An investigation of lag identification tools for vector nonlinear time series

Exploratory methods for determining appropriate lagged vsrlables in a vector nonlinear time series model are investigated. The first is a multivariate extension of the R statistic considered by Granger and Lin (1994), which is based on an estimate of the mutual information criterion. The second method uses Kendall's ρ and partial ρ statistics for lag determination. The methods provide nonlinear analogues of the autocorrelation and partial autocorrelation matrices for a vector time series. Simulation studies indicate that the R statistic reliabiy identifies appropriate lagged nonlinear moving average terms in a vector time series, while Kendall's ρ and partial ρ statistics have some power in identifying appropirate lagged nonlinear moving average and autoregressive terms, respectively, when the nonlinear relationship between lagged variables is monotonic. For illustration, the methods are applied to set of annual temperature and tree ring measurements at Campito Mountain In California.     

Evaluating the Effectiveness of State-Switching Time Series Models for U.S. Real Output

Two types of state-switching models for U.S. real output have been proposed: models that switch randomly between states and models that switch states deterministically, as in the threshold autoregressive model of Potter. These models have been justified primarily on how well they fit the sample data, yielding statistically significant estimates of the model coefficients. Here we propose a new approach to the evaluation of an estimated nonlinear time series model that provides a complement to existing methods based on in-sample fit or on out-of-sample forecasting. In this new approach, a battery of distinct nonlinearity tests is applied to the sample data, resulting in a set of p-values for rejecting the null hypothesis of a linear generating mechanism. This set of p-values is taken to be a “stylized fact” characterizing the nonlinear serial dependence in the generating mechanism of the time series. The effectiveness of an estimated nonlinear model for this time series is then evaluated in terms of the congruence between this stylized fact and a set of nonlinearity test results obtained from data simulated using the estimated model. In particular, we derive a portmanteau statistic based on this set of nonlinearity test p-values that allows us to test the proposition that a given model adequately captures the nonlinear serial dependence in the sample data. We apply the method to several estimated state-switching models of U.S. real output.     

基于EMD和神经网络的非线性时间序列预测方法

现实生活中的时间序列,通常伴随着大量的噪声和高度的波动性。对于这些非线性时间序列,运用传统的统计和计量经济模型进行分析预测,预测结果往往不够理想。文章基于经验模态分解(EMD)和人工神经网络提出改进方法。主体思想是"先分再合":先用EMD方法分解非线性时间序列,得到一系列易于分析的独立的子系列,然后利用神经网络(FNN)对每一个子系列进行分析和预测,最后再用自适应线性神经网络(ALNN)整合并得出最终结果。结合具体房价时间序列实例,证实了这种方法的优势。     

Boosting techniques for nonlinear time series models

Many of the popular nonlinear time series models require a priori the choice of parametric functions which are assumed to be appropriate in specific applications. This approach is mainly used in financial applications, when sufficient knowledge is available about the nonlinear structure between the covariates and the response. One principal strategy to investigate a broader class on nonlinear time series is the Nonlinear Additive AutoRegressive (NAAR) model. The NAAR model estimates the lags of a time series as flexible functions in order to detect non-monotone relationships between current and past observations. We consider linear and additive models for identifying nonlinear relationships. A componentwise boosting algorithm is applied for simultaneous model fitting, variable selection, and model choice. Thus, with the application of boosting for fitting potentially nonlinear models we address the major issues in time series modelling: lag selection and nonlinearity. By means of simulation we compare boosting to alternative nonparametric methods. Boosting shows a strong overall performance in terms of precise estimations of highly nonlinear lag functions. The forecasting potential of boosting is examined on the German industrial production (IP); to improve the model’s forecasting quality we include additional exogenous variables. Thus we address the second major aspect in this paper which concerns the issue of high dimensionality in models. Allowing additional inputs in the model extends the NAAR model to a broader class of models, namely the NAARX model. We show that boosting can cope with large models which have many covariates compared to the number of observations.     

Generalized fixed‐T panel unit root tests

Panel data unit root tests, which can be applied to data that do not have many time series observations, are based on very restrictive error and deterministic component specification assumptions. In this paper, we develop a new, doubly modified estimator, based on which we propose a panel unit root test that allows for multiple structural breaks, linear and nonlinear trends, heteroscedasticity, serial correlation, and error cross‐section heterogeneity, when the number of time series observations is finite. The test has the additional perk that it is invariant to the initial condition.     

Forecasting Study of Shanghai’s and Shenzhen’s Stock Markets Using a Hybrid Forecast Method

In this article, a novel hybrid method to forecast stock price is proposed. This hybrid method is based on wavelet transform, wavelet denoising, linear models (autoregressive integrated moving average (ARIMA) model and exponential smoothing (ES) model), and nonlinear models (BP Neural Network and RBF Neural Network). The wavelet transform provides a set of better-behaved constitutive series than stock series for prediction. Wavelet denoising is used to eliminate some slight random fluctuations of stock series. ARIMA model and ES model are used to forecast the linear component of denoised stock series, and then BP Neural Network and RBF Neural Network are developed as tools for nonlinear pattern recognition to correct the estimation error of the prediction of linear models. The proposed method is examined in the stock market of Shanghai and Shenzhen and the results are compared with some of the most recent stock price forecast methods. The results show that the proposed hybrid method can provide a considerable improvement for the forecasting accuracy. Meanwhile, this proposed method can also be applied to analysis and forecast reliability of products or systems and improve the accuracy of reliability engineering.     

Multiple Comparisons with More than One Control for Exponential Location Parameters Under Heteroscedasticity

In this article we present a simple bootstrap method for time series. The proposed method is model-free, and hence it enables us to avoid certain situations where the bootstrap samples may contain impossible values due to resampling from the residuals. The method is easy to implement and can be applied to stationary and nonstationary time series. The simulation results and the application to real time series data show that the method works very well.     

Nonparametric Nonlinear Cotrending Analysis,With an Application to Interest and Inflation in the United States

Given the assumption that the components of a vector time series are stationary around nonlinear deterministic time trends, nonlinear cotrending is the phenomenon that one or more linear combinations of the time series are stationary around a linear trend or a constant; hence, the series have common nonlinear deterministic time trends. In this article, I develop nonparametric tests for nonlinear cotrending, and I derive nonparametric estimators of the cotrending vectors. I apply this approach to the federal funds rate and the consumer price index inflation rate in the United States, using monthly data, to analyze the price puzzle.     

A simulation method for finite non-stationary time series

In this paper, we propose a novel simulation method which enables us to obtain a large number of simulated time series cheaply. The developed method can be applied to any non-stationary time series of finite length and it guarantees that not only the marginal distributions but also the autocorrelation structures of observed and simulated time series are the same. Extensive simulation studies have been conducted to check the performance of our method and to assess if the overall dynamics of the observed time series is preserved by the simulated realizations. The developed simulation method has also been applied to the real size data of cocoon filament, which can be reeled from a cocoon produced by a silkworm. Very good results have been achieved in all the cases considered in the paper.     

Semiparametric models of longitudinal and time-to-event data with applications to HIV viral dynamics and CD4 counts

We propose a semiparametric approach based on proportional hazards and copula method to jointly model longitudinal outcomes and the time-to-event. The dependence between the longitudinal outcomes on the covariates is modeled by a copula-based times series, which allows non-Gaussian random effects and overcomes the limitation of the parametric assumptions in existing linear and nonlinear random effects models. A modified partial likelihood method using estimated covariates at failure times is employed to draw statistical inference. The proposed model and method are applied to analyze a set of progression to AIDS data in a study of the association between the human immunodeficiency virus viral dynamics and the time trend in the CD4/CD8 ratio with measurement errors. Simulations are also reported to evaluate the proposed model and method.     

Two-step variable selection in partially linear additive models with time series data

Lots of semi-parametric and nonparametric models are used to fit nonlinear time series data. They include partially linear time series models, nonparametric additive models, and semi-parametric single index models. In this article, we focus on fitting time series data by partially linear additive model. Combining the orthogonal series approximation and the adaptive sparse group LASSO regularization, we select the important variables between and within the groups simultaneously. Specially, we propose a two-step algorithm to obtain the grouped sparse estimators. Numerical studies show that the proposed method outperforms LASSO method in both fitting and forecasting. An empirical analysis is used to illustrate the methodology.     

基于LSTAR模型的非线性协整检验

大量的经济理论和实践都表明,宏观经济时间序列经常会出现非平稳和非线性特征,因而在统计分析时,需要进行非线性协整检验。基于逻辑平滑转换自回归(LSTAR)模型将传统的线性协整表述方法拓展为非线性形式,构造实用的检验程序及合适的统计量,利用软件R进行蒙特卡洛模拟给出非线性协整检验统计量的临界值,并通过实际数据分析购买力平价动态系统的非线性协整关系,说明方法的有效性。     

Age,Trend, and Cohort Effects in a Macro Model of Canadian Expenditure Patterns

A quadratic almost ideal demand system allowing for age, cohort, and trend effects is developed at the macro level. The model is estimated by maximum likelihood, using a three-tier iterative/search method applied to pooled 1961–1992 time series for five regions of Canada and six categories of expenditure. Hypothesis tests indicate support for the model specification. Elasticities are compared with those reported in other studies, with special attention to food. Effects of demographic and trend variables on elasticities and expenditure shares are investigated. An overall conclusion is that such effects can be very important in a macro demand system.     

Nonlinearity,Breaks, and Long-Range Dependence in Time-Series Models

We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in time series models and apply our modeling framework to daily realized measures of integrated variance. We develop asymptotic theory for parameter estimation and propose two model-building procedures. The methodology is applied to stocks of the Dow Jones Industrial Average during the period 2000 to 2009. We find strong evidence of nonlinear effects in financial volatility. An out-of-sample analysis shows that modeling these effects can improve forecast performance. Supplementary materials for this article are available online.     

On representing maximin efficient designs by Taylor series

This paper considers exponential and rational regression models that are nonlinear in some parameters. Recently, locally D-optimal designs for such models were investigated in [Melas, V. B., 2005. On the functional approach to optimal designs for nonlinear models. J. Statist. Plann. Inference 132, 93–116] based upon a functional approach. In this article a similar method is applied to construct maximin efficient D-optimal designs. This approach allows one to represent the support points of the designs by Taylor series, which gives us the opportunity to construct the designs by hand using tables of the coefficients of the series. Such tables are provided here for models with two nonlinear parameters. Furthermore, the recurrent formulas for constructing the tables for arbitrary numbers of parameters are introduced.     

Partially adaptive estimation of nonlinear models via a normal mixture

This paper extends the partially adaptive method Phillips (1994) provided for linear models to nonlinear models. Asymptotic results are established under conditions general enough they cover both cross-sectional and time series applications. The sampling efficiency of the new estimator is illustrated in a small Monte Carlo study in which the parameters of an autoregressive moving average are estimated. The study indicates that, for non-normal distributions, the new estimator improves on the nonlinear least squares estimator in terms of efficiency.     

Partially adaptive estimation of nonlinear models via a normal mixture

This paper extends the partially adaptive method Phillips (1994) provided for linear models to nonlinear models. Asymptotic results are established under conditions general enough they cover both cross-sectional and time series applications. The sampling efficiency of the new estimator is illustrated in a small Monte Carlo study in which the parameters of an autoregressive moving average are estimated. The study indicates that, for non-normal distributions, the new estimator improves on the nonlinear least squares estimator in terms of efficiency.     

A Bayesian wavelet approach to estimation of a change-point in a nonlinear multivariate time series

ABSTRACT

We propose a semiparametric approach to estimate the existence and location of a statistical change-point to a nonlinear multivariate time series contaminated with an additive noise component. In particular, we consider a p-dimensional stochastic process of independent multivariate normal observations where the mean function varies smoothly except at a single change-point. Our approach involves conducting a Bayesian analysis on the empirical detail coefficients of the original time series after a wavelet transform. If the mean function of our time series can be expressed as a multivariate step function, we find our Bayesian-wavelet method performs comparably with classical parametric methods such as maximum likelihood estimation. The advantage of our multivariate change-point method is seen in how it applies to a much larger class of mean functions that require only general smoothness conditions.     

On unification of the asymptotic theory of nonlinear econometric models

After reading a few articles in the nonlinear econonetric literature one begins to notice that each discussion follows roughly the same lines as the classical treatment of maximum likelihood estimation. There are some technical problems having to do with simultaneously conditioning on the exogenous variables and subjecting the true parameter to a Pittman drift which prevent the use of the classical methods of proof but the basic impression of similarity is correct . An estimator – be it nonlinear least squares, three – stage nonlinear least squares, or whatever – is the solution of an optimization problem. And the objective function of the optimization problem can be treated as if it were the likelihood to derive the Wald test statistic, the likelihood ratio test statistic , and Rao's efficient score statistic. Their asymptotic null and non – null distributions can be found using arguments fairly similar to the classical maximum likelihood arguments. In this article we exploit these observations and unify much of the nonlinear econometric literature. That which escapes this unificationis that which has an objective function which is not twice continuously differentiable with respect to the parameters – minimum absolute deviations regression for example.

The model which generates the data need not bethe same as the model which was presumed to define the optimization problem. Thus, these results can be used to obtain the asymptotic behavior of inference procedures under specification error We think that this will prove to be the nost useful feature of the paper. For example, it i s not necessary toresortto Monte Carlo simulat ionto determine i f a Translog estimate of an elasticity of sub stitution obtained by nonlinear three-stage least squares is robust against a CES truestate of nature. The asymptotic approximations we give here w ill provide an analytic answer to the question, sufficiently accurate for most purposes.     

Estimation of conditional quantiles by a new smoothing approximation of asymmetric loss functions

In this paper, nonparametric estimation of conditional quantiles of a nonlinear time series model is formulated as a nonsmooth optimization problem involving an asymmetric loss function. This asymmetric loss function is nonsmooth and is of the same structure as the so-called lopsided absolute value function. Using an effective smoothing approximation method introduced for this lopsided absolute value function, we obtain a sequence of approximate smooth optimization problems. Some important convergence properties of the approximation are established. Each of these smooth approximate optimization problems is solved by an optimization algorithm based on a sequential quadratic programming approximation with active set strategy. Within the framework of locally linear conditional quantiles, the proposed approach is compared with three other approaches, namely, an approach proposed by Yao and Tong (1996), the Iteratively Reweighted Least Squares method and the Interior-Point method, through some empirical numerical studies using simulated data and the classic lynx pelt series. In particular, the empirical performance of the proposed approach is almost identical with that of the Interior-Point method, both methods being slightly better than the Iteratively Reweighted Least Squares method. The Yao-Tong approach is comparable with the other methods in the ideal cases for the Yao-Tong method, but otherwise it is outperformed by other approaches. An important merit of the proposed approach is that it is conceptually simple and can be readily applied to parametrically nonlinear conditional quantile estimation.