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非线性谱分析：局部高斯方法AI 解读

The spectral distribution f(ω) of a stationary time series {Yt}t∈Z can be used to investigate whether or not periodic structures are present in {Yt}t∈Z, but f(ω) has some limitations due to its dependence on the autocovariances γ(h). For example, f(ω) can not distinguish white iid noise from GARCH-type models (whose terms are dependent, but uncorrelated), which implies that f(ω) can be an inadequate tool when {Yt}t∈Z contains asymmetries and nonlinear dependencies.…

局部高斯偏相关AI 解读

It is well known in econometrics and other fields that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial correlation does not, however, characterize conditional dependence in many non-Gaussian populations. This article introduces the local Gaussian partial correlation (LGPC), a new measure of conditional…

零常返时间序列中的稳健非线性回归估计AI 解读

In this article, we study parametric robust estimation in nonlinear regression models with regressors generated by a class of non-stationary and null recurrent Markov processes. The nonlinear regression functions can be either integrable or asymptotically homogeneous, covering many commonly-used functional forms in parametric nonlinear regression. Under regularity conditions, we derive both the consistency and limit distribution results for the developed general robust…

两个时间序列之间非线性局部依赖的估计与检验AI 解读

The most common measure of dependence between two time series is the cross-correlation function. This measure gives a complete characterization of dependence for two linear and jointly Gaussian time series, but it often fails for nonlinear and non-Gaussian time series models, such as the ARCH-type models used in finance. The cross-correlation function is a global measure of dependence. In this article, we apply to bivariate time series the nonlinear local measure of…

非线性多元协整回归的设定检验AI 解读

This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that the model accommodates endogeneity. A new and simple test is proposed, and the resulting asymptotic theory is established. The test statistic is constructed based on a natural…

一类新的二元门限协整模型AI 解读

In this article, we introduce a new class of bivariate threshold VAR cointegration models. In the models, outside a compact region, the processes are cointegrated, while in the compact region, we allow different kinds of possibilities. We show that the bivariate processes form a 1/2-null recurrent system. We also find that the convergence rate for the estimators for the coefficients in the outside regime is T$\sqrt{T}$, while the convergence rate for the estimators for the…

Harris 常返马尔可夫链下非线性回归的估计AI 解读

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov…

单指标与部分线性单指标积分模型的估计AI 解读

Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially…

零常返时间序列中非参数估计量的一致收敛AI 解读

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.

兼含平稳区制与单位根区制的门限自回归模型估计AI 解读

This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models has basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result.

零常返单位根过程AI 解读

The classical nonstationary autoregressive models are both linear and Markov. They include unit root and cointegration models. A possible nonlinear extension is to relax the linearity and at the same time keep general properties such as nonstationarity and the Markov property. A null recurrent Markov chain is nonstationary, and β -null recurrence is of vital importance for statistical inference in nonstationary Markov models, such as, e.g., in nonparametric estimation in…

非线性非平稳时间序列自回归的设定检验AI 解读

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting and the results differ from earlier work on nonparametric autoregression with stationarity. In addition, we develop a new bootstrap simulation scheme for the selection of a suitable bandwidth parameter involved in the kernel test as well as…

泊松自回归AI 解读

In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the…

含非平稳性的非线性时间序列非参数设定检验AI 解读

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for…

自适应变系数时空模型AI 解读

Summary We propose an adaptive varying-coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non-linearity (both in space and in time) and non-stationarity (in space) by allowing the auto-regressive coefficients to vary with both spatial location and an unknown index variable. We suggest a two-step procedure to estimate both the coefficient functions and the index variable, which is…

时间序列面板的非参数加性模型AI 解读

This paper discusses nonparametric models for panels of time series. There is already a substantial literature on nonlinear models and nonparametric methods in a regression and time series setting. But almost without exception these developments have been limited to univariate and multivariate models of moderate dimensions. Very little has been done for panels, where the dimension, often corresponding to a number of individuals, typically is very large but where the number…

非线性协整型模型中的非参数估计AI 解读

We derive an asymptotic theory of nonparametric estimation for a time series regression model Zt=f(Xt)+Wt, where {Xt} and {Zt} are observed nonstationary processes and {Wt} is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent Markov chains. This…

零常返时间序列中的非参数估计AI 解读

We develop a nonparametric estimation theory in a nonstationary environment, more precisely in the framework of null recurrent Markov chains. An essential tool is the split chain, which makes it possible to decompose the times series under consideration into independent and identical parts. A tail condition on the distribution of the recurrence time is introduced. This condition makes it possible to prove weak convergence results for sums of functions of the process…

加性非线性 ARX 时间序列与投影估计AI 解读

We propose projections as means of identifying and estimating the components (endogenous and exogenous) of an additive nonlinear ARX model. The estimates are nonparametric in nature and involve averaging of kernel-type estimates. Such estimates have recently been treated informally in a univariate time series situation. Here we extend the scope to nonlinear ARX models and present a rigorous theory, including the derivation of asymptotic normality for the projection estimates…

非线性 ARCH 时间序列的非参数估计与识别：强收敛和渐近正态性AI 解读

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

时间序列线性的非参数检验AI 解读

We introduce tests of linearity for time series based on nonparametric estimates of the conditional mean and the conditional variance. The tests are compared to a number of parametric tests and to nonparametric tests based on the bispectrum. Asymptotic expressions give bad approximations, and the null distribution under linearity is constructed using resampling of the best linear approximation. The new tests perform well on the examples tested.

非线性时间序列的非参数模型辨识：投影方法AI 解读

We study the possibility of identifying general linear and nonlinear time series models using nonparametric methods. The kernel estimators of the conditional mean and variance are used as a basis, and the properties of these quantities as model indicators are briefly discussed. Some drawbacks are pointed out, and motivated by these we introduce projections as tools of identification. The projections are especially useful for additive modeling. Expressions for the asymptotic…

非线性时间序列的非参数识别：显著滞后选择AI 解读

In this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series. The procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series. The procedure is illustrated by simulations and sunspot data, lynx data, and blowfly data are analyzed. It is indicated that projectors can be used in conjunction with the procedure for selecting…

基于经验分布函数的序列独立性非参数检验AI 解读

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests…