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

Turaj Vazifedan,Mujde Erten-Unal,Homa Jalaeian Taghadomi,Xixi Wang

doi:10.6339/jds.202010_18(4).0007

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.

Highlights

Time series data with seasonal characteristics can be found in a variety of fields, such as economic, healthcare, environment, and climate change
According to Bourguignon et al (2016), Y-W and Conditional Least Squares (CLS) estimators were susceptible to a process that was closer to non-stationary such that the bias and RMSE increased by increasing α
They concluded that the performance of Maximum Likelihood Estimation (MLE) was profoundly better than Y-W and CLS estimators (Bourguignon et al, 2016)

Summary

Introduction

Time series data with seasonal characteristics can be found in a variety of fields, such as economic, healthcare, environment, and climate change. The number of rainy days is one example of the count time series with seasonal characteristics that have a profound influence on flooding. Several reasons affect the magnitude of flooding, such as sea-level rise (Wang et al, 2017), precipitation characteristics (Bracken , née Bull), and seasonal variability, and extreme storms (Niroomandi et al, 2018). The reduction in the number of rainy days can result in drought, while the upward trend in the frequency of days with precipitation can increase the runoff coefficient and the risk of flooding events. The critical impact of the aforementioned extreme events on human life emphasizes the importance of modelling and predicting the number of rainy days

Objectives

Methods

Results

Conclusion