Near‐optimal time series sampling based on the reduced Hessian

AIChE Journal ◽  
2020 ◽  
Vol 66 (7) ◽  
Author(s):  
Weifeng Chen ◽  
Lorenz T. Biegler
Keyword(s):  
Time Series ◽  
Optimal Time ◽  
Reduced Hessian

Construct Validity

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Construct Validity ◽  
Hypothesis Test ◽  
Secondary Data ◽  
Time Frame ◽  
Primary Data ◽  
Optimal Time ◽  
Intervention Model ◽  
Right Hand ◽  
The Right

Chapter 8 focuses on threats to construct validity arising from the left-hand side time series and the right-hand side intervention model. Construct validity is limited to questions of whether an observed effect can be generalized to alternative cause and effect measures. The “talking out” self-injurious behavior time series, shown in Chapter 5, are examples of primary data. Researchers often have no choice but to use secondary data that were collected by third parties for purposes unrelated to any hypothesis test. Even in those less-than-ideal instances, however, an optimal time series can be constructed by limiting the time frame and otherwise paying attention to regime changes. Threats to construct validity that arise from the right-hand side intervention model, such as fuzzy or unclear onset and responses, are controlled by paying close attention to the underlying theory. Even a minimal theory should specify the onset and duration of an impact.

scholarly journals Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Inga Timofejeva ◽  
Kristina Poskuviene ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Time Delays ◽  
Geometric Approach ◽  
Optimal Time ◽  
Effective Algorithm ◽  
Geometrical Properties ◽  
Finite Observation

A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

scholarly journals Forecasting the COVID-19 epidemic integrating symptom search behavior: an infodemiology study

2021 ◽  
Author(s):  
Alessandro Rabiolo ◽  
Eugenio Alladio ◽  
Esteban Morales ◽  
Andrew I McNaught ◽  
Francesco Bandello ◽  
...  
Keyword(s):  
Time Series ◽  
Web Application ◽  
Moving Average ◽  
Time Lag ◽  
Search Behavior ◽  
Google Trends ◽  
Optimal Time ◽  
Time Range ◽  
Prediction Ability ◽  
Time Series Modelling

ABSTRACTBackgroundPrevious studies have suggested associations between trends of web searches and COVID-19 traditional metrics. It remains unclear whether models incorporating trends of digital searches lead to better predictions.MethodsAn open-access web application was developed to evaluate Google Trends and traditional COVID-19 metrics via an interactive framework based on principal components analysis (PCA) and time series modelling. The app facilitates the analysis of symptom search behavior associated with COVID-19 disease in 188 countries. In this study, we selected data of eight countries as case studies to represent all continents. PCA was used to perform data dimensionality reduction, and three different time series models (Error Trend Seasonality, Autoregressive integrated moving average, and feed-forward neural network autoregression) were used to predict COVID-19 metrics in the upcoming 14 days. The models were compared in terms of prediction ability using the root-mean-square error (RMSE) of the first principal component (PC1). Predictive ability of models generated with both Google Trends data and conventional COVID-19 metrics were compared with those fitted with conventional COVID-19 metrics only.FindingsThe degree of correlation and the best time-lag varied as a function of the selected country and topic searched; in general, the optimal time-lag was within 15 days. Overall, predictions of PC1 based on both searched termed and COVID-19 traditional metrics performed better than those not including Google searches (median [IQR]: 1.43 [0.74-2.36] vs. 1.78 [0.95-2.88], respectively), but the improvement in prediction varied as a function of the selected country and timeframe. The best model varied as a function of country, time range, and period of time selected. Models based on a 7-day moving average led to considerably smaller RMSE values as opposed to those calculated with raw data (median [IQR]: 0.74 [0.47-1.22] vs. 2.15 [1.55-3.89], respectively).InterpretationThe inclusion of digital online searches in statistical models may improve the prediction of the COVID-19 epidemic.FundingEOSCsecretariat.eu has received funding from the European Union’s Horizon Programme call H2020-INFRAEOSC-05-2018-2019, grant Agreement number 831644.

Chaotic Characteristics Identification on Terminal Departing Passenger Traffic Time Series

2013 ◽  
Vol 409-410 ◽  
pp. 1303-1306 ◽  
Author(s):  
Ya Ping Zhang ◽  
Yuan Yuan Guo ◽  
Yu Wei ◽  
Shao Wu Cheng ◽  
Zhi Wei Xing
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Optimal Time ◽  
Largest Lyapunov Exponent ◽  
Reconstruction Method ◽  
Passenger Traffic ◽  
Traffic Time Series ◽  
Optimal Delay ◽  
Optimal Delay Time ◽  
Chaotic Time Series Prediction

On the basis of actual survey of departing passengers to reach terminal, chaotic time series prediction theory was adopted for data analysis in this paper. In order to find out the self-similarity of time series, this paper divided passenger traffic into two kinds: holiday traffic and non-holiday traffic by changing interval scale. The optimal delay time and the best embedding dimension had been calculated by using time series phase space reconstruction method. To confirm whether the time series have chaotic characteristics or not, it took the largest Lyapunov exponent as determining criterion.Then the optimal time intervals of passenger traffic time series with chaotic character were determined. The study provides a theoretical basis for the application of chaos theory in passenger traffic forecast.

scholarly journals Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 221
Author(s):  
Mariano Matilla-García ◽  
Isidro Morales ◽  
Jose Miguel Rodríguez ◽  
Manuel Ruiz Marín
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Mutual Information ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Optimal Time ◽  
Embedding Dimension ◽  
Simple Method ◽  
Correlation Integral

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

scholarly journals Predicting Electric Power Energy, Using Recurrent Neural Network Forecasting Model

2018 ◽  
Vol 4 (2) ◽  
pp. 53
Author(s):  
Nawzad M. Ahmed ◽  
Ayad O. Hamdeen
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Electric Power ◽  
Recurrent Neural Network ◽  
The Other ◽  
Optimal Time ◽  
Main Role ◽  
Complex Data ◽  
Suggested Model ◽  
Great Ability

Electricity is counted as a one of the most important energy sources in the world. It has played a main role in developing several sectors. In this study two types of electricity variables have been used, the first was the demand on power energy, and the second was the consumption or energy load in Sulaimani city. The main goal of the study was to construct an analytic model of the recurrent neural network (RNN) for both variables. This model has a great ability in detecting the complex patterns for the data of a time series, which is most suitable for the data under consideration. This model is also more sensitive and reliable than the other artificial neutral network (ANN), so it can deal with more complex data that might be chaotic, seismic….etc. this model can also deal with nonlinear data which are mostly found in time series, and it deals with them differently compared to the other models. This research determined and defined the best model of RNN for electricity demand and consumption to be run in two levels. The first level is to predict the complexity of the suggested model (1-5-10-1) with the error function as (MSE: mean square error, AIC, and R2: coefficient of determination). The second level uses the suggested model to forecast the demand on electric power energy and the value of each unit. Another result of this study is to determine the suitable algorithm that can deal with such complex data. The algorithm (Levenberg-Marquardt) was found to be the most reliable and has the most optimal time to give accurate and reliable results in this study.

scholarly journals An ensemble approach based on transformation functions for natural gas price forecasting considering optimal time delays

2021 ◽  
Vol 7 ◽  
pp. e409
Author(s):  
Faramarz Saghi ◽  
Mustafa Jahangoshai Rezaee
Keyword(s):  
Time Series ◽  
Natural Gas ◽  
Time Delays ◽  
Wavelet Decomposition ◽  
Vital Role ◽  
Optimal Time ◽  
Price Forecasting ◽  
Fuzzy Transform ◽  
Economic Sectors ◽  
Gas Price

Natural gas, known as the cleanest fossil fuel, plays a vital role in the economies of producing and consuming countries. Understanding and tracking the drivers of natural gas prices are of significant interest to the many economic sectors. Hence, accurately forecasting the price is very important not only for providing an effective factor for implementing energy policy but also for playing an extremely significant role in government strategic planning. The purpose of this study is to provide an approach to forecast the natural gas price. First, optimal time delays are identified by a new approach based on the Euclidean Distance between input and target vectors. Then, wavelet decomposition has been implemented to reduce noise. Moreover, fuzzy transform with different membership functions has been used for modeling uncertainty in time series. The wavelet decomposition and fuzzy transform have been integrated into the preprocessing stage. An ensemble method is used for integrating the outputs of various neural networks. The results depict that the proposed preprocessing methods used in this paper cause to improve the accuracy of natural gas price forecasting and consider uncertainty in time series.

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