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关于 GARCH 模型不等式约束的一则说明AI 解读

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH( p , q ) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH( p , q ) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH( p , q ) models with p ≥ 3. In…

风险、跳跃与分散化AI 解读

We test for price discontinuities, or jumps, in a panel of high-frequency intraday stock returns and an equiweighted index constructed from the same stocks. Using a new test for common jumps that explicitly utilizes the cross-covariance structure in the returns to identify non-diversifiable jumps, we find strong evidence for many modest-sized, yet highly significant, cojumps that simply pass through standard jump detection statistics when applied on a stock-by-stock basis.…

用于金融与预测的 t 分布混合AI 解读

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. Particularly desirable for econometric applications are closed-form expressions for antiderivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than…

时变 ARCH 模型中的归一化最小二乘估计AI 解读

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a…

This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions.The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis.Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for…

长期风险与收益的权衡AI 解读

Excess market returns are correlated with past market variance. This dependence is statistically mild at short horizons (thereby leading to a hard-to-detect risk-return trade-off, as in the existing literature) but increases with the horizon and is strong in the long run (i.e., between 6 and 10 years). From an econometric standpoint, we find that the long-run predictive power of past market variance is robust to the statistical properties of long-horizon stock-return…

具有内生状态转换的马尔可夫状态转换回归模型估计AI 解读

Following Hamilton [1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357-384], estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor…

克伦威尔法则与经济意义度量中的先验作用AI 解读

We show that using Bayesian decision theory to draw inference about the economic significance of a model requires careful specification of model uncertainty in the prior density. As an example, we use the Bayesian investor's portfolio allocation problem to show that failure to include probability point mass on the null hypothesis that returns are not predictable will overstate the economic significance of the predictive model. The dissonance between the statistical and…

资产收益的马尔可夫切换多重分形模型AI 解读

Multifractal processes have recently been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns—a feature that has been found in virtually all financial data. Initial difficulties stemming from nonstationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative…

真实还是伪长记忆？一种新检验AI 解读

It is well known that long memory characteristics observed in data can be generated by nonstationary structural-break or slow regime switching models. We propose a statistical test to distinguish between true long memory and spurious long memory based on invariance of the long memory parameter for temporal aggregates of the process under the null of true long memory. Geweke Porter-Hudak estimates of the long memory parameter obtained from different temporal aggregates of the…

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GARCH 模型估计：何时选择哪种方法？AI 解读

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of the innovation distribution plays an important role in determining the relative performance of the two competing estimation methods, namely the maximum quasi-likelihood estimator based…

New multivariate panel cointegration methods are used to analyze nominal exchange rates and prices in four major economies in Europe: France, Germany, Italy and the United Kingdom for the post‐Bretton Woods period. We test for purchasing power parity (PPP) between these four countries and find that the theoretical PPP relationship does not hold. However, the estimated unrestricted relationship is found to be remarkably close to the theoretical one (1, −1.5, 0.9 instead of 1,…

条件异方差分数单整 ARMA 模型的最小绝对偏差估计AI 解读

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau…

重尾模型的尾指数估计：加权对数超额中的偏差处理AI 解读

Summary We are interested in the derivation of the distributional properties of a weighted log-excesses estimator of a positive tail index γ. One of the main objectives of such an estimator is the accommodation of the dominant component of asymptotic bias, together with the maintenance of the asymptotic variance of the maximum likelihood estimator of γ, under a strict Pareto model. We consider the external estimation not only of a second-order shape parameter ρ but also of a…

非平稳波动率时间序列的自助法单位根检验AI 解读

The presence of permanent volatility shifts in key macroeconomic and financial variables in developed economies appears to be relatively common. Conventional unit root tests are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a bootstrap approach to unit root testing that is valid in the presence of a wide class of permanent variance changes that includes single and multiple (abrupt and smooth transition)…

多元 GARCH 过程的时间聚合AI 解读

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak mul- tivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables. It is shown that spurious instantaneous causality in variance will only appear in degenerated cases, but that spurious Granger…

幂变换与门限 GARCH 模型的估计和检验AI 解读

Consider a class of power transformed and threshold GARCH(p,q) (PTTGRACH(p,q)) model, which is a natural generalization of power-transformed and threshold GARCH(1,1) model in Hwang and Basawa (2004) and includes the standard GARCH model and many other models as special cases. We first establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has finite fourth moment. For the case of…

汇率波动率 GARCH 模型中的结构突变AI 解读

Abstract We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the…

财务比率的多变量部分调整：贝叶斯层级方法AI 解读

Abstract In this paper we propose a multivariate extension of the partial adjustment model of financial ratios. To that end, we use a dynamic factor model which assumes that financial ratios measuring, essentially, the same economic–financial dimension of the firm evolve in a similar way, reflecting the evolution of the common factor. The proposed model is hierarchical with three levels. The first describes the relationship between each ratio and its common factor; the…

GARCH 类模型标准化残差相关检验的统一方法AI 解读

Abstract In this paper, we propose a unified approach to generating standardized‐residuals‐based correlation tests for checking GARCH‐type models. This approach is valid in the presence of estimation uncertainty, is robust to various standardized error distributions, and is applicable to testing various types of misspecifications. By using this approach, we also propose a class of power‐transformed‐series (PTS) correlation tests that provides certain robustifications and…

异方差与自相关稳健检验的表现：蒙特卡洛研究及 Fama–French 三因子模型应用AI 解读

Abstract This paper illustrates the pitfalls of the conventional heteroskedasticity and autocorrelation robust (HAR) Wald test and the advantages of new HAR tests developed by Kiefer and Vogelsang in 2005 and by Phillips, Sun and Jin in 2003 and 2006. The illustrations use the 1993 Fama–French three‐factor model. The null that the intercepts are zero is tested for 5‐year, 10‐year and longer sub‐periods. The conventional HAR test with asymptotic P ‐values rejects the null for…

噪声下测度股票价格事后变差的已实现核设计AI 解读

This paper shows how to use realized kernels to carry out efficient feasible inference on the ex post variation of underlying equity prices in the presence of simple models of market frictions. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which equals that of the maximum likelihood estimator in the parametric version of this problem. Realized kernels can also be selected to (i) be analyzed using endogenously…

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