Featured Research

from universities, journals, and other organizations

New method in spectral analysis: Measuring the distance of processes

Date:
November 1, 2011
Source:
Ruhr-Universitaet-Bochum
Summary:
A milestone in the description of complex processes -- for example the ups and downs of share prices -- has been reached by mathematicians. Researchers 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. The approach also makes it possible to construct statistical tests that are considerably better and more accurate than previous methods.

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.
Credit: Image courtesy of Ruhr-Universitaet-Bochum

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-Universitδt 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. 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 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 Preuί 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.


Story Source:

The above story is based on materials provided by Ruhr-Universitaet-Bochum. Note: Materials may be edited for content and length.


Journal Reference:

  1. Holger Dette. A Measure of Stationarity in Locally Stationary Processes With Applications to Testing. Journal of the American Statistical Association, 2011; 106 (495): 1113 DOI: 10.1198/jasa.2011.tm10811

Cite This Page:

Ruhr-Universitaet-Bochum. "New method in spectral analysis: Measuring the distance of processes." ScienceDaily. ScienceDaily, 1 November 2011. <www.sciencedaily.com/releases/2011/10/111028103217.htm>.
Ruhr-Universitaet-Bochum. (2011, November 1). New method in spectral analysis: Measuring the distance of processes. ScienceDaily. Retrieved August 20, 2014 from www.sciencedaily.com/releases/2011/10/111028103217.htm
Ruhr-Universitaet-Bochum. "New method in spectral analysis: Measuring the distance of processes." ScienceDaily. www.sciencedaily.com/releases/2011/10/111028103217.htm (accessed August 20, 2014).

Share This




More Computers & Math News

Wednesday, August 20, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Ballmer Leaves Microsoft's Board, Has Advice For Nadella

Ballmer Leaves Microsoft's Board, Has Advice For Nadella

Newsy (Aug. 19, 2014) — In a letter to Microsoft CEO Satya Nadella, Ballmer said he's leaving the board of directors and offered tips on how the company can be successful. Video provided by Newsy
Powered by NewsLook.com
What Google Can Gain From Special Accounts For Children

What Google Can Gain From Special Accounts For Children

Newsy (Aug. 19, 2014) — Google will reportedly offer official accounts for children younger than 13 years old. Video provided by Newsy
Powered by NewsLook.com
Breakingviews: Ebola's Economic Impact Could Eclipse SARS

Breakingviews: Ebola's Economic Impact Could Eclipse SARS

Reuters - Business Video Online (Aug. 18, 2014) — The virus ravaging Africa has yet to spread elsewhere. Yet Asia’s SARS crisis in 2003 showed how changes to behaviour can hurt the economy more than the actual disease, says Breakingviews' Una Galani. Video provided by Reuters
Powered by NewsLook.com
Twitter Users Up In Arms After 'Favorites' Show Up In Feeds

Twitter Users Up In Arms After 'Favorites' Show Up In Feeds

Newsy (Aug. 17, 2014) — Twitter is testing a feature on some users that shows favorited tweets from people they follow in their own timeline, the same way a retweet appears. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins