Linear least squares prediction in non-stochastic time series

1969 ◽  
Vol 1 (01) ◽  
pp. 111-122
Author(s):  
P. D. Finch
Keyword(s):  
Time Series ◽  
Possible Worlds ◽  
Probabilistic Approach ◽  
Point Of View ◽  
Frequency Interpretation ◽  
Set Up ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Probabilistic Point ◽  
Conceptual Difficulties

Many problems arising in the physical and social sciences relate to processes which happen sequentially. Such processes are usually investigated by means of the theory of stationary stochastic processes, but there have been some attempts to develop techniques which are not subject to the conceptual difficulties inherent in the probabilistic approach. These difficulties stem from the fact that in practice one is often restricted to a single record which, from the probabilistic point of view, is only one sample from an ensemble of possible records. In some instances such a viewpoint seems artificial, and for some time series it is questionable whether any objective reality corresponds to the idea of an ensemble of possible time series. For example, as noted in Feller (1967), a theory of probability based on a frequency interpretation cannot meaningfully attach a probability to a statement such as “the sun will rise tomorrow”, because to do so one would have to set up a conceptual universe of possible worlds.

Linear least squares prediction in non-stochastic time series

1969 ◽  
Vol 1 (1) ◽  
pp. 111-122 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Time Series ◽  
Possible Worlds ◽  
Probabilistic Approach ◽  
Point Of View ◽  
Frequency Interpretation ◽  
Set Up ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Probabilistic Point ◽  
Conceptual Difficulties

Many problems arising in the physical and social sciences relate to processes which happen sequentially. Such processes are usually investigated by means of the theory of stationary stochastic processes, but there have been some attempts to develop techniques which are not subject to the conceptual difficulties inherent in the probabilistic approach. These difficulties stem from the fact that in practice one is often restricted to a single record which, from the probabilistic point of view, is only one sample from an ensemble of possible records. In some instances such a viewpoint seems artificial, and for some time series it is questionable whether any objective reality corresponds to the idea of an ensemble of possible time series. For example, as noted in Feller (1967), a theory of probability based on a frequency interpretation cannot meaningfully attach a probability to a statement such as “the sun will rise tomorrow”, because to do so one would have to set up a conceptual universe of possible worlds.

scholarly journals Identification of an unstable ARMA equation

2001 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Yulia R. Gel ◽  
Vladimir N. Fomin
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Infinite Order ◽  
Time Series Model ◽  
Identification Algorithm ◽  
Data Handling ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Strongly Consistent ◽  
Minimal Phase

Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.

Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

Fractal and Multifractal in Stochastic Time Series

2020 ◽  
pp. 129-151
Author(s):  
Santo Banerjee ◽  
M K Hassan ◽  
Sayan Mukherjee ◽  
A Gowrisankar
Keyword(s):  
Time Series ◽  
Stochastic Time Series ◽  
Stochastic Time

A Recurrent Probabilistic Neural Network for EMG Pattern Recognition

2011 ◽  
pp. 130-153 ◽  
Author(s):  
Toshio Tsuji ◽  
Nan Bu ◽  
Osamu Fukuda
Keyword(s):  
Time Series ◽  
Pattern Recognition ◽  
Hidden Markov ◽  
Probabilistic Neural Network ◽  
Temporal Characteristic ◽  
Gaussian Mixture ◽  
Neural Computation ◽  
Emg Pattern Recognition ◽  
Stochastic Time Series ◽  
Stochastic Time

In the field of pattern recognition, probabilistic neural networks (PNNs) have been proven as an important classifier. For pattern recognition of EMG signals, the characteristics usually used are: (1) amplitude, (2) frequency, and (3) space. However, significant temporal characteristic exists in the transient and non-stationary EMG signals, which cannot be considered by traditional PNNs. In this article, a recurrent PNN, called recurrent log-linearized Gaussian mixture network (R-LLGMN), is introduced for EMG pattern recognition, with the emphasis on utilizing temporal characteristics. The structure of R-LLGMN is based on the algorithm of a hidden Markov model (HMM), which is a routinely used technique for modeling stochastic time series. Since R-LLGMN inherits advantages from both HMM and neural computation, it is expected to have higher representation ability and show better performance when dealing with time series like EMG signals. Experimental results show that R-LLGMN can achieve high discriminant accuracy in EMG pattern recognition.

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