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In this work, we introduce an extension of the so-called beta autoregressive moving average (β ARMA) models. β ARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher's information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented. [ABSTRACT FROM AUTHOR]

We study estimation on parameter-driven models for time series of counts. This class of models follows the structure of a generalized linear model in which the serial dependency is included in the model by the link function through a time-dependent latent process. The likelihood function for this class of models commonly cannot be calculated explicitly and computationally intensive methods like importance sampling and Markov chain Monte Carlo are used to estimate the model parameters. Here, we propose a simple and fast estimation procedure in a wide class of models that accommodate both discrete and continuous data. The maximum likelihood methodology is used to obtain the parameter estimates for the models under study. The simplicity of the procedure allows for build bootstrap confidence intervals for the hyperparameters and latent states of parameter-driven models. We perform extensive simulation studies to verify the asymptotic behavior of the parameter estimates, as well as present application of the proposed procedure through set of real data. [ABSTRACT FROM AUTHOR]

In this work, we introduce an extension of the so-called beta autoregressive moving average (βARMA) models. βARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher’s information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented.

Multilevel autoregressive models are popular choices for the analysis of intensive longitudinal data in psychology. Empirical studies have found a positive correlation between autoregressive parameters of affective time series and the between-person measures of psychopathology, a phenomenon known as the staging effect. However, it has been argued that such findings may represent a statistical artifact: Although common models assume normal error distributions, empirical data (for instance, measurements of negative affect among healthy individuals) often exhibit the floor effect, that is response distributions with high skewness, low mean, and low variability. In this paper, we investigated whether—and to what extent—the floor effect leads to erroneous conclusions by means of a simulation study. We describe three dynamic models which have meaningful substantive interpretations and can produce floor-effect data. We simulate multilevel data from these models, varying skewness independent of individuals' autoregressive parameters, while also varying the number of time points and cases. Analyzing these data with the standard multilevel AR(1) model we found that positive bias only occurs when modeling with random residual variance, whereas modeling with fixed residual variance leads to negative bias. We discuss the implications of our study for data collection and modeling choices [ABSTRACT FROM AUTHOR]

In this work we introduce the class of Unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in (0, 1). The proposed model is an observation driven one, for which, conditionally on a set of covariates and the process' history, the random component is assumed to follow a Unit-Weibull distribution parameterized through its ρ th quantile. The systematic component prescribes an ARMA-like structure to model the conditional ρ th quantile by means of a link. Parameter estimation in the proposed model is performed using partial maximum likelihood, for which we provide closed formulas for the score vector and partial information matrix. We also discuss some inferential tools, such as the construction of confidence intervals, hypotheses testing, model selection, and forecasting. A Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed partial maximum likelihood approach. Finally, we examine the prediction power by contrasting our method with others in the literature using the Manufacturing Capacity Utilization from the US. [ABSTRACT FROM AUTHOR]

We revisit the generalized method of moments (GMM) estimation of the non-Gaussian structural vector autoregressive (SVAR) model. It is shown that in the n-dimensional SVAR model, global and local identification of the contemporaneous impact matrix is achieved with as few as n 2 + n (n − 1) / 2 suitably selected moment conditions, when at least n – 1 of the structural errors are all leptokurtic (or platykurtic). We also relax the potentially problematic assumption of mutually independent structural errors in part of the previous literature to the requirement that the errors be mutually uncorrelated. Moreover, we assume the error term to be only serially uncorrelated, not independent in time, which allows for univariate conditional heteroscedasticity in its components. A small simulation experiment highlights the good properties of the estimator and the proposed moment selection procedure. The use of the methods is illustrated by means of an empirical application to the effect of a tax increase on U.S. gasoline consumption and carbon dioxide emissions. [ABSTRACT FROM AUTHOR]

We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ , which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case. [ABSTRACT FROM AUTHOR]

We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.

Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary MTD models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a prespecified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

We consider estimation of the structural vector autoregression (SVAR) by the generalized method of moments (GMM). Given non-Gaussian errors and a suitable set of moment conditions, the GMM estimator is shown to achieve local identification of the structural shocks. The optimal set of moment conditions can be found by well-known moment selection criteria. Compared to recent alternatives, our approach has the advantage that the structural shocks need not be mutually independent, but only orthogonal, provided they satisfy a number of co-kurtosis conditions that prevail under independence. According to simulation results, the finite-sample performance of our estimation method is comparable, or even superior to that of the recently proposed pseudo maximum likelihood estimators. The two-step estimator is found to outperform the alternative GMM estimators. An empirical application to a small macroeconomic model estimated on postwar United States data illustrates the use of the methods. [ABSTRACT FROM AUTHOR]

: A stationary sequence of random variables with Birnbaum‐Saunders marginal distribution is constructed using a Gaussian autoregressive moving average sequence. The parameters of the model are then estimated by the maximum likelihood method, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is carried out to assess the performance of the estimators. The proposed model is finally used to analyze 2 real data sets. [ABSTRACT FROM AUTHOR]

This article investigates maximum a-posteriori (MAP) estimation of autoregressive model parameters when the innovations (errors) follow a finite mixture of distributions that, in turn, are scale-mixtures of skew-normal distributions (SMSN), an attractive and extremely flexible family of probabilistic distributions. The proposed model allows to fit different types of data which can be associated with different noise levels, and provides a robust modelling with great flexibility to accommodate skewness, heavy tails, multimodality and stationarity simultaneously. Also, the existence of convenient hierarchical representations of the SMSN random variables allows us to develop an EM-type algorithm to perform the MAP estimates. A comprehensive simulation study is then conducted to illustrate the superior performance of the proposed method. The new methodology is also applied to annual barley yields data. [ABSTRACT FROM AUTHOR]

Franses (Empir Econ, 2018. https://doi.org/10.1007/s00181-018-1417-8) criticised the practice in the empirical literature of replacing expected inflation by the sum of realised future inflation and an error in estimating the parameters of the new Keynesian Phillips curve (NKPC). In particular, he argued that this assumption goes against the Wold decomposition theorem and makes the error term in the hybrid NKPC equation correlated with future inflation, invalidating the maximum likelihood (ML) estimator of Lanne and Luoto (J Econ Dyn Control 37:561–570, 2013). We argue that despite the correlation, the Wold theorem is not violated, and the ML estimator is consistent. [ABSTRACT FROM AUTHOR]

A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) process with randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal. A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed. The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressive process is fitted from the autocorrelation of the squared values of the model. The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution. Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method. It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely Gaussian model. [ABSTRACT FROM AUTHOR]

This work develops maximum likelihood-based unit root tests in the noncausal autoregressive (NCAR) model with a non-Gaussian error term formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Issue 3, Article 2). Finite-sample properties of the tests are examined via Monte Carlo simulations. The results show that the size properties of the tests are satisfactory and that clear power gains against stationary NCAR alternatives can be achieved in comparison with available alternative tests. In an empirical application to a Finnish interest rate series, evidence in favour of an NCAR model with leptokurtic errors is found. [ABSTRACT FROM AUTHOR]

Highlights: [•] Multivariate time series of given marginals and correlation structure are generated. [•] The proposed algorithm uses a closed form solution for the Gaussian correlations. [•] The algorithm is time effective in simulating non-Gaussian stationary processes. [•] A practical scheme corrects the correlation matrix to give stable processes. [Copyright &y& Elsevier]

This paper investigates testing for parameter constancy in models for non-Gaussian time series. Models for discrete valued count time series are investigated as well as more general models with autoregressive conditional expectations. Both sup-tests and CUSUM procedures are suggested depending on the complexity of the model being used. The asymptotic distribution of the CUSUM test is derived for a general class of conditional autoregressive models. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide a critical discussion on real-time estimation of dynamic generalized linear models. We describe and contrast three estimation schemes, the first of which is based on conjugate analysis and linear Bayes methods, the second based on posterior mode estimation, and the third based on sequential Monte Carlo sampling methods, also known as particle filters. For the first scheme, we give a summary of inference components, such as prior/posterior and forecast densities, for the most common response distributions. Considering data of arrivals of tourists in Cyprus, we illustrate the Poisson model, providing a comparative analysis of the above three schemes. [ABSTRACT FROM AUTHOR]

Abstract: A non-Gaussian autoregressive model with epsilon-skew-normal innovations is introduced. Moments and maximum likelihood estimators of the parameters are proposed and their limit distributions are derived. Monte Carlo simulation results are analysed and the model is fitted to a real time series. [Copyright &y& Elsevier]

We develop methods for performing smoothing computations in general state-space models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filtered trajectories. [ABSTRACT FROM AUTHOR]

In this paper, we report results regarding bispectral analysis of the long range dependent ATM WAN traffic. Six different data sets were measured on 155 Mbps links of the SUNET by a custom-built tracing tool capable of recording over eight million consecutive cell arrivals. The complex fractal behavior of the ATM traffic claims utilization of the higher-order spectra analysis. For each of the analyzed data sets, it was found that the Gamma distribution fits very well. The bispectrum was studied for extracting some additional information with respect to the long memory parameter. The nonlinearity of the time series was also tested with the help of the bispectrum. [Copyright &y& Elsevier]

Many time series encountered in practice are non-Gaussian. Because of the process of data collection or the practice or researchers, time series used in analysis and modelling are frequently temporal aggregates. In this paper, we study the effects of the use of aggregate time series on testing for Gaussianity. We analyse how the test statistic is affected by aggregation and how that affects the power of the test. The results show that the use of aggregate time series induces Gaussianity and that the degree of inducement increases with the order of aggregation. In fact, the use of aggregate time series reduces the power of the test, although the effect is not significant for low orders of aggregation. [ABSTRACT FROM AUTHOR]

Environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes, for example, in modeling the relationship between air pollution and hospital admissions or mortality rates. We present a case study examining the association between pollen counts and meteorologic covariates. Although such time series data are inadequately described by standard methods for Gaussian time series, they are often autocorrelated, and warrant an analysis beyond those provided by ordinary generalized linear models (GLMs). Transitional regression models (TRMs), signifying nonlinear regression models expressed in terms of conditional means and variances given past observations, provide a unifying framework for two mainstream approaches to extending the GLM for autocorrelated data. The first approach models current outcomes with a GLM that incorporates past outcomes as covariates, whereas the second models individual outcomes with marginal GLMs and then couples the error terms with an autoregressive covariance matrix. Although the two approaches coincide for the Gaussian GLM, which serves as a helpful introductory example, in general they yield fundamentally different models. We analyze the pollen study using TRM's of both types and present parameter estimates together with asymptotic and bootstrap standard errors. In several cases we find evidence of residual autocorrelation; however, when we relax the TRM to allow for a nonparametric smooth trend, the autocorrelation disappears. This kind of trade-off between autocorrelation and flexibility is to be expected, and has a natural interpretation in terms of the covariance function for a nonparametric smoother. We provide an algorithm for fitting these flexible TRM's that is relatively easy to program with the generalized additive model software in S-PLUS. [ABSTRACT FROM AUTHOR]

The nonparametric bootstrap is applied to the problem of prediction in autoregression. Let {Yt t = 0, ±1, ±2, ...} be a stationary autoregressive process of known order p [AR(p)]. Given a realization of the series up to time t, (y1, y2, ..., Yt), a 100β% prediction interval for Yt+k is desired Standard forecasting techniques, which assume that the error sequence of the process {Yt} is Gaussian, rely on the fact that the conditional distribution of Yt+k, given the data, is Gaussian as well. As a nonparametric alternative, the bootstrap provides an estimate of the conditional distribution of Yt+k. The method is similar to other applications of the bootstrap for linear models, because the residuals are resampled. The proposed methodology represents a different approach, since an alternative representation for AR(p) series is used, allowing for bootstrap replicates generated backward in time. It follows that the resulting replicates all have the same conditionally fixed values at the end of every series. A simulation that compares the proposed technique with the standard technique for low-order Gaussian and non-Gaussian autoregressive models demonstrates the potential of the bootstrap technique. [ABSTRACT FROM AUTHOR]

The main topic of the paper is on-line filtering for non-Gaussian dynamic (state space) models by approximate computation of the first two posterior moments using efficient numerical integration. Based on approximating the prior of the state vector by a normal density, we prove that the posterior moments of the state vector are related to the posterior moments of the linear predictor in a simple way. For the linear predictor Gauss-Hermite integration is carried out with automatic reparametrization based on an approximate posterior mode filter. We illustrate how further topics in applied state space modelling, such as estimating hyperparameters, computing model likelihoods and predictive residuals, are managed by integration-based Kalman-filtering. The methodology derived in the paper is applied to on-line monitoring of ecological time series and filtering for small count data. [ABSTRACT FROM AUTHOR]

This study compares X-12-ARIMA and MING, two new seasonal adjustment methods designed to handle outliers and structural changes in a time series. X-12-ARIMA is a successor to the X-11-ARIMA seasonal adjustment method, and is being developed at the US Bureau of the Census. MING is a 'Mixture based Non-Gaussian' method for seasonal adjustment using time series structural models and is implemented as a function in the S-Plus language. The procedures are compared using 29 macroeconomic time series from the US Bureau of the Census. These series have both outliers and structural changes, providing a good testbed for comparing non-Gaussian methods. For the 29 series, the X-12-ARIMA decomposition consistently leads to smoother seasonal factors which are as or more 'flexible' than the MING seasonal component. On the other hand, MING is more stable, particularly in the way it handles outliers and level shifts. This study relies heavily on graphical tools for comparing seasonal adjustment methods. [ABSTRACT FROM AUTHOR]