Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

We propose a state-space approach for GARCH models with time-varying parameters able to deal with non-stationarity that is usually observed in a wide variety of time series. The parameters of the non-stationary model are allowed to vary smoothly over time through non-negative deterministic functions. We implement the estimation of the time-varying parameters in the time domain through Kalman filter recursive equations, finding a state-space representation of a class of time-varying GARCH models. We provide prediction intervals for time-varying GARCH models and, additionally, we propose a simple methodology for handling missing values. Finally, the proposed methodology is applied to the Chilean Stock Market (IPSA) and to the American Standard&Poor's 500 index (S&P500).     

Non-stationary structural model with time-varying demand elasticities

The paper considers local linear regression of a time series model with non-stationary regressors and errors. Asymptotic property of the local linear estimator is derived under a new dependence measure of non-stationary time series. We apply the local linear regression method to estimate the “time-varying” coefficients of an economic-causal model for the industrial sector of the U.S. economy. Nonparametric bootstrap test on the time-varying coefficients strongly suggests that the price/income elasticities of the U.S. durable goods demand are time-varying.     

Estimating the parameters of a BINMA Poisson model for a non-stationary bivariate time series

This article proposes a novel non-stationary BINMA time series model by extending two INMA processes where their innovation series follow the bivariate Poisson under time-varying moment assumptions. This article also demonstrates, through simulation studies, the use and superiority of the generalized quasi-likelihood (GQL) approach to estimate the regression effects, which is computationally less complicated as compared to conditional maximum likelihood estimation (CMLE) and the feasible generalized least squares (FGLS). The serial and bivariate dependence correlations are estimated by a robust method of moments.     

Bootstrap prediction intervals for autoregressive conditional duration models

In the recent past, the autoregressive conditional duration (ACD) models have gained popularity in modelling the durations between successive events. The aim of this paper is to propose a simple and distribution free re-sampling procedure for developing the forecast intervals of linear ACD Models. We use the conditional least squares method to estimate the parameters of the ACD Model instead of the conditional Maximum Likelihood Estimation or Quasi-Maximum Likelihood Estimation and show that they are consistent for large samples. The properties of the proposed procedure are illustrated by a simulation study and an application to two real data sets.     

A case study of MCB and SBMH stock transaction using a novel BINMA(1) with non-stationary NB correlated innovations

This paper focuses on the modeling of the intra-day transactions at the Stock Exchange Mauritius (SEM) of the two major banking companies: Mauritius Commercial Bank Group Limited (MCB) and State Bank of Mauritius Holdings Ltd (SBMH) in Mauritius using a flexible non-stationary bivariate integer-valued moving average of order 1 (BINMA(1)) process with negative binomial (NB) innovations that may cater for different levels of over-dispersion. The generalized quasi-likelihood (GQL) approach is used to estimate the regression, dependence and over-dispersion effects. However, for the over-dispersion parameters, the auto-covariance structure in the GQL is constructed using some higher order moments. This new model is tested over some Monte-Carlo experiments and is applied to analyze the inter-related intra-day series of volume of stocks for the two banking institutions using data collected from 3 August to 16 October 2015 in the presence of some time-varying covariates such as the news effect, Friday effect and time of the day effect.     

Modelling a non-stationary BINAR(1) Poisson process

ABSTRACT

Non-stationarity in bivariate time series of counts may be induced by a number of time-varying covariates affecting the bivariate responses due to which the innovation terms of the individual series as well as the bivariate dependence structure becomes non-stationary. So far, in the existing models, the innovation terms of individual INAR(1) series and the dependence structure are assumed to be constant even though the individual time series are non-stationary. Under this assumption, the reliability of the regression and correlation estimates is questionable. Besides, the existing estimation methodologies such as the conditional maximum likelihood (CMLE) and the composite likelihood estimation are computationally intensive. To address these issues, this paper proposes a BINAR(1) model where the innovation series follow a bivariate Poisson distribution under some non-stationary distributional assumptions. The method of generalized quasi-likelihood (GQL) is used to estimate the regression effects while the serial and bivariate correlations are estimated using a robust moment estimation technique. The application of model and estimation method is made in the simulated data. The GQL method is also compared with the CMLE, generalized method of moments (GMM) and generalized estimating equation (GEE) approaches where through simulation studies, it is shown that GQL yields more efficient estimates than GMM and equally or slightly more efficient estimates than CMLE and GEE.     

非参数可加ACD模型及其应用研究

非参数可加ACD模型对条件期望的函数形式与随机误差项的分布形式要求都没有参数ACD模型强，因此不会像参数ACD模型那样因模型形式设定错误而得出错误结论。非参数可加ACD模型估计出来的各个可加部分图形的形状对于正确设定参数ACD模型具有一定的指导作用。     

Bank Business Models at Zero Interest Rates

We propose a novel observation-driven finite mixture model for the study of banking data. The model accommodates time-varying component means and covariance matrices, normal and Student’s t distributed mixtures, and economic determinants of time-varying parameters. Monte Carlo experiments suggest that units of interest can be classified reliably into distinct components in a variety of settings. In an empirical study of 208 European banks between 2008Q1–2015Q4, we identify six business model components and discuss how their properties evolve over time. Changes in the yield curve predict changes in average business model characteristics.     

A mixture integer-valued ARCH model

We propose a mixture integer-valued ARCH model for modeling integer-valued time series with overdispersion. The model consists of a mixture of K stationary or non-stationary integer-valued ARCH components. The advantages of the mixture model over the single-component model include the ability to handle multimodality and non-stationary components. The necessary and sufficient first- and second-order stationarity conditions, the necessary arbitrary-order stationarity conditions, and the autocorrelation function are derived. The estimation of parameters is done through an EM algorithm, and the model is selected by three information criterions, whose performances are studied via simulations. Finally, the model is applied to a real dataset.     

Departure from independence and stationarity in a handball match

This paper analyses direct and indirect forms of dependence in the probability of scoring in a handball match, taking into account the mutual influence of both playing teams. Non-identical distribution (i.d.) and non-stationarity, which are commonly observed in sport games, are studied through the specification of time-varying parameters.

The model accounts for the binary character of the dependent variable, and for unobserved heterogeneity. The parameter dynamics is specified by a first-order auto-regressive process.

Data from the Handball World Championships 2001–2005 show that the dynamics of handball violate both independence and i.d., in some cases having a non-stationary behaviour.     

中国价格型货币政策的系统性与非系统性时变效应研究

本文建立兼具随机波动率和时变参数的VAR模型,刻画经济系统中结构冲击和传导机制的时变性,并在同一框架内分析价格型货币政策的系统性和非系统性效应。研究结果显示：（1）对应于货币政策冲击,货币政策的非系统性效应在大波动时期存在“价格之谜”现象,在大稳定时期则出现政策冲击波动以及经济活动对其同向响应程度的双重下降现象,甚至在有些时段出现负向响应,其平抑经济波动的作用得到一定程度的体现。（2）系统性效应显示货币政策对于通货膨胀的响应强度整体呈消极特征,但存在一种往积极方向转变的动态学习模式,而且这种转变呈现不同状态的频繁转换。（3）反事实分析显示货币政策系统性和非系统性效应虽然有所改善,但这并不是宏观经济从大波动向大稳定转变的主要原因。     

贝叶斯隐马尔科夫异质面板模型及应用研究

针对不可观测异质性非时变假设导致的删失变量偏差及推断无效问题,构建贝叶斯隐马尔科夫异质面板模型,刻画截面个体间的动态时变不可观测异质性,诊断经济系统环境中可能存在的隐性变点,设计相应的马尔科夫链蒙特卡洛抽样算法估计模型参数,并对中国各地区的金融发展与城乡收入差距关系进行实证分析,捕捉到金融发展与城乡收入差距间长期稳定关系的隐性变化,发现了区域个体不可观测异质性存在的动态时变特征。研究结果表明各参数的迭代轨迹收敛且估计误差非常小,验证了贝叶斯隐马尔科夫异质面板模型的有效性。     

Non-stationary quasi-likelihood and asymptotic optimality

This article is concerned with non-stationary time series which does not require the full knowledge of the likelihood function. Consequently, a quasi-likelihood is employed for estimating parameters instead of the maximum (exact) likelihood. For stationary cases, Wefelmeyer (1996) and Hwang and Basawa (2011a,b), among others, discussed the issue of asymptotic optimality of the quasi-likelihood within a restricted class of estimators. For non-stationary cases, however, the asymptotic optimality property of the quasi-likelihood has not yet been adequately addressed in the literature. This article presents the asymptotic optimal property of the non-stationary quasi-likelihood within certain estimating functions. We use a random norm instead of a constant norm to get limit distributions of estimates. To illustrate main results, the non-stationary ARCH model, branching Markov process, and non-stationary random-coefficient AR process are discussed.     

非参数ACD模型及其在中国股票市场的实证研究

文章利用中国证券市场的日内交易数据实证了非参数ACD模型。非参数ACD模型不依赖条件均值的函数形式和误差项的分布形式,更具有一般意义。文章从多个方面进行实证分析。利用非参数方法进行分析的结果表明:数据不能用线性ACD模型来刻画,根据非参数拟合曲面的形状可以把此ACD模型的函数形式设定为某种非线性形式。     

A nonparametric time-varying coefficient model for panel count data

In this research, we describe a nonparametric time-varying coefficient model for the analysis of panel count data. We extend the traditional panel count data models by incorporating B-splines estimates of time-varying coefficients. We show that the proposed model can be implemented using a nonparametric maximum pseudo-likelihood method. We further examine the theoretical properties of the estimators of model parameters. The operational characteristics of the proposed method are evaluated through a simulation study. For illustration, we analyse data from a study of childhood wheezing, and describe the time-varying effect of an inflammatory marker on the risk of wheezing.     

Multichannel electroencephalographic analyses via dynamic regression models with time-varying lag–lead structure

Multiple time series of scalp electrical potential activity are generated routinely in electroencephalographic (EEG) studies. Such recordings provide important non-invasive data about brain function in human neuropsychiatric disorders. Analyses of EEG traces aim to isolate characteristics of their spatiotemporal dynamics that may be useful in diagnosis, or may improve the understanding of the underlying neurophysiology or may improve treatment through identifying predictors and indicators of clinical outcomes. We discuss the development and application of non-stationary time series models for multiple EEG series generated from individual subjects in a clinical neuropsychiatric setting. The subjects are depressed patients experiencing generalized tonic–clonic seizures elicited by electroconvulsive therapy (ECT) as antidepressant treatment. Two varieties of models—dynamic latent factor models and dynamic regression models—are introduced and studied. We discuss model motivation and form, and aspects of statistical analysis including parameter identifiability, posterior inference and implementation of these models via Markov chain Monte Carlo techniques. In an application to the analysis of a typical set of 19 EEG series recorded during an ECT seizure at different locations over a patient's scalp, these models reveal time-varying features across the series that are strongly related to the placement of the electrodes. We illustrate various model outputs, the exploration of such time-varying spatial structure and its relevance in the ECT study, and in basic EEG research in general.     

Geographically Weighted Negative Binomial Regression—incorporating overdispersion

Global regression assumes that a single model adequately describes all parts of a study region. However, the heterogeneity in the data may be sufficiently strong that relationships between variables can not be spatially constant. In addition, the factors involved are often sufficiently complex that it is difficult to identify them in the form of explanatory variables. As a result Geographically Weighted Regression (GWR) was introduced as a tool for the modeling of non-stationary spatial data. Using kernel functions, the GWR methodology allows the model parameters to vary spatially and produces non-parametric surfaces of their estimates. To model count data with overdispersion, it is more appropriate to use a negative binomial distribution instead of a Poisson distribution. Therefore, we propose the Geographically Weighted Negative Binomial Regression (GWNBR) method for the modeling of data with overdispersion. The results obtained using simulated and real data show the superiority of this method for the modeling of non-stationary count data with overdispersion compared with competing models, such as global regressions, e.g., Poisson and negative binomial and Geographically Weighted Poisson Regression (GWPR). Moreover, we illustrate that these competing models are special cases of the more robust model GWNBR.     

Bayesian Bandwidth Estimation in Nonparametric Time-Varying Coefficient Models

Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this article, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time-varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown parameters involved in the error density. A Monte Carlo simulation study shows that (i) the proposed Bayesian estimators for bandwidth and parameters in the error density have satisfactory finite sample performance; and (ii) our proposed Bayesian approach achieves better performance in estimating the bandwidths than the normal reference rule and cross-validation. Moreover, we apply our proposed Bayesian bandwidth estimation method for the time-varying coefficient models that explain Okun’s law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric forms of the time-varying coefficients. Supplementary materials for this article are available online.     

Non-parametric Curve Estimation by Wavelet Thresholding with Locally Stationary Errors

An important aspect in the modelling of biological phenomena in living organisms, whether the measurements are of blood pressure, enzyme levels, biomechanical movements or heartbeats, etc., is time variation in the data. Thus, the recovery of a 'smooth' regression or trend function from noisy time-varying sampled data becomes a problem of particular interest. Here we use non-linear wavelet thresholding to estimate a regression or a trend function in the presence of additive noise which, in contrast to most existing models, does not need to be stationary. (Here, non-stationarity means that the spectral behaviour of the noise is allowed to change slowly over time). We develop a procedure to adapt existing threshold rules to such situations, e.g. that of a time-varying variance in the errors. Moreover, in the model of curve estimation for functions belonging to a Besov class with locally stationary errors, we derive a near-optimal rate for the -risk between the unknown function and our soft or hard threshold estimator, which holds in the general case of an error distribution with bounded cumulants. In the case of Gaussian errors, a lower bound on the asymptotic minimax rate in the wavelet coefficient domain is also obtained. Also it is argued that a stronger adaptivity result is possible by the use of a particular location and level dependent threshold obtained by minimizing Stein's unbiased estimate of the risk. In this respect, our work generalizes previous results, which cover the situation of correlated, but stationary errors. A natural application of our approach is the estimation of the trend function of non-stationary time series under the model of local stationarity. The method is illustrated on both an interesting simulated example and a biostatistical data-set, measurements of sheep luteinizing hormone, which exhibits a clear non-stationarity in its variance.     

中国现阶段环境约束下的适度经济增长率研究——基于废气排放量视角的分析

经济发展与环境污染的关系历来都是一对不可回避的矛盾,也是学术界研究的热点,国内外大多数学者都在考察人均GDP与环境污染的库兹涅茨曲线,但对于环境与经济增长率的关系却很少有人研究。首先建立环境变量与经济增长率关系的变参数状态空间模型,并将建立的状态空间模型转化成线性规划中的决策方程,之后应用参数区间估计和集合论两种方法,通过约束相应的变量及变量的系数来估计中国现阶段环境约束下的适度经济增长率。