchange rate fundamentals and other factors.…

双阈值自回归条件异方差时间序列模型AI 解读

Tong's threshold models have been found useful in modelling nonlinearities in the conditional mean of a time series. The threshold model is extended to the so-called double-threshold ARCH(DTARCH) model, which can handle the situation where both the conditional mean and the conditional variance specifications are piecewise linear given previous information. Potential applications of such models include financial data with different (asymmetric) behaviour in a visiting versus…

作为降秩回归的套利定价理论模型AI 解读

Integrating the two steps of an arbitrage pricing theory (APT) model leads to a reduced rank regression (RRR) model. So the results on RRR can be used to estimate APT models, making estimation very simple. The authors give a succinct derivation of estimation of RRR, derive the asymptotic variance of RRR estimators for a general cause, and discuss how undersized samples (more assets than time periods) can be dealt with.

周期性自回归条件异方差AI 解读

Most high frequency asset returns exhibit seasonal volatility patterns. This paper proposes a new class of periodic ARCH, or P-ARCH, models explicitly designed to capture the repetitive variation in the second order moments. The importance of the informational loss associated with the implicit relation between P-GARCH structures and the corresponding time-invariant seasonal weak GARCH processes are quantified through the use of Monte Carlo simulation methods. Two empirical…

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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…

滚动样本方差估计量的连续记录渐近理论AI 解读

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. One popular strategy is performing 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. The authors develop continuous record asymptotic approximations for the measurement error in…

含随机波动率与跳跃的连续时间套利定价模型AI 解读

We formulate and test a continuous-time asset-pricing model using U.S. equity market data. We assume that stock returns are driven by common factors including random jump-size Poisson processes and Brownian motions with stochastic volatility. The model places overidentifying restrictions on the mean returns, allowing one to identify risk-neutral probability distributions useful in pricing derivative securities. We test for the restrictions and decompose moments of the asset…

外汇汇率的高频数据与波动率AI 解读

This article uses tick-by-tick foreign exchange rates to explore the feature of high frequency financial data. In this article, the author proposes a model that explains the negative autocorrelation of high frequency financial time series. The empirical results indicate that the heavy tail of financial time series is mostly caused by the heteroscedasticity of the time series. The estimates of intraday volatility reveal a strong seasonal patter across all currencies.

具有移动平均误差的线性资产定价模型的有效估计AI 解读

This paper studies alternative methods for estimating parameters from multiperiod conditional moment restrictions. The authors' discussion is couched in the context of a multivariate linear time series model and they use the log-linear intertemporal asset pricing model as a prototype when comparing alternative econometric methods. They propose a generalized method of moments estimator that is scale invariant and is asymptotically equivalent to one used previously in…