Continuous time Brownian motion models for analysis of sequential data

The paper discusses techniques for analysis of sequential data from variable processes, particularly techniques that can be used even when the data are not equally spaced in time. The techniques are based on models which use continuous time Brownian motion and its integrals to describe the pattern o...

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Bibliographic Details
Published in:Applied statistics 2010-05, Vol.59 (3), p.477-494
Main Author: Robinson, G. K.
Format: Article
Language:English
Subjects:
Applications
Brownian motion
Data models
Data smoothing
Exact sciences and technology
Integrals
Integrated Brownian motion
Interval estimators
Kalman filtering
Mathematical intervals
Mathematics
Maximum likelihood estimation
Mixed models
Multivariate analysis
Musical intervals
Noise
Probability and statistics
Probability theory and stochastic processes
Process controls
Sciences and techniques of general use
Sequential methods
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Statistical process control
Statistical variance
Statistics
Stochastic models
Studies
Tonnage
Variance analysis
Variograms
White noise
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Summary:The paper discusses techniques for analysis of sequential data from variable processes, particularly techniques that can be used even when the data are not equally spaced in time. The techniques are based on models which use continuous time Brownian motion and its integrals to describe the pattern of variation in an underlying physical process and use white noise to describe variation due to measurement processes. The paper concentrates on making statements about what has been happening in the region that is covered by the data rather than on making predictions about regions that are far from the data. It is argued that the continuous time integrated Brownian motion plus white noise model is always preferable to its discrete time analogue: the local linear trend model. Further integrals of Brownian motion can be fitted as an alternative to using splines. All of these continuous time Brownian motion models can be fitted to data that are associated with a time interval (interval data) as well as to data that are associated with a single time (spot data). They can be fitted by using mixed model methodology as well as by using Kalman filtering and smoothing.
ISSN:0035-9254
1467-9876
DOI:10.1111/j.1467-9876.2009.00705.x