Statistical tests and economic forecasting are something of a joke; Paul Krugman is fun because he rants about Republicans in the New York Times but no one would ever actually let him manage money. 

As we have seen in recent times,  the description of complex processes are based on a false premise. They assume that the average fluctuation of individual prices and the dependence characteristics between different shares do not change over time. This would make the development of share prices "stationary". This assumption mostly turns out to be wrong in times of crisis, because, for example, under normal market conditions many prices barely affect each other or not at all, whereas in a crash they almost all collapse together. This proves that such a process is generally non-stationary.

Researchers led by Prof. Dr. Holger Dette at the Ruhr-Universität Bochum say they have developed a new method in spectral analysis, which allows the classical mathematical model assumption of stationarity to be precisely measured and determined for the first time. The approach also makes it possible to construct statistical tests that are considerably better and more accurate than previous methods, they write in Journal of the American Statistical Association. 

The solution: a new distance dimension

Bochum's stochasticians Prof. Dr. Holger Dette, M.Sc. Philip Preuß and Dr. Mathias Vetter, found the key to the whole issue by calculating a distance dimension between the stationary and non-stationary process.

"Just as we can determine distances on Earth between two places, we were able to measure the distances or the intervals between the processes" said Dette.

The measure is exactly 0 when the assumption of stationarity applies to the process. This distance can be estimated from the data and thus provides a reliable tool for the spectral analysis of so-called time series, such as share prices or climate data.

"The goal of statistical analyses of time series is always to understand the underlying dependencies in order to then deliver the most accurate predictions possible for the future behaviour of these processes" said Dette.

"Our research is strongly motivated by the recent financial crises. At that time, nearly all economic models and forecasts for loan losses failed because they do not take appropriate account of extreme dependencies. In the long term, we aim to develop models and methods that predict such events better" said Dette.