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Econometrics
Special Issues
Discrete-Valued Time Series: Modelling, Estimation and Forecasting
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Discrete-Valued Time Series: Modelling, Estimation and Forecasting

A special issue of Econometrics (ISSN 2225-1146).

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 41563

Special Issue Editors

Prof. Brendan McCabe

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Guest Editor
University of Liverpool
Interests: time series modelling and estimation; forecasting count data; Bayesian analysis
Prof. Andrew Tremayne

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Guest Editor
University of Liverpool
Interests: time series econometrics; modelling count data; inference

Special Issue Information

Dear Colleagues,

This Special Issue is concerned with publishing a range of new contributions to the field of Discrete-Valued Time Series. Both methodological advances and applications are encouraged; papers which combine the two are particularly sought. Contributions may involve univariate and, particularly, multivariate time series models; these may be either observation- or parameter-driven. Topics include specification and estimation, as well as inference methods.

Count time series are usually non-negative integers, but papers dealing with binary and categorical variables are also welcome. Methodology may be classical or Bayesian in nature. There is, as of yet, a limited literature on goodness-of-fit methods in this area of modelling and so we would welcome contributions in this field. Other ripe topics for advancement would include forecasting and its applications, change-point detection and diagnostic and model testing methods. General dynamic analysis including impulse response analysis would also be of interest.

The Special Issue seeks to bring together a burgeoning stream of literature across a range of fields including, but not limited to, medicine; epidemiology; finance; and economics, discussing advances.

Overall, the main thrust of the Special Issue is to develop and refine extant methods for analysis of count time series data and to advance knowledge and applicability in novel and exciting directions.

Prof. Brendan McCabe
Prof. Andrew R. Tremayne
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Econometrics is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Count data
  • Time series
  • Estimation
  • Testing
  • Forecasting
  • Model validation

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Published Papers (7 papers)

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Research

20 pages, 447 KiB  
Article
Goodness–of–Fit Tests for Bivariate Time Series of Counts
by Šárka Hudecová, Marie Hušková and Simos G. Meintanis
Econometrics 2021, 9(1), 10; https://doi.org/10.3390/econometrics9010010 - 4 Mar 2021
Cited by 6 | Viewed by 3813
Abstract
This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric [...] Read more.
This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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15 pages, 664 KiB  
Article
Maximum-Likelihood Estimation in a Special Integer Autoregressive Model
by Robert C. Jung and Andrew R. Tremayne
Econometrics 2020, 8(2), 24; https://doi.org/10.3390/econometrics8020024 - 8 Jun 2020
Cited by 1 | Viewed by 3831
Abstract
The paper is concerned with estimation and application of a special stationary integer autoregressive model where multiple binomial thinnings are not independent of one another. Parameter estimation in such models has hitherto been accomplished using method of moments, or nonlinear least squares, but [...] Read more.
The paper is concerned with estimation and application of a special stationary integer autoregressive model where multiple binomial thinnings are not independent of one another. Parameter estimation in such models has hitherto been accomplished using method of moments, or nonlinear least squares, but not maximum likelihood. We obtain the conditional distribution needed to implement maximum likelihood. The sampling performance of the new estimator is compared to extant ones by reporting the results of some simulation experiments. An application to a stock-type data set of financial counts is provided and the conditional distribution is used to compare two competing models and in forecasting. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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36 pages, 950 KiB  
Article
Distributions You Can Count On …But What’s the Point?
by Brendan P. M. McCabe and Christopher L. Skeels
Econometrics 2020, 8(1), 9; https://doi.org/10.3390/econometrics8010009 - 4 Mar 2020
Cited by 2 | Viewed by 4610
Abstract
The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions [...] Read more.
The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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26 pages, 1368 KiB  
Article
Generalized Binary Time Series Models
by Carsten Jentsch and Lena Reichmann
Econometrics 2019, 7(4), 47; https://doi.org/10.3390/econometrics7040047 - 14 Dec 2019
Cited by 10 | Viewed by 7815
Abstract
The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a [...] Read more.
The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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13 pages, 334 KiB  
Article
Likelihood Inference for Generalized Integer Autoregressive Time Series Models
by Harry Joe
Econometrics 2019, 7(4), 43; https://doi.org/10.3390/econometrics7040043 - 11 Oct 2019
Cited by 6 | Viewed by 5418
Abstract
For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an [...] Read more.
For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an observation given the past p observations. Two data examples are included and show that thinning operators based on compounding can substantially improve the model fit compared with the commonly used binomial thinning operator. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
28 pages, 786 KiB  
Article
Evaluating Approximate Point Forecasting of Count Processes
by Annika Homburg, Christian H. Weiß, Layth C. Alwan, Gabriel Frahm and Rainer Göb
Econometrics 2019, 7(3), 30; https://doi.org/10.3390/econometrics7030030 - 6 Jul 2019
Cited by 14 | Viewed by 6337
Abstract
In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is analyzed. The [...] Read more.
In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is analyzed. The considered data-generating processes include different autoregressive schemes with varying model orders, count models with overdispersion or zero inflation, counts with a bounded range, and counts exhibiting trend or seasonality. We conclude that Gaussian forecast approximations should be avoided. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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23 pages, 581 KiB  
Article
Measures of Dispersion and Serial Dependence in Categorical Time Series
by Christian H. Weiß
Econometrics 2019, 7(2), 17; https://doi.org/10.3390/econometrics7020017 - 22 Apr 2019
Cited by 9 | Viewed by 7735
Abstract
The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. [...] Read more.
The analysis and modeling of categorical time series requires quantifying the extent of dispersion and serial dependence. The dispersion of categorical data is commonly measured by Gini index or entropy, but also the recently proposed extropy measure can be used for this purpose. Regarding signed serial dependence in categorical time series, we consider three types of κ -measures. By analyzing bias properties, it is shown that always one of the κ -measures is related to one of the above-mentioned dispersion measures. For doing statistical inference based on the sample versions of these dispersion and dependence measures, knowledge on their distribution is required. Therefore, we study the asymptotic distributions and bias corrections of the considered dispersion and dependence measures, and we investigate the finite-sample performance of the resulting asymptotic approximations with simulations. The application of the measures is illustrated with real-data examples from politics, economics and biology. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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