A Bayesian analysis on time series structural equation models

Structural equation models (SEM) have been extensively used in behavioral, social, and psychological research to model relations between the latent variables and the observations. Most software packages for the fitting of SEM rely on frequentist methods. Traditional models and software are not appropriate for analysis of the dependent observations such as time-series data. In this study, a structural equation model with a time series feature is introduced. A Bayesian approach is used to solve the model with the aid of the Markov chain Monte Carlo method. Bayesian inferences as well as prediction with the proposed time series structural equation model can also reveal certain unobserved relationships among the observations. The approach is successfully employed using real Asian, American and European stock return data.     

Time-Varying Smooth Transition Autoregressive Models

Nonlinear regime-switching behavior and structural change are often perceived as competing alternatives to linearity. In this article we study the so-called time-varying smooth transition autoregressive (TV-STAR) model, which can be used both for describing simultaneous nonlinearity and structural change and for distinguishing between these features. Two modeling strategies for empirical specification of TV-STAR models are developed. Monte Carlo simulations show that neither of the two strategies dominates the other. A specific-to-general-to-specific procedure is best suited for obtaining a first impression of the importance of nonlinearity and/or structural change for a particular time series. A specific-to-general procedure is most useful in careful specification of a model with nonlinear and/or time-varying properties. An empirical application to a large dataset of U.S. macroeconomic time series illustrates the relative merits of both modeling strategies.     

The Construction and Use of Approximations for Missing Quarterly Observations: A Model-Based Approach

We use a model-based approach to derive quarterly figures on several variables for the aggregate labor market in the Netherlands that are only observed annually. These approximations are conditional expectations derived from univariate and bivariate quarterly time series models for the series under consideration. They are subsequently used as proxies to estimate and analyze the structural labor market equations. Attention is given to the properties of estimation procedures based on proxy variables.     

Tests for Structural Changes in Time Series of Counts

We propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.     

Page's sequential procedure for change-point detection in time series regression

In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change and is best under early change scenarios. For later changes their finite sample behavior is rather questionable. We therefore propose modified CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple time series regression models, that show a higher stability with respect to the time of change than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the consistency of the procedures are provided. In a simulation study it is shown that the proposed procedures behave well in finite samples. Finally the procedures are applied to a set of capital asset pricing data related to the Fama–French extension of the CAPM.     

Sparse Change-point HAR Models for Realized Variance

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.     

Invertibility of non-linear time series models

Sufficient conditions for invertibility of non-linear time series models are available in the literature only for a few special cases. In this paper a practical and general method for checking invertibility is presented. Briefly stated, it consists of feeding independent and identically distributed innovations into the non-linear model and then observing whether the model blows up or not. Using this idea invertibility conditions are derived for several recently proposed non-linear moving average models. Finally, the method is applied to a number of bilinear models fitted to economic time series.     

Integer autoregressive models with structural breaks

Even though integer-valued time series are common in practice, the methods for their analysis have been developed only in recent past. Several models for stationary processes with discrete marginal distributions have been proposed in the literature. Such processes assume the parameters of the model to remain constant throughout the time period. However, this need not be true in practice. In this paper, we introduce non-stationary integer-valued autoregressive (INAR) models with structural breaks to model a situation, where the parameters of the INAR process do not remain constant over time. Such models are useful while modelling count data time series with structural breaks. The Bayesian and Markov Chain Monte Carlo (MCMC) procedures for the estimation of the parameters and break points of such models are discussed. We illustrate the model and estimation procedure with the help of a simulation study. The proposed model is applied to the two real biometrical data sets.     

Structural vector autoregressive analysis for cointegrated variables

Summary Vector autoregressive (VAR) models are capable of capturing the dynamic structure of many time series variables. Impulse response functions are typically used to investigate the relationships between the variables included in such models. In this context the relevant impulses or innovations or shocks to be traced out in an impulse response analysis have to be specified by imposing appropriate identifying restrictions. Taking into account the cointegration structure of the variables offers interesting possibilities for imposing identifying restrictions. Therefore VAR models which explicitly take into account the cointegration structure of the variables, so-called vector error correction models, are considered. Specification, estimation and validation of reduced form vector error correction models is briefly outlined and imposing structural short- and long-run restrictions within these models is discussed. I thank an anonymous reader for comments on an earlier draft of this paper that helped me to improve the exposition.     

Inference for the Hyperparameters of Structural Models Under Classical and Bayesian Perspectives: A Comparison Study

Structural models—or dynamic linear models as they are known in the Bayesian literature—have been widely used to model and predict time series using a decomposition in non observable components. Due to the direct interpretation of the parameters, structural models are a powerful and simple methodology to analyze time series in several areas, such as economy, climatology, environmental sciences, among others. The parameters of such models can be estimated either using maximum likelihood or Bayesian procedures, generally implemented using conjugate priors, and there are plenty of works in the literature employing both methods. But are there situations where one of these approaches should be preferred? In this work, instead of conjugate priors for the hyperparameters, the Jeffreys prior is used in the Bayesian approach, along with the uniform prior, and the results are compared to the maximum likelihood method, in an extensive Monte Carlo study. Interval estimation is also evaluated and, to this purpose, bootstrap confidence intervals are introduced in the context of structural models and their performance is compared to the asymptotic and credibility intervals. A real time series of a Brazilian electric company is used as illustration.     

Confidence intervals for impulse responses under departures from normality

Monte Carlo evidence shows that in structural VAR models with fat-tailed or skewed innovations the coverage accuracy of impulse response confidence intervals may deterorate substantially compared to the same model with Gaussian innovations. Empirical evidance suggests that such departures from normality are quite plausible for economic time series. The simulation results suggest that applied researchers are best off using nonparametric bootstrap intervals for impulse responses, regardless of whether or not there is evidence of fat tails or skewness in the error distribution. Allowing for departures from normality is shown to considerably weaken the evidence of the delayed overshooting puzzle in Eichenbaum and Evans (1995).     

基于图方法的MA和ARMA模型系数检验

应用图模型方法来讨论传统的MA和ARMA模型,证明了MA和ARMA模型的系数为去掉其他时间序列分量线性效应的条件下的偏相关系数,且利用图模型推断算法提出了一种新的参数估计和检验方法。     

Bayesian Forecasting of Many Count-Valued Time Series

Abstract

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level provide more incisive inferences on shared patterns such as trends and seasonality. A novel multiscale approach—one new example of the concept of decouple/recouple in time series—enables information sharing across series. This incorporates cross-series linkages while insulating parallel estimation of univariate models, and hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multistep forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics, comparisons with existing methods, and broader questions of probabilistic forecast assessment.     

Testing nested and non-nested periodically integrated autoregressive models

Periodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing sea- sonal fluctuations for the non-periodic integrated series can be described by seasonal dummy variables for which the corresponding parameters are not constant within the sampie, such a series may not be easily & stinguished from a periodically integrated time series. In this paper, nested and non-nested testing procedures are proposed to distinguish between these two alternative stochastic and non-stochastic seasonal processes, When it is assumed there is a single unknown structural break in the seasonal dummy parameters. Several empirical examples using quarterly real macroeconomic time series for the United Kingdom illustrate the nested and non-nested approaches.     

On a mixture autoregressive model

We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co-workers to the mixture autoregressive (MAR) model for the modelling of non-linear time series. The models consist of a mixture of K stationary or non-stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series. The stationarity conditions and autocorrelation function are derived. The estimation is easily done via a simple EM algorithm and the model selection problem is addressed. The shape changing feature of the conditional distributions makes these models capable of modelling time series with multimodal conditional distributions and with heteroscedasticity. The models are applied to two real data sets and compared with other competing models. The MAR models appear to capture features of the data better than other competing models do.     

Forecasting Economic Time Series With Structural and Box-Jenkins Models: A Case Study

The basic structural model is a univariate time series model consisting of a slowly changing trend component, a slowly changing seasonal component, and a random irregular component. It is part of a class of models that have a number of advantages over the seasonal ARIMA models adopted by Box and Jenkins (1976). This article reports the results of an exercise in which the basic structural model was estimated for six U.K. macroeconomic time series and the forecasting performance compared with that of ARIMA models previously fitted by Prothero and Wallis (1976).     

Inference for linear and nonlinear stable error processes via estimating functions

This paper describes an estimating function approach for parameter estimation in linear and nonlinear times series models with infinite variance stable errors. Joint estimates of location and scale parameters are derived for classes of autoregressive (AR) models and random coefficient autoregressive (RCA) models with stable errors, as well as for AR models with stable autoregressive conditionally heteroscedastic (ARCH) errors. Fast, on-line, recursive parametric estimation for the location parameter based on estimating functions is discussed using simulation studies. A real financial time series is also discussed in some detail.     

Fractional integration versus level shifts: the case of realized asset correlations

Long memory has been widely documented for realized financial market volatility. As a novelty, we consider daily realized asset correlations and we investigate whether the observed persistence is (i) due to true long memory (i.e. fractional integration) or (ii) artificially generated by some structural break processes. These two phenomena are difficult to be distinguished in practice. Our empirical results strongly indicate that the hyperbolic decay of the autocorrelation functions of pair-wise realized correlation series is indeed not driven by a truly fractionally integrated process. This finding is robust against user specific parameter choices in the applied test statistic and holds for all 15 considered time series. As a next step, we apply simple models with deterministic level shifts. When selecting the number of breaks, estimating the breakpoints and the corresponding structural break models we find a substantial degree of co-movement between the realized correlation series hinting at co-breaking. The estimated structural break models are interpreted in the light of the historic economic and financial development.     

Testing for intercept‐scale switch in linear autoregression

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi‐likelihood‐based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427–446; 2012 © 2012 Statistical Society of Canada     

Asymmetric Volatility Models with Structural Breaks

This article develops an asymmetric volatility model that takes into consideration the structural breaks in the volatility process. Break points and other parameters of the model are estimated using MCMC and Gibbs sampling techniques. Models with different number of break points are compared using the Bayes factor and BIC. We provide a formal test and hence a new procedure for Bayes factor computation to choose between models with different number of breaks. The procedure is illustrated using simulated as well as real data sets. The analysis shows an evidence to the fact that the financial crisis in the market from the first week of September 2008 has caused a significant break in the structure of the return series of two major NYSE indices viz., S & P 500 and Dow Jones. Analysis of the USD/EURO exchange rate data also shows an evidence of structural break around the same time.