Affiliation:
1. Tinbergen Institute Amsterdam Netherlands
2. Aleksander Welfe Chair of Econometric Models and Forecasts University of Lodz Lodz Poland
Abstract
AbstractMany 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.
Subject
Management Science and Operations Research,Statistics, Probability and Uncertainty,Strategy and Management,Computer Science Applications,Modeling and Simulation,Economics and Econometrics
Reference9 articles.
1. Statistics
2. Series with central binomial coefficients, catalan numbers, and harmonic numbers;Boyadzhiev K. N.;Journal of Integer Sequences,2012
3. Forecasting Economic Time Series
4. Infinitely Divisible Distributions and Bessel Functions Associated with Random Walks