Statistical Properties of Threshold Models

This article focuses the attention on the Self Exciting Threshold Autoregressive Moving Average model (SETARMA) proposed in Tong (1983 Tong , H. ( 1983 ). Threshold Models in Nonlinear Time Series Analysis . London : Springer-Verlag .[Crossref] , [Google Scholar]). The stochastic structure of the model is discussed and different specifications are presented. Starting from one of them, we give sufficient conditions for the weak stationarity of the model that are discussed and critically compared to other results given in literature. In particular, after showing that the SETARMA model belongs to the class of the Random Coefficients Autoregressive models, widely discussed in Nicholls and Quinn (1982 Nicholls , D. F. , Quinn , B. G. (1982). Random Coefficients Autoregressive Models. An Introduction . New York : Springer-Verlag.[Crossref] , [Google Scholar]), we give some issues on the weak stationarity of its stochastic structure that are more general than those given in the existing literature and appear not affected by the moving average component.     

Integer-Valued Self-Exciting Threshold Autoregressive Processes

In this article, we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.     

Empirical Likelihood for Threshold Autoregressive Models

This article develops empirical likelihood for threshold autoregressive models. We propose general estimating equations based on moment constraint. Under some suitable conditions, we show the empirical likelihood estimators for parameter are asymptotically normally distributed, and the proposed log empirical likelihood ratio statistic asymptotically follows a standard chi-squared distribution.     

Endogeneity in Threshold Nonlinearity Tests

This article shows the conditions under which endogeneity of a regressor variable does not affect threshold nonlinearity tests. Inference on the values of the parameters derived from standard statistics is also appropriate. Simulation techniques are used to approximate the p-value of the test. Monte Carlo simulations confirm the validity of Wald tests in the presence of endogeneity in the regressors.     

Theory of Bilinear Time Series Models

ABSTRACT

In this paper, we prove some theoretic properties of bilinear time series models which are extension of ARMA models. The sufficient conditions for asymptotic stationarity and ivertibility of some types of bilinear models are derived. The structural theory of discussed bilinear models is similar to that of ARMA models. For illustration, a bilinear model has been fitted to the Wolfer sunspot numbers and a substantial reduction in sum of squared residuals is obtained as comparing with Box-Jenkins ARMA model.     

Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.     

平稳阈值自回归下的伪回归研究

 研究表明相互独立的平稳阈值自回归(TAR)模型之间的回归存在伪回归,且伪回归的产生与样本容量和随机干扰项的分布无关。通过一系列的MC模拟,不仅证实了理论结论,而且模拟结果还表明当持久性相同时,两机制TAR回归模型比三机制TAR回归模型具有更大的拒绝率,原因在于两机制TAR下,OLS法估计得到的标准误具有更厚的左尾。此外在模拟中也发现当随机干扰项服从TAR模型时,Newey-West(1987)的一致异方差估计法是不适用的。     

Flexible Threshold Models for Modelling Interest Rate Volatility

This paper focuses on interest rate models with regime switching and extends previous nonlinear threshold models by relaxing the assumption of a fixed number of regimes. Instead we suggest automatic model determination through Bayesian inference via the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. Moreover, we allow the thresholds in the volatility to be driven not only by the interest rate but also by other economic factors. We illustrate our methodology by applying it to interest rates and other economic factors of the American economy.     

Flexible Threshold Models for Modelling Interest Rate Volatility

This paper focuses on interest rate models with regime switching and extends previous nonlinear threshold models by relaxing the assumption of a fixed number of regimes. Instead we suggest automatic model determination through Bayesian inference via the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. Moreover, we allow the thresholds in the volatility to be driven not only by the interest rate but also by other economic factors. We illustrate our methodology by applying it to interest rates and other economic factors of the American economy.     

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online.     

A Short-Cut Derivation for the Solution of Autoregressive Models from Sharp Algebraic Arguments

This article uses algebraic arguments to cast light on the solution of vector autoregressive models in the presence of unit roots. First, the linear case and then the multi-lag specification are investigated. Clear-cut representations of the model solutions are obtained, closed-form expressions of the coefficient matrices are provided, and integration features and cointegration mechanisms for stationarity recovery are elucidated.     

On Mixture Periodic Vector Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007 Fong, P.W., Li, W.K., Yau, C.W., Wong, C.S. (2007). On a mixture vector autoregressive model. The Canadian Journal of Statistics 35:135–150.[Crossref], [Web of Science ®] , [Google Scholar]). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVAR_S(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.     

Threshold autoregression analysis for finite-range time series of counts with an application on measles data

This article studies the threshold autoregression analysis for the self-exciting threshold binomial autoregressive processes. Parameters' point estimation and interval estimation problems are considered via the empirical likelihood method. A new algorithm to estimate the threshold value of the threshold model is also given. Simulation study is conducted for the evaluation of the developed approach. An application on measles data is provided to show the applicability of the method.     

Bayesian Analysis of DSGE Models

This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the non-linear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models and a DSGE model that was solved with a second-order perturbation method.     

门限自回归下的单位根检验可靠性研究

在非对称的门限自回归模型下,由于传统单位根检验式的误设,会导致单位根检验势下降。本文通过一系列的Monte-Carlo模拟表明：非对称性对ADF和PP检验的检验势会产生较大影响,而对其他四种常用的单位根检验势产生的影响较小,也就是说,在非对称的门限自回归下,非对称性对退势单位根检验势产生的影响较小。模拟中也发现：NP单位根检验对TAR模型和持久性都具有稳健性。     

Sharp Threshold Detection Based on Sup-Norm Error Rates in High-Dimensional Models

We propose a new estimator, the thresholded scaled Lasso, in high-dimensional threshold regressions. First, we establish an upper bound on the ?_∞ estimation error of the scaled Lasso estimator of Lee, Seo, and Shin. This is a nontrivial task as the literature on high-dimensional models has focused almost exclusively on ?₁ and ?₂ estimation errors. We show that this sup-norm bound can be used to distinguish between zero and nonzero coefficients at a much finer scale than would have been possible using classical oracle inequalities. Thus, our sup-norm bound is tailored to consistent variable selection via thresholding. Our simulations show that thresholding the scaled Lasso yields substantial improvements in terms of variable selection. Finally, we use our estimator to shed further empirical light on the long-running debate on the relationship between the level of debt (public and private) and GDP growth. Supplementary materials for this article are available online.     

Single-Index Additive Vector Autoregressive Time Series Models

Abstract.  We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selection of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Niño phenomenon, the unusual warming of water in the Pacific Ocean.     

贝叶斯非线性混合效应模型及其应用研究

由于常用的线性混合效应模型对具有非线性关系的纵向数据建模具有一定的局限性,因此对线性混合效应模型进行扩展,根据变量间的非线性关系建立不同的非线性混合效应模型,并根据因变量的分布特征建立混合分布模型。基于一组实际的保险损失数据,建立多项式混合效应模型、截断多项式混合效应模型和B样条混合效应模型。研究结果表明,非线性混合效应模型能够显著改进对保险损失数据的建模效果,对非寿险费率厘定具有重要参考价值。     

门限协整套利:理论与实证研究

 不同市场上的同质或相似商品的价格存在长期均衡关系,当价格偏离均衡时,由于套利交易的存在,偏离会迅速回到均衡。在一定的门限值以外,二者服从协整关系,在门限值以内,二者没有协整关系,这种关系称为门限协整。本文在Balke,Fomby(1997)[1]和Hasen（1996）[6]的基础上提出了基于门限向量误差修正模型（T-VECM）的sup-Wald检验,用Bootstrap方法模拟统计量的渐进分布,验证了英国富时指数期货（uk100）和德国法兰克福指数期货（ger30）的门限协整关系,并用Hasen,Seo（2002）[11]提出的极大似然估计方法（MLE）同时估计出门限参数和协整向量,并给出了在这种门限协整关系下进行跨市场无风险套利的策略。