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Lévy 驱动的连续时间 CARMA 随机波动率模型模拟方法AI 解读

We develop simulation schemes for the new classes of non-Gaussian pure jump Lévy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Lévy process, which makes series approximation methods directly applicable. These methods entail simulation of the Lévy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function or specification of a copula…

基于价格极差的 EGARCH 模型与波动率预测AI 解读

We provide a simple, yet highly effective framework for forecasting return volatility by combining exponential generalized autoregressive conditional heteroscedasticity models with data on the range. Using Standard and Poor's 500 index data for 1983–2004, we demonstrate the importance of a long-memory specification, based on either a two-factor structure or fractional integration, that allows for some asymmetry between market returns and volatility innovations. Out-of-sample…

一类 GARCH 过程严格平稳的充要条件AI 解读

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a, Journal of Econometrics 92, 173–192). This family contains various popular generalized autoregressive conditional heteroskedasticity (GARCH) models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.This research was financially supported by the Jan Wallander's and Tom Hedelius' Foundation, Grant J03–41. The author thanks the…

一类 GARCH 过程的尾部行为AI 解读

In this paper, some structural properties of a family of generalized autoregressive conditionally heteroskedastic (GARCH) processes are considered. First, a sufficient and necessary condition for the strict stationarity of this family of GARCH processes is given. Second, some simple conditions for the existence of the moments of the family of GARCH processes are also derived. Finally, we describe the tail of the marginal distribution of the family of GARCH processes.I am…

无需观测过程矩假设的一般 GARCH(1,1) 模型混合性质AI 解读

We consider general, and possibly nonparametric, GARCH(1,1) processes. First we give conditions for the existence and the uniqueness of stationary ergodic solutions. Then we identify additional conditions for geometric ergodicity. These conditions consist of mild restrictions on the distribution of the latent independent process. No moment assumption is made on the generalized autoregressive conditionally heteroskedastic (GARCH) process. Applications to the asymptotic…

用于局部平稳波动率估计的 Haar–Fisz 技术AI 解读

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common characteristics of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in this model, in which Haar wavelets are…

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用二元混合转移分布模型刻画带标记点过程AI 解读

We propose new probability models for the analysis of marked point processes. These models deal with the type of data that arrive or are observed in possibly unequal time intervals, such as financial transactions and earthquakes, among others. The models treat both the time between event arrivals and the observed marks as stochastic processes. We adopt a class of bivariate distributions to form the bivariate mixture transition distribution. In these models the conditional…

状态空间模型中的有效似然估计AI 解读

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root…

重尾分布高分位数的置信域AI 解读

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.

扩散过程与Itô过程的方差分析AI 解读

Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Itô processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the…

金融计量中双幂变差的极限定理AI 解读

In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen's work is…

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基于奇异值分解的广义降秩检验AI 解读

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: necessity of a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson (1951), sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald (1996) and Gill and Lewbel (1992), a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and…

利用已实现测度对随机波动率模型进行半参数比较AI 解读

This paper proposes a procedure to test for the correct specification of the functional form of the volatility process within the class of eigenfunction stochastic volatility models. The procedure is based on the comparison of the moments of realized volatility measures with the corresponding ones of integrated volatility implied by the model under the null hypothesis.We first provide primitive conditions on the measurement error associated with the realized measure, which…

利率的树结构多状态模型AI 解读

This article develops a generalized tree-structured (GTS) model of the short-term interest rate that accommodates regime-dependent mean reversion and regime-dependent volatility clustering and level effects in the conditional variance. The model is constructed using the idea of multivariate tree-structured thresholds and nests the popular generalized autoregressive conditional heteroscedasticity and square root processes as simple special cases. It allows us to estimate the…

基于 Wishart 过程的多变量随机波动率模型AI 解读

Financial models for asset and derivatives pricing, risk management, portfolio optimization, and asset allocation rely on volatility forecasts. Time-varying volatility models, such as generalized autoregressive conditional heteroscedasticity and stochastic volatility (SVOL), have been successful in improving forecasts over constant volatility models. We develop a new multivariate SVOL framework for modeling financial data that assumes covariance matrices stochastically…

长记忆时间序列的离散傅里叶变换相关矩阵与大型 Toeplitz 系统快速求解AI 解读

We show that for long-memory time series, the Toeplitz system Σn(f)x = b can be solved in O(nlog5/2n) operations using a well-known version of the preconditioned conjugate gradient method, where Σn(f) is the n × n covariance matrix, f is the spectral density, and b is a known vector. Solutions of such systems are needed for optimal linear prediction and interpolation. We establish connections between this preconditioning method and the frequency domain analysis of time…

ARCH 无穷阶模型的伪极大似然估计AI 解读

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.

时变 ARCH 过程的统计推断AI 解读

In this paper the class of ARCH(∞) models is generalized to the nonstationary class of ARCH(∞) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation “locally stationary ARCH(∞) process.” The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p<∞) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is…

GARCH 模型的经验似然方法AI 解读

This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both…

条件异方差时间序列的方差恒定性监测AI 解读

We propose several methods of on-line detection of a change in unconditional variance in a conditionally heteroskedastic time series. We follow the paradigm of Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) in which the first m observations are assumed to follow a stationary process and the monitoring scheme has asymptotically controlled probability of falsely rejecting the null hypothesis of no change. Our theory is applicable to broad classes of GARCH-type…