A method for locating gradual changes in time series
Related Experiment Video
Updated: Jul 16, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Heiko Hofer1, Gerhard Staude, Werner Wolf
1Institute of Mathematics and Computer Science, University of the Armed Forces, Munich, Germany. heiko.hofer@unibw.de
Abstract:
A variation to the change-point problem is addressed. The classical problem involves locating abrupt changes in the mean value of a signal. In contrast, a generalisation to gradual changes with constant speed is considered, which frequently occurs in biomedical signal-processing tasks. Formulas are derived that are easy to adopt by application scientists. The estimation quality is investigated theoretically and using Monte Carlo simulations. Results show that the change-point estimates were close to their true values. In contrast, a systematic error of approximately half the change duration occurred when the gradual nature of the signal was neglected.
Related Concept Videos
Time-Series Graph
Increasing Function
Derivatives: Problem Solving
Velocity and Position by Graphical Method
Basic Discrete Time Signals
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
Properties of Laplace Transform-II
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...

