A COMPARATIVE STUDY OF MODEL SELECTION METHODS FOR NONLINEAR TIME SERIES

2004 ◽  
Vol 14 (03) ◽  
pp. 1129-1146 ◽  
Author(s):  
TOMOMICHI NAKAMURA ◽  
DEVIN KILMINSTER ◽  
KEVIN JUDD ◽  
ALISTAIR MEES
Keyword(s):  
Time Series ◽  
Simulated Annealing ◽  
Computation Time ◽  
Nonlinear Time Series ◽  
Np Hard ◽  
Local Minima ◽  
Selection Methods ◽  
New Methods ◽  
Sunspot Data ◽  
Hard Problems

Constructing models of nonlinear time series is typically NP-hard. One of the difficulties is the local minima, and it is difficult to find a global best model. Some methods have already been proposed that attempt to find good models with reasonable computation time. In this paper we propose new methods that can compensate for a drawback of a method previously proposed by Judd and Mees. A standard approach to NP-hard problems is simulated annealing. We apply these methods to build models of annual sunspot numbers and a laser time series, and compare the results. The results indicate that the performance of the proposed method is comparable to that of simulated annealing in both time series. The performance of Judd and Mees method is almost the same as that of the other methods for the annual sunspot data, but not as good for laser time series. The Judd and Mees method is computationally the fastest of all the methods, and the proposed method is faster than simulated annealing.

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.

scholarly journals Nonlinear Time Series Analysis of Sunspot Data

Solar Physics ◽  
2009 ◽  
Vol 260 (2) ◽  
pp. 441-449 ◽  
Author(s):  
Vinita Suyal ◽  
Awadhesh Prasad ◽  
Harinder P. Singh
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Sunspot Data

Recent progress and new methods for detecting causal relations in large nonlinear time series datasets

2020 ◽  
Author(s):  
Jakob Runge
Keyword(s):  
Time Series ◽  
Recent Progress ◽  
Nonlinear Time Series ◽  
Causal Discovery ◽  
Major Drawback ◽  
Causal Relations ◽  
Climate Research ◽  
Modes Of Variability ◽  
New Methods ◽  
Time Lagged

<p>Detecting causal relationships from observational time series datasets is a key problem in better understanding the complex dynamical system Earth. Recent methodological advances have addressed major challenges such as high-dimensionality and nonlinearity, e.g., PCMCI (Runge et al. Sci. Adv. 2019), but many more remain. In this talk I will give an overview of challenges and methods and present a novel algorithm to identify causal directions among contemporaneous (or instantaneous) relationships. Such contemporaneous relations frequently appear when time series are aggregated (e.g., at a monthly resolution). Then approaches such as Granger Causality and PCMCI fail because they currently only address time-lagged causal relations.<br>We present extensive numerical examples and results on the causal relations among major climate modes of variability. The work overcomes a major drawback of current causal discovery methods and opens up entirely new possibilities to discover causal relations from time series in climate research and other fields in geosciences.</p><p>Runge et al., Detecting and quantifying causal associations in large nonlinear time series datasets, Science Advances eeaau4996 (2019).</p>

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 Using Machine Learning for Quantum Annealing Accuracy Prediction

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 187
Author(s):  
Aaron Barbosa ◽  
Elijah Pelofske ◽  
Georg Hahn ◽  
Hristo N. Djidjev
Keyword(s):  
Machine Learning ◽  
Maximum Clique ◽  
Classification Model ◽  
Maximum Clique Problem ◽  
Problem Instance ◽  
Np Hard ◽  
Machine Learning Classification ◽  
Hard Problems ◽  
Problem Instances ◽  
D Wave

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

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