Forecasting nonstationary time series

Many variables show a tendency to increase over time in line with their nonstationary nature. It is notable, however, that the original time series can be transformed into a sequence of jumps measured by time distances between the successive maxima and present the resulting series as the compound Poisson process, which has powerful consequences discussed in the paper. Firstly, the jump-generating process is stationary, unlike the one generating the original data. Secondly, the dynamics of a variable can be determined using solely the properties of the derived stationary counterpart. Thirdly, using this framework for prediction offers substantial advantages. The proposed methodology allows forecasting the number of periods necessary for a process to achieve the desired level and decomposing the path leading to that level into jumps of different size. It also gives a unique insight into the shape of the trajectory over the prediction horizon, which the traditional approach to the forecasting of nonstationary time series is incapable of providing.

Automated summary

The paper finds that the original time series can be transformed into a sequence of jumps measured by time distances and represented as a compound Poisson process, which has significant implications. Firstly, the jump-generating process is stationary, unlike the one generating the original data. Secondly, the dynamics of a variable can be determined using solely the properties of the derived stationary counterpart. Thirdly, the proposed methodology provides advantages in prediction, allowing for forecasting the number of periods needed to achieve a desired level and decomposing the path into jumps of different sizes. It also offers insights into the trajectory shape that traditional approaches to forecasting nonstationary time series lack.