Exact Likelihood Estimation and Probabilistic Forecasting in Higher-order INAR(p) Models

Lu, Yang (2018): Exact Likelihood Estimation and Probabilistic Forecasting in Higher-order INAR(p) Models.

Abstract

The computation of the likelihood function and the term structure of probabilistic forecasts in higher-order INAR(p) models are qualified numerically intractable and the literature has considered various approximations. Using the notion of compound autoregressive process, we propose an exact and fast algorithm for both quantities. We find that existing approximation schemes induce significant errors for forecasting.

• Item Type: MPRA Paper
• Language: English
• Keywords: compound autoregressive process, probabilistic forecast of counts, matrix arithmetic.
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Al-Osh, M. and Alzaid, A. A. (1987). First-order Integer-valued Autoregressive (INAR(1)) Process. Journal of Time Series Analysis, 8(3):261-275.