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一阶指数 GARCH 模型族的矩结构AI 解读

In this paper we consider the moment structure of a class of first-order exponential generalized autoregressive conditional heteroskedasticity (GARCH) models. This class contains as special cases both the standard exponential GARCH model and the symmetric and asymmetric logarithmic GARCH model. Conditions for the existence of any arbitrary moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of positive powers of absolute-valued…

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股票市场收益中的条件跳跃动态AI 解读

This article develops a new conditional jump model to study jump dynamics in stock market returns. We propose a simple filter to infer ex post the distribution of jumps. This permits construction of the shock affecting the time t conditional jump intensity and is the main input into an autoregressive conditional jump intensity model. The model allows the conditional jump intensity to be time-varying and follows an approximate autoregressive moving average (ARMA) form. The…

连续时间扩散过程极大似然估计的数值技术AI 解读

Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulation-based approach suggested by Pedersen (1995) has great theoretical appeal, but…

外汇收益中的波动率、动量与时变偏度AI 解读

This article tests a stochastic volatility model of exchange rates that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency. In particular, the model implies that the return-volatility covariance behaves like a weighted average of recent returns and hence switches signs according to the direction of trends in the data. This implies that the skewness of the finite-horizon return distribution likewise switches…

滚动样本波动率估计量AI 解读

We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed for estimating the quadratic variation of asset returns, referred to as integrated or realized volatility. We treat integrated volatility as a continuous time stochastic process sampled at high frequencies and suggest rolling sample estimators which share many features with spot volatility estimators. We discuss asymptotically efficient window lengths and…

具有时变相关性的多元广义自回归条件异方差模型AI 解读

In this article we propose a new multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. Whereas each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analog. Our new model retains the…

动态条件相关AI 解读

Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with…

GARCH 模型与扩散模型的渐近不等价性AI 解读

This paper investigates the statistical relationship of the GARCH model and its diffusion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's deficiency distance. To our surprise, we are able to show that the GARCH model and its diffusion limit are asymptotically equivalent only under deterministic volatility. With stochastic volatility, due to the…

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ABSTRACT We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that range‐based volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence range‐based Gaussian quasi‐maximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine…

GARCH 与非对称幂 GARCH 模型矩存在的充要条件AI 解读

Although econometricians have been using Bollerslev's (1986, Journal of Econometrics 31, 307–327) GARCH( r , s ) model for over a decade, the higher order moment structure of the model remains unresolved. The sufficient condition for the existence of the higher order moments of the GARCH( r , s ) model was given by Ling (1999a, Journal of Applied Probability 36, 688–705). This paper shows that Ling's condition is also necessary. As an extension, the necessary and sufficient…

After a forecast failure, a respecification is usually necessary to account for the data ex post, in which case there is a gain in knowledge as a result of the forecast failure. Using Norwegian consumption as an example, we show that the financial deregulation in the mid‐1980s led to forecast failure both for consumption functions (CFs) and Euler equations (EEs). We argue in the paper that such forecast failures would appear to be at odds with an underlying DGP belonging to…

已实现波动率的计量分析及其在随机波动率模型估计中的应用AI 解读

Summary The availability of intraday data on the prices of speculative assets means that we can use quadratic variation-like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated…

连续时间过程的经验特征函数估计AI 解读

This article examines the class of continuous-time stochastic processes commonly known as affine diffusions (AD's) and affine jump diffusions (AJD's). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an efficient estimation technique based on empirical characteristic functions (ECF's) and a generalized method of moments (GMM) estimation procedure based on exact moment conditions. We demonstrate that our…

短期利率的马尔可夫切换与随机波动率扩散模型AI 解读

This article empirically compares the Markov-switching and stochastic volatility diffusion models of the short rate. The evidence supports the Markov-switching diffusion model. Estimates of the elasticity of volatility parameter for single-regime models unanimously indicate an explosive volatility process, whereas the Markov-switching models estimates are reasonable. It is found that either Markov switching or stochastic volatility, but not both, is needed to adequately fit…

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利用 Hansen–Jagannathan 界评价资产定价模型：蒙特卡洛研究AI 解读

Abstract We use recent statistical tests, based on a ‘distance’ between the model and the Hansen–Jagannathan bound, to compute the rejection rates of true models. For asset‐pricing models with time‐separable preferences, the finite‐sample distribution of the test statistic associated with the risk‐neutral case is extreme, in the sense that critical values based on this distribution deliver type I errors no larger than intended—regardless of risk aversion or the rate of time…

ARCH(∞) 模型的平稳性AI 解读

We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model.

多类 GARCH 与随机波动率模型的混合性和矩性质AI 解读

This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments…

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压缩映射不动点的最坏情形计算存在维数灾难吗？AI 解读

This paper analyzes the complexity of the contraction fixed point problem: compute an e-approximation to the fixed point V * = Γ(V * ) of a contraction mapping r that maps a Banach space B d of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and…

日度汇率传递的信息AI 解读

Formal testing procedures confirm the presence of a unit root in the autoregressive ploynomial of the univariate time series representation of daily exchange-rate data. the first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and…