Document Type

Article

Publication Date

2020

DOI

10.6339/JDS.202010_18(4).0007

Publication Title

Journal of Data Science

Volume

18

Issue

4

Pages

697-717

Abstract

Analysing seasonality in count time series is an essential application of statistics to predict phenomena in different fields like economics, agriculture, healthcare, environment, and climatic change. However, the information in the existing literature is scarce regarding the performances of relevant statistical models. This study provides the Yule-Walker (Y-W), Conditional Least Squares (CLS), and Maximum Likelihood Estimation (MLE) for First-order Non-negative Integer-valued Autoregressive, INAR(1), process with Poisson innovations with different monthly means. The performance of Y-W, CLS, and MLE are assessed by the Monte Carlo simulation method. The performance of this model is compared with another seasonal INAR(1) model by reproducing the monthly number of rainy days in the Blackwater River watershed located in coastal Virginia. Two forecast-coherent methods in terms of mode and probability function are applied to make predictions. The models’ performances are assessed using the Root Mean Square Error and Index of Agreement criteria. The results reveal the similar performance of Y-W, CLS, and MLE for estimating the parameters of data sets with larger sample size and values of α close to unite root. Moreover, the results indicate that INAR(1) with different monthly Poisson innovations is more appropriate for modelling and predicting seasonal count time series.

Rights

© 2020 The Authors.

"The authors retain copyright in their articles, subject only to the specific rights given to Journal of Data Science and the Publisher, The Chung-hwa Data Mining Society (CDMS)2. By retaining the copyright, the authors are reserving for themselves among other things unlimited rights of electronic distribution, and the right to license the work to other publishers, once the article has been published in JDS by CDMS. After first publication, authors’ only obligation is to ensure that appropriate first publication credit is given to JDS and CDMS"

ORCID

0000-0002-8319-7499 (Vazifedan), 0000-0001-6660-0330 (Taghadomi), 0000-0003-3455-3124 (Wang),

Original Publication Citation

Vazifedan, T., Taghadomi, H. J., Wang, X., & Erten-Unal, M. (2020). Parameter estimation of a seasonal Poisson INAR(1) model with different monthly means. Journal of Data Science, 18(4), 697-717. https://doi.org/10.6339/jds.202010_18(4).0007

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