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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…

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…

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…

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…

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…

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…

含持久协变量的ARCH过程的时间序列性质AI 解读

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the…

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Bootstrap 单位根检验AI 解读

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op(n−1/4) and Op(n−1/2), and involve…

时间序列筛自助法的不变原理AI 解读

This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form…

含协整与确定性趋势解释变量的非线性计量模型AI 解读

This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear coin-tegrating regressions.The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the…

含单整时间序列的非线性回归AI 解读

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable and asymptotically homogeneous functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. The rates of convergence depend on the properties of the nonlinear regression…

非平稳二元选择AI 解读

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the…

具有时变系数的协整回归AI 解读

This paper considers cointegrating regressions with time varying coefficients. The coefficients are modeled as smooth functions evolving over time. It is shown that they can be estimated nonparametrically, using suitably modified series estimators. Presented is the efficient method of estimation, which relies on simple prefiltering of the data and preestimation of the model. The test for the adequacy of model specification is also developed. Our model and statistical methods…

单整时间序列非线性变换的渐近理论AI 解读

An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such functions are obtained and analyzed. The transformations considered in the paper include a variety of functions that are used in practical nonlinear statistical analysis. It is shown that…

含 I(1) 与 I(2) 变量的典范协整回归与协整检验AI 解读

This paper introduces tests for the null of cointegration in the presence of I (1) and I (2) variables. These tests use residuals from Park's (1992, Econometrica 60,119–143) canonical cointegrating regression (CCR) and the leads-and-lags regression of Saikkonen (1991, Econometric Theory 9,1–21) and Stock and Watson (1993, Econometrica 61, 783–820). Asymptotic theory for CCR in the presence of I (1) and I (2) variables is also introduced. The distributions of the…