Biography
Piet M.T. Broersen was born in Zijdewind in the Netherlands, in 1944. He received the M.Sc. degree in Applied Physics in 1968 and the Ph.D degree in 1976, both from the Delft University of Technology, Delft, the Netherlands.
He is currently with the Department of Multi Scale Physics of the Delft University of Technology. His main research interest is in automatic identification on statistical grounds by letting measured data speak for themselves. He developed a practical solution for the spectral and the autocorrelation analysis of stochastic data by the automatic selection of a suitable order and type for a time series model of the data. |
Abstract
Automatic spectral estimation gives random data a language to communicate the information it contains. This tutorial treats the recently developed automatic identification of a single time series model for measured random data. One model is selected, with statistical rules, from hundreds of candidates. That model provides an accurate parametric representation of the power spectral density and of the autocorrelation function of the stochastic data. The accuracy of this autocorrelation function is always better than the usual autocorrelation estimate obtained with lagged products of the random observations. Likewise, the accuracy of the spectral density is always better than the accuracy of tapered and windowed periodograms.
Let the data themselves decide about their best representation, they can!
Three types of time series models can be distinguished: autoregressive (AR), moving average (MA) and combined ARMA. The recent ability to identify an appropriate time series model for measured stochastic data has three causes: increased computational speed, finite sample order selection criteria, and developments in the reliability of time series algorithms. Time series models are excellent for random data, if the best model type and the best model order are known. With the new ARMAsel toolbox, that a priori information is no longer required. For unknown data characteristics, a large number of candidate models are computed. The ARMAsel Matlab® computer program automatically selects the best model order for each of the three model types and also the best model type. That single selected model includes precisely the significant details that are present in the autocorrelation function and in the spectrum of the data. It is now possible to compute more than 500 or 1000 different time series models and to let the computer select only one, which certainly is one of the better models if not the very best. That model characterizes the spectral density and the autocorrelation function of the data with an accuracy that is always close to the best possible attainable statistical accuracy.
The tutorial treats time series theory, estimation methods, finite sample order selection and many practical examples in physics, prosthesis control, radar, satellite data, improved forecasting of river levels and the application to missing data problems and to irregular data. The textbook “Automatic Autocorrelation and Spectral Analysis” will be published by Springer in June 2006. |
