Linear Time Series and Optimal Linear Prediction

2015 ◽  
pp. 97-112
Author(s):  
Dimitris N. Politis
Keyword(s):  
Time Series ◽  
Linear Prediction ◽  
Linear Time ◽  
Optimal Linear

Some thoughts on stationary processes and linear time series analysis

1988 ◽  
Vol 25 (A) ◽  
pp. 309-318
Author(s):  
C. C. Heyde
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Asymptotic Analysis ◽  
Linear Prediction ◽  
Linear Time ◽  
Weak Form ◽  
Asymptotic Independence ◽  
Stationary Processes ◽  
Prediction Errors ◽  
Martingale Difference

In this paper we trace the development of the asymptotic analysis of autocorrelations for stationary purely non-deterministic time series. We emphasize the interplay between mathematical requirements and modelling philosophy. We then proceed to extend the theory to the case where only a certain weak form of asymptotic independence of the linear prediction errors is needed rather than the earlier martingale difference or independence requirements.

The Prediction Model of Chaotic Series Based on Support Vector Machine and its Application to Runoff

2011 ◽  
Vol 255-260 ◽  
pp. 3594-3599 ◽  
Author(s):  
Guo Rong Yu ◽  
Ju Rui Yang ◽  
Zi Qiang Xia
Keyword(s):  
Time Series ◽  
Support Vector Machine ◽  
Phase Space ◽  
Prediction Model ◽  
Linear Prediction ◽  
Linear Time ◽  
Surface Flow ◽  
Support Vector ◽  
Good Prediction ◽  
Non Linear

Chaos and support vector machine theory has opened up a new route to study complicated and changeable non-linear hydrology time series. Applying the Chaos and non-linear time series based on the support vector machine regression principle, this paper proposes a method and its characteristic and the choosing of key parameters to forecast and set up models. According to Phase Space Reconstruction theory carry on reconstruction of Phase Space to monthly surface flow course, have discussed that probed into the non-linear prediction model of time series of Chaos of the support vector machine, application in the monthly surface flow, have introduce it through to the nuclear function of the base in the course of setting up the model of support vector machine, has simplified the course of solving the non-linear problems. The instance indicates that the model can deal with the complicated hydrology data array well, and there is the good prediction precision.

Some thoughts on stationary processes and linear time series analysis

1988 ◽  
Vol 25 (A) ◽  
pp. 309-318
Author(s):  
C. C. Heyde
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Asymptotic Analysis ◽  
Linear Prediction ◽  
Linear Time ◽  
Weak Form ◽  
Asymptotic Independence ◽  
Stationary Processes ◽  
Prediction Errors ◽  
Martingale Difference

In this paper we trace the development of the asymptotic analysis of autocorrelations for stationary purely non-deterministic time series. We emphasize the interplay between mathematical requirements and modelling philosophy. We then proceed to extend the theory to the case where only a certain weak form of asymptotic independence of the linear prediction errors is needed rather than the earlier martingale difference or independence requirements.

scholarly journals Combining Nonparametric and Optimal Linear Time Series Predictions

2010 ◽  
Vol 105 (492) ◽  
pp. 1554-1565 ◽  
Author(s):  
Sophie Dabo-Niang ◽  
Christian Francq ◽  
Jean-Michel Zakoïan
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Optimal Linear

Nonlinear Time Series Analysis with R

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Particle Physics ◽  
Linear Time ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Linear Behavior ◽  
Non Linear ◽  
Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

scholarly journals Hybrid forecasting model for non-linear time series

2020 ◽  
Author(s):  
E. Priyadarshini ◽  
G. Raj Gayathri ◽  
M. Vidhya ◽  
A. Govindarajan ◽  
Samuel Chakkravarthi
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Forecasting Model ◽  
Non Linear ◽  
Hybrid Forecasting

scholarly journals Recurrent Multiplicative Neuron Model Artificial Neural Network for Non-linear Time Series Forecasting

2014 ◽  
Vol 41 (2) ◽  
pp. 249-258 ◽  
Author(s):  
Erol Egrioglu ◽  
Ufuk Yolcu ◽  
Cagdas Hakan Aladag ◽  
Eren Bas
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Artificial Neural Network ◽  
Neuron Model ◽  
Linear Time ◽  
Time Series Forecasting ◽  
Non Linear ◽  
Artificial Neural
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