Coherent Forecasting for a Mixed Integer-Valued Time Series Model

Abstract

In commerce, economics, engineering and the sciences, quantitative methods based on statistical models for forecasting are very useful tools for prediction and decision. There is an abundance of papers on forecasting for continuous-time series but relatively fewer papers for time series of counts which require special consideration due to the integer nature of the data. A popular method for modelling is the method of mixtures which is known for its flexibility and thus improved prediction capability. This paper studies the coherent forecasting for a flexible stationary mixture of Pegram and thinning (MPT) process, and develops the likelihood-based asymptotic distribution. Score functions and the Fisher information matrix are presented. Numerical studies are used to assess the performance of the forecasting methods. Also, a comparison is made with existing discrete-valued time series models. Finally, the practical application is illustrated with two sets of real data. It is shown that the mixture model provides good forecasting performance.

Integer-Valued Split-BREAK Process with a General Family of Innovations and Application to Accident Count Data Modeling

“…Non-negative integer-valued (NNIV) time series are the subject of numerous research studies (see, among the more recently published, e.g., [1][2][3][4][5][6]) on the modeling and analysis of count time series. In the class of NNIV series, some of the frequently used models are the so-called integer-valued autoregressive (INAR) processes (see, among the more recently published, e.g., [7][8][9][10][11][12][13][14]).…”

Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

“…This approach started from the famous work by Al-Osh and Alzaid [6], which first introduced the so-called INAR(1) process, and since then many results related to these models have been obtained (cf. [7][8][9][10][11][12][13][14][15][16][17]). One of the recently frequent problems in count data modeling is the presence of inflated zero-and-one values in the data, which can appear in various areas of human activity (e.g., the number of requests for issuing policies, breakdowns in the production process, injury in traffic accidents, etc.).…”