Joint Probability Distribution of Prediction Errors of ARIMA
It provides a theoretical foundation for probabilistic guarantees in temporal logic monitoring, but the contribution is incremental as it extends existing ARIMA error distribution results.
The paper derives a method to compute the joint probability distribution of prediction errors for multiple steps in ARIMA models, covering stationary and intrinsically stationary processes for both univariate and multivariate cases.
Producing probabilistic guarantee for several steps of a predicted signal follow a temporal logic defined behavior has its rising importance in monitoring. In this paper, we derive a method to compute the joint probability distribution of prediction errors of multiple steps based on Autoregressive Integrated Moving Average(ARIMA) model. We cover scenarios in stationary process and intrinsically stationary process for univariate and multivariate.