Time Series Literature Research Articles

Dynamic structure of the spot price of crude oil: does time aggregation matter?

This paper assesses nonlinear structures in the time series data generating mechanism of crude oil prices. We apply well-known univariate tests for nonlinearity, with distinct power functions over alternatives, but with different null hypotheses reflecting the existence of different concepts of linearity and nonlinearity in the time series literature. We utilize daily data on crude oil spot price for over 26years, as well as monthly data on crude oil spot price for 41years. Investigating the monthly price of crude oil along with the daily price distinguishes the approach of this paper from existing studies focusing on the time series structure of crude oil price. All the tests detect strong evidence of general nonlinear serial dependence, as well as nonlinearity in the mean, variance, and skewness functions in the daily spot price of crude oil. Since evidence of nonlinear dependence is less dramatic in monthly observations, nonlinear serial dependence is moderated by time aggregation in crude oil prices but not significantly.

Modeling volatility in heat rate variability.

Modeling Heart Rate Variability (HRV) data has become important for clinical applications and as a research tool. These data exhibit long memory and time-varying conditional variance (volatility). In HRV, volatility is traditionally estimated by recursive least squares combined with short memory AutoRegressive (AR) models. This work considers a parametric approach based on long memory Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with heteroscedastic errors. To model the heteroscedasticity nonlinear Generalized Autoregressive Conditionally Heteroscedastic (GARCH) and Exponential Generalized Autoregressive Conditionally Heteroscedastic (EGARCH) models are considered. The latter are necessary to model empirical characteristics of conditional volatility such as clustering and asymmetry in the response, usually called leverage in time series literature. The ARFIMA-EGARCH models are used to capture and remove long memory and characterize conditional volatility in 24 hour HRV recordings from the Noltisalis database.

Berry–Esseen theorems under weak dependence

Let $\{{X}_k\}_{k\geq\mathbb{Z}}$ be a stationary sequence. Given $p\in(2,3]$ moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate $n^{p/2-1}$. For $p\geq4$, we also show a convergence rate of $n^{1/2}$ in $\mathcal{L}^q$-norm, where $q\geq1$. Up to $\log n$ factors, we also obtain nonuniform rates for any $p>2$. This leads to new optimal results for many linear and nonlinear processes from the time series literature, but also includes examples from dynamical system theory. The proofs are based on a hybrid method of characteristic functions, coupling and conditioning arguments and ideal metrics.

Vector autoregressive moving average identification for macroeconomic modeling: A new methodology

This paper develops a new methodology for identifying the structure of VARMA time series models. The analysis proceeds by examining the echelon form and presents a fully automatic, strongly consistent, data driven approach to model specification. A novel feature of the inferential procedures developed here is that they work in terms of a canonical representation based on the Kronecker invariants in which the variables are expressed in the form of scalar dynamic structural equations derived from the VARMA system. This feature facilitates the construction of procedures which, from the perspective of macroeconomic modeling, can be efficacious in that they do not rely on VAR approximations. Techniques that are applicable to both asymptotically stationary and unit-root, partially nonstationary (cointegrated) time series models are presented. The inferential potential of the techniques is illustrated via simulation experiments that use data generating mechanisms based on real world examples drawn from the time series literature. Aspects of the Kronecker invariants that impinge on practical application and that have not hitherto been discussed in the literature are explored.

On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms

In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.

Estimating fiscal policy reaction functions: The role of model specification

The literature has not yet come to a consensus on the actual responses of fiscal policy to output and to past public debt levels within industrialized countries. While the cyclical adjustment literature has suggested a strong response of the primary surplus to the output gap, the time-series literature has tended to report a far smaller response. However, recent theoretical findings suggest that some of this difference may be due to the way in which the time-series literature has typically handled the issue of autocorrelation, in a way which is incompatible with the timing of automatic stabilizers. In order to find a way around this problem, we formulate and estimate a set of fiscal policy reaction functions for the euro area, which allow for the primary surplus to feature three components: a fast-moving (stabilizing) response to the output gap, a consolidating response to the debt-GDP ratio, and an exogenous, persistent fiscal policy shifter. When we formulate a fiscal reaction function in this way, our estimates are compatible in magnitude with previous estimates from the cyclical adjustment literature. Furthermore, based on a set of model comparison exercises in line with what has been done in the monetary policy literature, we argue that our specification explains the data better than does the more commonly used specification.

Public debt and growth: Heterogeneity and non-linearity

We study the long-run relationship between public debt and growth in a large panel of countries. Our analysis builds on theoretical arguments and data considerations in modelling the debt–growth relationship as heterogeneous across countries. We investigate the debt–growth nexus adopting linear and non-linear specifications, employing novel methods and diagnostics from the time-series literature adapted for use in the panel. We find some support for a negative relationship between public debt and long-run growth across countries, but no evidence for a similar, let alone common, debt threshold within countries.

A New High Order Fuzzy ARMA Time Series Forecasting Method by Using Neural Networks to Define Fuzzy Relations

Linear time series methods are researched under 3 topics, namely, AR (autoregressive), MA (moving averages), and ARMA (autoregressive moving averages) models. On the other hand, the univariate fuzzy time series forecasting methods proposed in the literature are based on fuzzy lagged (autoregressive (AR)) variables, having not used the error lagged (moving average (MA)) variables except for only two studies in the fuzzy time series literature. Not using MA variables could cause the model specification error in solutions of fuzzy time series. For this reason, this model specification error should be eliminated. In this study, a solution algorithm based on artificial neural networks has been proposed by defining a new high order fuzzy ARMA time series forecasting model that contains fuzzy MA variables along with fuzzy AR variables. It has been pointed out by the applications that the forecasting performance could have been increased by the proposed method in accordance with the fuzzy AR models in the literature since the proposed method is a high order model and also utilizes artificial neural networks to identify the fuzzy relation.

A Note on Tractable State-Space Model for Symmetric Positive-Definite Matrices

This article discusses Windle and Carvalho's (2014) state-space model for observations and latent variables in the space of positive symmetric matrices. The present discussion focuses on the model specification and on the contribution to the positive-value time series literature. I apply the proposed model to financial data with a view to shedding light on some modeling issues.

Comment on Article by Windle and Carvalho

This article discusses Windle and Carvalho’s (2014) state-space model for observations and latent variables in the space of positive symmetric matrices. The present discussion focuses on the model specification and on the contribution to the positive-value time series literature. I apply the proposed model to financial data with a view to shedding light on some modeling issues.

A critical assessment of the time-series literature in accounting pertaining to quarterly accounting numbers

This paper summarizes, critiques, and synthesizes the time-series literature in accounting pertaining to quarterly accounting numbers. It reviews work on quarterly earnings, quarterly balance sheet and income statement subcomponents, and quarterly cash-flows from operations (CFOs). Several salient findings emerge. First, the premier ARIMA models attributed to Foster (1977), Griffin (1977) and Brown and Rozeff (1979) were identified on relatively small samples dominated by “old economy” firms. It appears that the descriptive validity of these ARIMA structures must be called into question when analyzing more current databases replete with high-technology, regulated, and financial-service firms (Lorek & Willinger, 2007). Second, the use of ARIMA-based analytical review procedures in audit settings is not cost effective. Third, recent evidence (Lorek & Willinger, 2008, 2011) supports the univariate Brown & Rozeff (100) × (011) ARIMA model as the best statistically-based prediction model for quarterly CFO, a finding of considerable import to analysts, investors, and researchers.

EFFICIENT METHOD OF MOMENTS ESTIMATORS FOR INTEGER TIME SERIES MODELS

The parameters of integer autoregressive models with Poisson, or negative binomial innovations can be estimated by maximum likelihood where the prediction error decomposition, together with convolution methods, is used to write down the likelihood function. When a moving average component is introduced this is not the case. To address this problem an efficient method of moment estimator is proposed where the estimated standard errors for the parameters are obtained using subsampling methods. The small sample properties of the estimator are investigated using Monte Carlo methods, while the approach is demonstrated using two well‐known examples from the time series literature.

A PARAMETER‐DRIVEN LOGIT REGRESSION MODEL FOR BINARY TIME SERIES

We consider a parameter‐driven regression model for binary time series, where serial dependence is introduced by an autocorrelated latent process incorporated into the logit link function. Unlike in the case of parameter‐driven Poisson log‐linear or negative binomial logit regression model studied in the literature for time series of counts, generalized linear model (GLM) estimation of the regression coefficient vector, which suppresses the latent process and maximizes the corresponding pseudo‐likelihood, cannot produce a consistent estimator. As a remedial measure, in this article, we propose a modified GLM estimation procedure and show that the resulting estimator is consistent and asymptotically normal. Moreover, we develop two procedures for estimating the asymptotic covariance matrix of the estimator and establish their consistency property. Simulation studies are conducted to evaluate the finite‐sample performance of the proposed procedures. An empirical example is also presented.

Reexamining the PPP hypothesis: A nonlinear asymmetric heterogeneous panel unit root test

In this study, we re-examine the PPP hypothesis in the light of the new developments in the unit root testing literature. The recent theoretical findings have pointed out that the real exchange rate series exhibit asymmetric nonlinear behavior. A unit root test applied to analyze the PPP hypothesis therefore, should also take into account this asymmetry inherent in the real exchange rate. Different unit root tests that consider the presence of these data features have been developed in the time series literature. However, a true attempt to test the PPP hypothesis should take a panel data approach. To this end, we propose a nonlinear heterogeneous panel unit root test where the alternative hypothesis allows for symmetric or asymmetric exponential smooth transition autoregressive nonlinearity and provide its finite sample properties. We apply our test to the real exchange rates of the 15 European Union countries against the US dollar. While the results of the linear and symmetric nonlinear heterogeneous panel unit root tests are against the PPP hypothesis, the asymmetric nonlinear heterogeneous panel test that we propose gives support for the PPP hypothesis as expected. Therefore, the conclusions drawn from the linear panel unit root tests or the nonlinear panel unit root tests that do not take asymmetry into account might be misleading.

A Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models

Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multilevel factor models. A brief outline of the state space formulation is provided and then state space forms for univariate and multivariate multilevel regression models, and a multilevel confirmatory factor model, are illustrated. The utility of the state space approach is demonstrated with either a simulated or real example for each multilevel model. It is concluded that the results from the state space approach are essentially identical to those from specialized multilevel regression modeling and structural equation modeling software. More importantly, the state space approach offers researchers a computationally more efficient alternative to fit multilevel regression models with a large number of Level 1 units within each Level 2 unit or a large number of observations on each subject in a longitudinal study.

Evolving Bayesian Emulators for Structured Chaotic Time Series, with Application to Large Climate Models

We develop Bayesian dynamic linear model Gaussian processes for emulation of time series output for computer models that may exhibit chaotic behavior, but where this behavior retains some underlying structure. The statistical technology is particularly suited to emulating the time series output of large climate models that exhibit this feature and where we want samples from the posterior of the emulator to evolve in the same way as dynamic processes in the computer model do. The methodology combines key features of good uncertainty quantification (UQ) methods such as using complex mean functions to capture large-scale signals within parameter space, with dynamic linear models in a way that allows UQ to borrow strength from the Bayesian time series literature. We present an MCMC algorithm for sampling from the posterior of the emulator parameters when the roughness lengths of the Gaussian process are unknown. We discuss an interpretation of the results of this algorithm that allows us to use MCMC to fix the correlation lengths, making future online samples from the emulator tractable when used in practical applications where online MCMC is infeasible. We apply this methodology to emulate the Atlantic Meridional Overturning Circulation (AMOC) as a time series output of the fully coupled non--flux-adjusted atmosphere-ocean general circulation model HadCM3.

Selecting the Number of Principal Components in Functional Data

Functional principal component analysis (FPCA) has become the most widely used dimension reduction tool for functional data analysis. We consider functional data measured at random, subject-specific time points, contaminated with measurement error, allowing for both sparse and dense functional data, and propose novel information criteria to select the number of principal component in such data. We propose a Bayesian information criterion based on marginal modeling that can consistently select the number of principal components for both sparse and dense functional data. For dense functional data, we also develop an Akaike information criterion based on the expected Kullback–Leibler information under a Gaussian assumption. In connecting with the time series literature, we also consider a class of information criteria proposed for factor analysis of multivariate time series and show that they are still consistent for dense functional data, if a prescribed undersmoothing scheme is undertaken in the FPCA algorithm. We perform intensive simulation studies and show that the proposed information criteria vastly outperform existing methods for this type of data. Surprisingly, our empirical evidence shows that our information criteria proposed for dense functional data also perform well for sparse functional data. An empirical example using colon carcinogenesis data is also provided to illustrate the results. Supplementary materials for this article are available online.

Measurement error in air pollution epidemiology: Guidance for uncertain times.

EnvironmetricsVolume 24, Issue 8 p. 529-530 Discussion Paper Measurement error in air pollution epidemiology: guidance for uncertain times Roger D. Peng, Corresponding Author Roger D. Peng Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, U.S.A.Correspondence to: Roger D. Peng, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, U.S.A. [email protected]Search for more papers by this author Roger D. Peng, Corresponding Author Roger D. Peng Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, U.S.A.Correspondence to: Roger D. Peng, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, U.S.A. [email protected]Search for more papers by this author First published: 21 January 2014 https://doi.org/10.1002/env.2242Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume24, Issue8December 2013Pages 529-530 RelatedInformation

A comparison of some criteria for states selection in the latent Markov model for longitudinal data

We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent characteristic of a group of individuals over time. Then, the response variables observed at different occasions are assumed to be conditionally independent given this chain. Maximum likelihood estimation of the model is carried out through an Expectation–Maximization algorithm based on forward–backward recursions which are well known in the hidden Markov literature for time series. The selection criteria we consider are based on penalized versions of the maximum log-likelihood or on the posterior probabilities of belonging to each latent state, that is, the conditional probability of the latent state given the observed data. Among the latter criteria, we propose an appropriate entropy measure tailored for the latent Markov models. We show the results of a Monte Carlo simulation study aimed at comparing the performance of the above states selection criteria on the basis of a wide set of model specifications.

Editorial Announcement

It is my very sad duty to inform the readership of the Journal of Time Series Analysis that the Founding Editor of the Journal, Professor Maurice Priestley, passed away on Saturday, 15 June 2013, after a long illness. Professor Priestley will be hugely missed by the entire time series community. He consistently made seminal contributions to the time series literature over many decades. He can genuinely be described as one of the ‘founding fathers’ of the discipline of time series analysis. His contribution to the time series community was also immense, and the Journal of Time Series Analysis represents an enduring legacy of that contribution. Maurice Priestley was a very kind, warm and generous-spirited man, admired and respected by those of us who were lucky enough to have known him. A detailed obituary will be published in a subsequent issue of the Journal. ROBERT TAYLOR Editor-in-Chief J. Time Ser. Anal.