Parameter Estimation of a Seasonal Poisson INAR(1) Model with Different Monthly Means

Journal of Data Science

article

Turaj Vazifedan¹  Homa Jalaeian Taghadomi²  Xixi Wang²  Mujde Erten-Unal² 

[1] Division of Biostatics, Department of Paediatrics, Eastern Virginia Medical School;Department of Civil and Environmental Engineering, Old Dominion University

关键词: Blackwater River;    conditional least square;    count time series;    forecast;    maximum likelihood estimation;    rainfall;    Yule–Walker;   

DOI  :  10.6339/JDS.202010_18(4).0007

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

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.

【 授权许可】

CC BY