scholarly journals Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 666
Author(s):  
Manuel Stapper
Keyword(s):  
Time Series ◽  
Real Life ◽  
Theoretical Background ◽  
Information Criteria ◽  
Finite Sample ◽  
Ml Estimation ◽  
Real Life Data ◽  
Time Series Modelling ◽  
Finite Sample Properties ◽  
Count Data Time Series

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

scholarly journals Targets Detection in Sea Clutter Based on Echo State Network

2012 ◽  
Vol 4 ◽  
pp. 255-258
Author(s):  
Zhan Xu ◽  
Jian Wei Wan ◽  
Gang Li ◽  
Fang Su
Keyword(s):  
Time Series ◽  
Mean Squared Error ◽  
Real Life ◽  
Radar Data ◽  
Recursive Least Squares ◽  
Echo State Network ◽  
Sea Clutter ◽  
Rls Algorithm ◽  
Real Life Data ◽  
Novel Method

A novel method to predict the sea clutter time series and detect target embedded in sea clutter is presented. The method is actually a recurrent neural network called an echo state network (ESN). A recursive least squares (RLS) algorithm is used for updating the output weights of ESN. A set of time series from IPIX radar data is tested. Numerical experiments reveal that the proposed network shows higher prediction precision in pure sea clutter data. Moreover, the mean squared error (MSE) between real-life data and prediction value by ESN can be used to detect target effectively.

scholarly journals Finite-sample properties of estimators for first and second order autoregressive processes

2021 ◽  
Author(s):  
Sigrunn H. Sørbye ◽  
Pedro G. Nicolau ◽  
Håvard Rue
Keyword(s):  
Time Series ◽  
Polynomial Regression ◽  
Gaussian Copula ◽  
Finite Sample ◽  
Coefficient Estimates ◽  
Ecological Data ◽  
Data Set ◽  
Finite Sample Properties ◽  
The Relationship ◽  
Corrected Coefficient

AbstractThe class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like . A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying -package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

scholarly journals Dynamic Factor Copula Models with Estimated Cluster Assignments

2021 ◽  
Vol 2021 (026) ◽  
pp. 1-52
Author(s):  
Dong Hwan Oh ◽  
◽  
Andrew J. Patton ◽  
Keyword(s):  
Time Series ◽  
Clustering Algorithm ◽  
Ad Hoc ◽  
High Dimensional ◽  
Dynamic Factor ◽  
Finite Sample ◽  
Copula Models ◽  
Finite Sample Properties ◽  
Out Of Sample ◽  
Individual Variables

This paper proposes a dynamic multi-factor copula for use in high dimensional time series applications. A novel feature of our model is that the assignment of individual variables to groups is estimated from the data, rather than being pre-assigned using SIC industry codes, market capitalization ranks, or other ad hoc methods. We adapt the k-means clustering algorithm for use in our application and show that it has excellent finite-sample properties. Applying the new model to returns on 110 US equities, we find around 20 clusters to be optimal. In out-of-sample forecasts, we find that a model with as few as five estimated clusters significantly outperforms an otherwise identical model with 21 clusters formed using two-digit SIC codes.

scholarly journals TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

scholarly journals DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

2013 ◽  
Vol 29 (5) ◽  
pp. 1009-1056 ◽  
Author(s):  
Frédéric Lavancier ◽  
Remigijus Leipus ◽  
Anne Philippe ◽  
Donatas Surgailis
Keyword(s):  
Time Series ◽  
Long Memory ◽  
General Setting ◽  
Partial Sums ◽  
Gradual Change ◽  
Test Statistics ◽  
Finite Sample ◽  
Testing Procedures ◽  
Finite Sample Properties ◽  
Memory Parameter

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I (d) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I (d1) to I (d2), −.5 < d1 < d2. We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests (see Kwiatkowski, Phillips, Schmidt and Shin, 1992) considered in some previous works.

TESTING FOR DISTRIBUTIONAL CHANGE IN TIME SERIES

2001 ◽  
Vol 17 (1) ◽  
pp. 156-187 ◽  
Author(s):  
Atsushi Inoue
Keyword(s):  
Time Series ◽  
A Priori ◽  
Nuisance Parameter ◽  
Nonparametric Tests ◽  
Local Power ◽  
Finite Sample ◽  
Null Distributions ◽  
Monte Carlo Experiments ◽  
Simulation Based ◽  
Finite Sample Properties

This paper proposes nonparametric tests of change in the distribution function of a time series. The limiting null distributions of the test statistics depend on a nuisance parameter, and critical values cannot be tabulated a priori. To circumvent this problem, a new simulation-based statistical method is developed. The validity of our simulation procedure is established in terms of size, local power, and test consistency. The finite-sample properties of the proposed tests are evaluated in a set of Monte Carlo experiments, and the distributional stability in financial markets is examined.

scholarly journals Estimation Methods for a Flexible INAR(1) COM-Poisson Time Series Model

2018 ◽  
Vol 14 (1) ◽  
pp. 57-82 ◽  
Author(s):  
Y. Sunecher ◽  
N. Mamode Khan ◽  
V. Jowaheer
Keyword(s):  
Time Series ◽  
Real Life ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Simulation Experiments ◽  
Time Series Of Counts ◽  
First Order ◽  
Life Data ◽  
Data Application ◽  
Real Life Data

Abstract Time series of counts occur in many real-life situations where they exhibit various forms of dispersion. To facilitate the modeling of such time series, this paper introduces a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process where the innovation terms follow a Conway-Maxwell Poisson distribution (COM-Poisson). To estimate the unknown parameters in this model, different estimation approaches based on likelihood and quasi-likelihood formulations are considered. From simulation experiments and a real-life data application, the Generalized Quasi-Likelihood (GQL) approach yields estimates with lower bias than the other estimation approaches.

Modal Analysis of Multiple Eigenvalue Systems by Data Dependent Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 416-417 ◽  
Author(s):  
N. P. Mehta ◽  
S. M. Pandit
Keyword(s):  
System Theory ◽  
Time Series ◽  
Modal Analysis ◽  
System Analysis ◽  
Real Life ◽  
Life Data ◽  
Real Life Data ◽  
Time Series Approach ◽  
Modeling Strategy

This note outlines an extension of the Data Dependent Systems (DDS) methodology to the modal analysis of vibratory systems with eigenvalues of arbitrary multiplicity. DDS [1, 2] is a time-series approach to system analysis that combines a rational modeling strategy with elements of linear system theory. The use of an appropriate state-space setting makes it a powerful tool for system identification, and the approach has been successfully applied to the modal characterization of mechanical systems in references [2–4], which provide many examples with real life data.

scholarly journals Multivariate Time Series Modelling with Seasonal Univariate Components; Evidence from Nigeria GDP

2019 ◽  
pp. 1-20
Author(s):  
Taofikat Abidemi Azeez ◽  
Yusuf Olufemi Olusola ◽  
Hamzat Kayode Idris ◽  
Salawu Monsuru Micheal
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Positive Association ◽  
Information Criteria ◽  
Strong Positive Correlation ◽  
Positive Correlation ◽  
Pairwise Correlation ◽  
Time Series Modelling ◽  
Adf Test ◽  
Time Plot

The patterns of GDP variables are graphically examined using time plot presented the time plot for the GDP variables concerning time presented a combined single time plot for all the considered GDP variables. The relationship, as well as the degree of relationship between/among the GDP variables, was further revealed by computing the pairwise correlation. Based on the output, each variable when crossed classified with itself have a strong positive correlation with an output of (1), while pairwise correlation reveals a positive figure with the least estimate being (0.3149), this implies that for all the variables there exist a positive correlation. All the pairwise relationship reveals a strong positive association with all the estimates revealing a value between (0.8-0.9) except ‘trade and industry' that shows a positive relationship but not strong with an estimate of (0.3149). The initial test in fitting a time series model is to examine the series for stationarity. The Augmented Dickey-Fuller test revealed that ‘Agriculture’, ‘Construction’, and Services’” satisfies the requirement of stationarity while the series ‘industry and “Trade” are non-stationary initially but later became stationary after the application of the first difference transformation which was confirmed after the application of the ADF test to the first differenced series. The Johansen co-integration's Trace test was employed to determine the order of co-integration and it was revealed that the series are cointegrated hence presentation of the equation of integration. We presented the lag length estimation criteria which revealed that the lag length of order 5 is appropriate for the VAR model as suggested by Akaike Information Criteria (AIC), Hannan-Quinn (HQ) Information Criteria, Schwarz Information Criteria (SC). The VAR(5) model was fitted for all the considered GDP variables.

scholarly journals On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Tahir ◽  
Ibrahim M. Almanjahie ◽  
Muhammad Abid ◽  
Ishfaq Ahmad
Keyword(s):  
Real Life ◽  
Mixture Distribution ◽  
Type I ◽  
Component Mixture ◽  
Ml Estimation ◽  
Noninformative Priors ◽  
Data Application ◽  
Real Life Data ◽  
Detailed Simulation ◽  
Raphson Method

In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study.

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