A milestone in the description of complex processes - for example the ups and downs of share prices - has been reached by mathematicians at the Ruhr-Universität Bochum. Researchers led by Prof. Dr. Holger Dette (stochastics) have developed a new method in spectral analysis, which allows a classical mathematical model assumption, so-called stationarity, to be precisely measured and determined for the first time.
Spectral density of a local and a stationary process – here taking the example of the ECG data of a newborn child (right side). If the assumption of stationarity was fulfilled (left side), the area would not vary in both directions
The approach also makes it possible to construct statistical tests that are considerably better and more accurate than previous methods. The researchers report on their results in the prestigious “Journal of the American Statistical Association”.
Stationary or not stationary - that is the question
Example, share prices: almost all economic models and forecasting tools “suffer” because they 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.
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 Prof. 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 Prof. Dette.
Motivated by the financial crises
“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. New methods of asymptotic statistics are crucial to this success and have been researched for years by Bochum’s mathematicians, funded by the German Research Foundation in the Collaborative Research Centre SFB 823 “Statistical modelling of nonlinear dynamic processes” (Host university: TU Dortmund University). Here, statisticians from Bochum work together with colleagues from the TU Dortmund University on new statistical methods to statistically verify frequently used model assumptions and develop new and better models where appropriate.
Holger Dette, Philip Preuß, Mathias Vetter. A Measure of Stationarity in Locally Stationary Processes With Applications to Testing. Journal of the American Statistical Association Sep 2011, Vol. 106, No. 495, 1113-1124. doi:10.1198/jasa.2011.tm10811
Prof. Dr. Holger Dette, Institute of Statistics, Faculty of Mathematics at the RUB, Tel. +49 234 32 28284, firstname.lastname@example.org
Editor: Jens Wylkop
Dr. Josef König | idw
Microtechnology industry is hiring – positive developments of past years continue
09.04.2018 | IVAM Fachverband für Mikrotechnik
RWI/ISL-Container Throughput Index with minor decline on a high overall level
20.03.2018 | RWI – Leibniz-Institut für Wirtschaftsforschung
Biochips have been developed at TU Wien (Vienna), on which tissue can be produced and examined. This allows supplying the tissue with different substances in a very controlled way.
Cultivating human cells in the Petri dish is not a big challenge today. Producing artificial tissue, however, permeated by fine blood vessels, is a much more...
Faster and secure data communication: This is the goal of a new joint project involving physicists from the University of Würzburg. The German Federal Ministry of Education and Research funds the project with 14.8 million euro.
In our digital world data security and secure communication are becoming more and more important. Quantum communication is a promising approach to achieve...
On Saturday, 10 November 2018, the research icebreaker Polarstern will leave its homeport of Bremerhaven, bound for Cape Town, South Africa.
When choosing materials to make something, trade-offs need to be made between a host of properties, such as thickness, stiffness and weight. Depending on the application in question, finding just the right balance is the difference between success and failure
Now, a team of Penn Engineers has demonstrated a new material they call "nanocardboard," an ultrathin equivalent of corrugated paper cardboard. A square...
Physicists at ETH Zurich demonstrate how errors that occur during the manipulation of quantum system can be monitored and corrected on the fly
The field of quantum computation has seen tremendous progress in recent years. Bit by bit, quantum devices start to challenge conventional computers, at least...
09.11.2018 | Event News
06.11.2018 | Event News
23.10.2018 | Event News
13.11.2018 | Life Sciences
13.11.2018 | Life Sciences
13.11.2018 | Awards Funding