Beyond Integration: A Symmetry-Based Approach to Reaching Stationarity in Economic Time Series

Abstract

Many efficient data processing techniques assume that the corresponding process is stationary. However, in areas like economics, most processes are not stationery: with the exception of stagnation periods, economies usually grow. A known way to apply stationarity-based methods to such processes—integration—is based on the fact that often, while the process itself is not stationary, its first or second differences are stationary. This idea works when the trend polynomially depends on time. In practice, the trend is usually non-polynomial: it is often exponentially growing, with cycles added. In this paper, we show how integration techniques can be expanded to such trends.