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跳跃扩散模型的渐近理论AI 解读

This paper presents an asymptotic theory for recurrent jump diffusion models with well-defined scale functions. The class of such models is broad, including general nonstationary as well as stationary jump diffusions with state-dependent jump sizes and intensities. The asymptotics for recurrent jump diffusion models with scale functions are largely comparable to the asymptotics for the corresponding diffusion models without jumps. For stationary jump diffusions, our…

理解长时间跨度下的高频观测回归AI 解读

In this paper, we analyze regressions with observations collected at small time intervals over a long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast…

利用截断双幂增量估计跳跃扩散的波动率函数AI 解读

In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by…

跳跃扩散模型的非参数估计AI 解读

This paper develops the asymptotics for nonparametric kernel estimators of local time, drift and volatilities, and Lévy measure in jump diffusion models. Our asymptotics are developed in a very general set-up, allowing the sample span to increase as the sampling interval decreases, and without assuming stationarity. For drift and volatilities, we analyze both local constant and local linear estimators. We consider not only estimators for instantaneous conditional second…

高频采样下的平稳性检验AI 解读

The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its long-run variance estimate is chosen suitably in our framework. We also analyze the…

分布时间序列的趋势评估：人类气候影响的空间指纹AI 解读

We analyze a time series of global temperature anomaly distributions to identify and estimate persistent features in climate change. We employ a formal test for the existence of functional unit roots in the time series of these densities, and we develop a new test to distinguish functional unit roots from functional deterministic trends or explosive behavior. Results suggest that temperature anomalies contain stochastic trends (as opposed to deterministic trends or explosive…

利用离散样本估计连续时间随机过程的长期方差AI 解读

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longrun variance of continuous time process, but also how to choose bandwidth…

区制转换建模的新方法AI 解读

This paper introduces a new approach to model regime switching using an autoregressive latent factor, which determines regimes depending upon whether it takes a value above or below some threshold level. In our approach, the latent factor is allowed to be correlated with the innovation to the observed time series. If the latent factor becomes exogenous, our approach reduces to the conventional Markov switching. We develop a modified Markov switching filter to estimate the…

常返扩散过程的渐近理论及高频回归应用AI 解读

We provide the asymptotic theory for functionals of recurrent diffusions. Our asymptotics are completely general and applicable for all cases, including positive and null recurrent diffusions, and diffusions with and without the integrability conditions. They are established directly from the representation of diffusion as time-changed Brownian motion. Our approach provides a unified framework, and combines all existing theories of diffusion asymptotics with new results that…

利用高频面板评估因子定价模型AI 解读

This paper develops a new framework and statistical tools to analyze stock returns using high-frequency data. We consider a continuous-time multifactor model via a continuous-time multivariate regression model incorporating realistic empirical features, such as persistent stochastic volatilities with leverage effects. We find that the conventional regression approach often leads to misleading and inconsistent test results when applied to high-frequency data. We overcome this…

股票收益可预测性的再考察AI 解读

We provide a simple and innovative approach to test for predictability in stock returns. Our approach consists of two methodologies, time change and instrumental variable estimation, which are employed respectively to deal effectively with persistent stochastic volatility in stock returns and endogenous nonstationarity in their predictors. These are prominent characteristics of the data used in predictive regressions, which are known to have a substantial impact on the test…

状态密度时间序列的非平稳性AI 解读

This paper proposes a new framework to analyze the nonstationarity in the time series of state densities, representing either cross-sectional or intra-period distributions of some underlying economic variables. We regard each state density as a realization of Hilbertian random variable, and use a functional time series model to fit a given time series of state densities. This allows us to explore various sources of the nonstationarity of such time series. The potential unit…

可能非平稳连续时间模型中局部非参数估计的带宽选择与渐近性质AI 解读

We derive the asymptotic properties of nonparametric estimators of the drift and diffusion functions, and the local time, of a discretely sampled diffusion process that is possibly nonstationary. We provide complete two-dimensional asymptotics in both the time span and the sampling interval, allowing for a precise characterization of their distribution, as well as the determination of optimal bandwidths for these estimators.

模糊性重要吗？多重先验递归效用资产定价模型的估计AI 解读

This paper considers asset pricing models with stochastic differential utility incorporating decision makers׳ concern with ambiguity on true probability measure. Under a representative agent setting, we empirically evaluate alternative preference specifications including a multiple-priors recursive utility. We find that relative risk aversion is estimated around 1–8 with ambiguity aversion and 7.4–15 without ambiguity aversion. Estimated ambiguity aversion is both…

非平稳非线性：Peter Phillips 贡献的综述与新视角AI 解读

In this paper, we provide a survey of Peter Phillips’s works on the econometrics for models with nonstationary nonlinearity, and some of the extensions that were made possible due to his original contributions. Parametric and nonparametric models are considered in both discrete time and continuous time setups. Although some of the asymptotics in the paper are applicable more generally for a wide variety of nonstationary models, we mainly analyze models with nonstationary…

基于高频数据的似然扩散模型选择：渐近分析AI 解读

We provide a new asymptotic analysis of model selection procedure that compares likelihoods of two candidate diffusion models. Our asymptotic analysis relies on two dimensional asymptotic expansions with shrinking sampling interval Δ and increasing sampling span T, and clarifies the different roles of drift and diffusion functions in the selection of diffusion models. In particular, we show that the model with superior diffusion function specification is always preferred to…

过程非平稳时基于平稳性的扩散模型设定检验AI 解读

We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the local to unity analysis in classical unit root theory. We find that the behavior of the test predicted by the asymptotic distribution under an integrated process provides a better…

随机游走还是混沌：基于李雅普诺夫指数的正式检验AI 解读

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given by the range of standard Brownian motion on the unit interval. The test is consistent against the chaotic alternatives. A simulation study shows that the test performs reasonably well…

连续状态分布的函数型回归AI 解读

In this paper, we consider a regression model to study the distributional relationship between economic variables. Unlike the classical regression dealing exclusively with mean relationship, our model can be used to analyze the entire dependent structure in distribution. Technically, we treat density functions as random elements and represent the regression relationship as a compact linear operator in the Hilbert spaces of square integrable functions. We propose a consistent…

含持久协变量的 ARCH/GARCH：极大似然渐近理论AI 解读

The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit distribution. The limit distribution is generally non-Gaussian and represented as a functional of Brownian motions. However, it becomes Gaussian if the covariate has innovation…

半参数协整回归：年龄分布对消费与储蓄的影响AI 解读

We consider a semiparametric cointegrating regression model, for which the disequilibrium error is further explained nonparametrically by a functional of distributions changing over time. The paper develops the statistical theories of the model. We propose an efficient econometric estimator and obtain its asymptotic distribution. A specification test for the model is also investigated. The model and methodology are applied to analyze how an aging population in the US…

非线性、非平稳性与厚尾如何共同产生记忆持久性AI 解读

We consider nonlinear functions of random walks driven by thick-tailed innovations. Nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of autocorrelation patterns consistent with the observed persistence in memory of many economic and financial time series. Depending upon the type of transformation considered and whether it is observed with noise, the autocorrelations are given by unity, random constants, or hyperbolically decaying deterministic…

共同随机趋势的提取：理论与应用AI 解读

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models--those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that…

非平稳时间序列的函数系数模型AI 解读

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean…