scholarly journals Wavelet estimation of functional coefficient regression models

2018 ◽  
Vol 16 (01) ◽  
pp. 1850004
Author(s):  
Michel H. Montoril ◽  
Pedro A. Morettin ◽  
Chang Chiann
Keyword(s):  
Time Series ◽  
Real Data ◽  
Rates Of Convergence ◽  
Nonlinear Time Series ◽  
Local Linear Regression ◽  
Nonparametric Model ◽  
Time Series Models ◽  
Data Set ◽  
Wide Range ◽  
Functional Coefficient

The area of nonlinear time series models has experienced a great development since the 1980s. Although there is a wide range of parametric nonlinear time series models, in general, we do not know if the postulated model is the most appropriated one for a specific data set. This situation highlights the importance of nonparametric models. An interesting nonparametric model to fit nonlinear time series is the well-known functional coefficient regression model. Nonparametric estimations by, e.g., local linear regression and splines, are developed in the literature. In this work, we study the estimation of such a model using wavelets. It is a proposal that takes into account both, classical and warped wavelets. We present the rates of convergence of the proposed estimators and carry out simulation studies to evaluate automatic procedures (among AIC, AICc and BIC) for selecting the coarsest and finest levels to be used during the estimation process. Moreover, we illustrate the methodology with an application to a real data set, where we also calculate multi-step-ahead forecasts and compare the results with other methods known in the literature.

Multivariate linear time series models

1984 ◽  
Vol 16 (3) ◽  
pp. 492-561 ◽  
Author(s):  
E. J. Hannan ◽  
L. Kavalieris
Keyword(s):  
Limit Theorems ◽  
Analysis Of Algorithms ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Real Data ◽  
Rates Of Convergence ◽  
Structure Theory ◽  
Time Series Models ◽  
Transfer Model ◽  
Rational Transfer

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree, n, because of the fact that this space, M(n), can be realised as a kind of high-dimensional algebraic surface of dimension n(2s + m) where s and m are the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determining n and then the appropriate element of M(n). However, the fact that M(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

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.

Empirical analysis of time series using feature selection algorithms

2021 ◽  
Author(s):  
Mikhail Kanevski
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Feature Selection ◽  
Dimensional Space ◽  
Multivariate Time Series ◽  
Feature Space ◽  
Real Data ◽  
Theoretical Concepts ◽  
Wide Range ◽  
Linear And Nonlinear

<p>Nowadays a wide range of methods and tools to study and forecast time series is available. An important problem in forecasting concerns embedding of time series, i.e. construction of a high dimensional space where forecasting problem is considered as a regression task. There are several basic linear and nonlinear approaches of constructing such space by defining an optimal delay vector using different theoretical concepts. Another way is to consider this space as an input feature space – IFS, and to apply machine learning feature selection (FS) algorithms to optimize IFS according to the problem under study (analysis, modelling or forecasting). Such approach is an empirical one: it is based on data and depends on the FS algorithms applied. In machine learning features are generally classified as relevant, redundant and irrelevant. It gives a reach possibility to perform advanced multivariate time series exploration and development of interpretable predictive models.</p><p>Therefore, in the present research different FS algorithms are used to analyze fundamental properties of time series from empirical point of view. Linear and nonlinear simulated time series are studied in detail to understand the advantages and drawbacks of the proposed approach. Real data case studies deal with air pollution and wind speed times series. Preliminary results are quite promising and more research is in progress.</p>

scholarly journals Modeling and Short-Term Forecasts of Indicators for COVID-19 Outbreak in 25 Countries at the end of March

2020 ◽  
pp. 6-20
Author(s):  
Handan Ankaralı ◽  
Nadire Erarslan ◽  
Özge Pasin ◽  
Abu Kholdun Al Mahmood
Keyword(s):  
Time Series ◽  
Medical Science ◽  
Exponential Smoothing ◽  
Seasonal Effects ◽  
Time Series Models ◽  
Double Exponential ◽  
Wide Range ◽  
Simple Exponential Smoothing ◽  
Double Exponential Smoothing ◽  
Prediction And Forecasting

Objective: The coronavirus, which originated in Wuhan, causing the disease called COVID-19, spread more than 200 countries and continents end of the March. In this study, it was aimed to model the outbreak with different time series models and also predict the indicators. Materials and Methods: The data was collected from 25 countries which have different process at least 20 days. ARIMA(p,d,q), Simple Exponential Smoothing, Holt’s Two Parameter, Brown’s Double Exponential Smoothing Models were used. The prediction and forecasting values were obtained for the countries. Trends and seasonal effects were also evaluated. Results and Discussion: China has almost under control according to forecasting. The cumulative death prevalence in Italy and Spain will be the highest, followed by the Netherlands, France, England, China, Denmark, Belgium, Brazil and Sweden respectively as of the first week of April. The highest daily case prevalence was observed in Belgium, America, Canada, Poland, Ireland, Netherlands, France and Israel between 10% and 12%.The lowest rate was observed in China and South Korea. Turkey was one of the leading countries in terms of ranking these criteria. The prevalence of the new case and the recovered were higher in Spain than Italy. Conclusion: More accurate predictions for the future can be obtained using time series models with a wide range of data from different countries by modelling real time and retrospective data. Bangladesh Journal of Medical Science Vol.19(0) 2020 p.06-20

scholarly journals Estimation for a class of positive nonlinear time series models

1996 ◽  
Vol 63 (2) ◽  
pp. 139-152 ◽  
Author(s):  
Tim C. Brown ◽  
Paul D. Feigin ◽  
Diana L. Pallant
Keyword(s):  
Time Series ◽  
Nonlinear Time Series ◽  
Time Series Models
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