Phase Characterization in Experimental Chaotic Systems

2014 ◽  
Vol 706 ◽  
pp. 137-148
Author(s):  
R. Follmann ◽  
E. Rosa ◽  
E.E.N. Macau ◽  
J.R.C. Piqueira
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Mean Square ◽  
Attractor Reconstruction ◽  
Wide Range ◽  
Experimental Time Series ◽  
The Mean ◽  
Phase Characterization ◽  
Scalar Time Series ◽  
Sinusoidal Function

In this work we present and discuss a method for measuring the phase of chaotic systems. This method has as input a scalar time series and operates by estimating a fundamental frequency for short segments, or windows, along the whole extension of the signal. It minimizes the mean square error of fitting a sinusoidal function to the series segment. This approach does not require following the trajectory on the attractor, works well over a wide range of adjustable parameters, is of easy implementation, and is particularly appealing for experimental settings with single signal outputs since there is no need of attractor reconstruction. We demonstrate the applicability of this method on experimental time series obtained from two coupled Chua circuits.

IDENTIFYING PHASE SYNCHRONOUS REGIMES IN NON-COHERENT AND MULTIPLE SCROLL ATTRACTOR SYSTEMS

2013 ◽  
Vol 23 (11) ◽  
pp. 1350179 ◽  
Author(s):  
ROSANGELA FOLLMANN ◽  
EPAMINONDAS ROSA ◽  
ELBERT E. N. MACAU ◽  
JOSÉ ROBERTO CASTILHO PIQUEIRA
Keyword(s):  
Time Series ◽  
Phase Synchronization ◽  
Time Series Data ◽  
Series Data ◽  
Similarity Function ◽  
Attractor Reconstruction ◽  
Experimental Time Series ◽  
Data Output ◽  
Scalar Time Series

This work discusses the applicability of a method for phase determination of scalar time series from nonlinear systems. We apply the method to detect phase synchronization in different scenarios, and use the phase diffusion coefficient, the Lyapunov spectrum, and the similarity function to characterize synchronization transition in nonidentical coupled Rössler oscillators, both in coherent and non-coherent regimes. We also apply the method to detect phase synchronous regimes in systems with multiple scroll attractors as well as in experimental time series from coupled Chua circuits. The method is of easy implementation, requires no attractor reconstruction, and is particularly convenient in the case of experimental setups with a single time series data output.

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

2006 ◽  
Vol 36 (02) ◽  
pp. 521-542 ◽  
Author(s):  
Markus Buchwalder ◽  
Hans Bühlmann ◽  
Michael Merz ◽  
Mario V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Model ◽  
Mean Square ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

scholarly journals Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Wuwei Liu ◽  
Jingdong Yan
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Mean Square Error ◽  
Financial Time Series ◽  
Prediction Method ◽  
Mean Square ◽  
Rbf Network ◽  
Network Prediction ◽  
The Mean ◽  
Hidden Layer

In recent years, people are more and more interested in time series modeling and its application in prediction. This paper mainly discusses a financial time series image algorithm based on wavelet analysis and data fusion. In this research, we conducted an in-depth study on the scale decomposition sequence and wavelet transform sequence in different scale domains of wavelet transform according to the scale change rule based on wavelet transform. We use wavelet neural network with different input neurons and hidden neurons to predict, respectively. Finally, the prediction results are integrated into the final prediction results based on the original time series by using wavelet reconstruction technology. Using RBF algorithm in neural network and SPSS Clementine, the wavelet transform sequences on five scales are modeled. Each network model has three layers: one input layer, one hidden layer, and one output layer, and each output layer has only one output element. In order to compare the prediction effect of the model proposed in this study, the ordinary RBF network is used to model and predict the log yield itself. When the input sample is 5, the minimum mean square error is obtained when the hidden layer is 6, and the mean square error is 1.6349. The mean square error of the training phase is 0.0209, and the validation error is 1.6141. The results show that the prediction results of the wavelet prediction method combined with the RBF network prediction method are better than those of wavelet prediction or RBF network prediction.

scholarly journals Forecasting Modelling of Cockles in Malaysia by Using Time Series Analysis

2018 ◽  
Vol 7 (4.30) ◽  
pp. 488
Author(s):  
Hani Nabihah Aziz ◽  
Mohd Saifullah Rusiman ◽  
Siti Noor Asyikin Mohd Razali ◽  
Abdul Wahab Abdulla ◽  
Nur Amira Azmi
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Moving Average ◽  
Linear Method ◽  
Mean Square ◽  
Cyclic Pattern ◽  
Mangrove Estuary ◽  
Auto Regressive ◽  
The Mean ◽  
Blood Cockle

Cockle farmed in Malaysia are from Anadara genes and Arcidae family which known as blood cockle. Normally, it was found in the farmed around mangrove estuary areas in the muddy and sandy shores. This study aims to predict the production of cockle to ensure sure the cockle supplies are synchronised with the demand. Then, based on the demand, the prediction result could be used to make decision either to import or export the cockle. The data were taken from the Department of Fisheries Malaysia (DFM) and it has cyclic pattern data. There are two methods used in this study which are Holt-Linear method and Auto regressive moving average (ARMA). In determining the best fitted model between the two methods, the mean square error (MSE) values will be compared and the lowest value of MSE will assign as the best model. Result shows that ARMA(1,1) is the best model compared to Holt-Linear. Therefore, ARMA(1,1) model will be used to forecast the production of cockle in Malaysia.

Data‐adaptive polarization filters for multichannel geophysical data

Geophysics ◽  
1981 ◽  
Vol 46 (10) ◽  
pp. 1423-1431 ◽  
Author(s):  
J. C. Samson ◽  
J. V. Olson
Keyword(s):  
Time Series ◽  
Seismic Data ◽  
Adaptive Filters ◽  
Spectral Content ◽  
Temporal Features ◽  
Wide Range ◽  
Data Adaptive ◽  
Vector Time Series ◽  
Multichannel Seismic Data ◽  
Scalar Time Series

The design of data‐adaptive filters requires that the noise be defined, statistically or otherwise, by parameters which allow some means of separating the noise from the signal. We consider here multichannel data in which one knows only that the noise is less polarized than the signal in a unitary space. This description of the noise is not sufficient for designing filters which are optimum in any sense; consequently, the filters may require a number of changes in the parameters before a satisfactory design can be found. Once this design has been achieved, the filters can be used to enhance waveforms of arbitrary shape, requiring little prior knowledge of the spectral content or temporal features of the signal. In contrast to many other data‐adaptive filters which give a scalar time‐series output, the filters we describe here with vector time series input have an equal number of input and output channels. A number of examples of filtered magnetic and seismic data are given in order to emphasize the wide range of uses for the filters. Some suggestions for application of the filters to multichannel seismic data are given.

scholarly journals Prediksi Kedatangan Turis Asing ke Indonesia Menggunakan Backpropagation Neural Networks

2016 ◽  
Vol 4 (4) ◽  
pp. 485
Author(s):  
Haviluddin Haviluddin ◽  
Zainal Arifin ◽  
Awang Harsa Kridalaksana ◽  
Dedy Cahyadi
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Mean Square Error ◽  
Time Series Data ◽  
Alternative Methods ◽  
Series Data ◽  
Mean Square ◽  
Backpropagation Neural Network ◽  
Forecasting Accuracy ◽  
The Mean

In this paper, a backpropagation neural network (BPNN) method with time series data have been explored. The BPNN method to predict the foreign tourist’s arrival to Indonesia datasets have been implemented. The foreign tourist’s arrival datasets were taken from the center agency on statistics (BPS) Indonesia. The experimental results showed that the BPNN method with two hidden layers were able to forecast foreign tourist’s arrival to Indonesia. Where, the mean square error (MSE) as forecasting accuracy has been indicated. In this study, the BPNN method is able and recommended to be alternative methods for predicting time series datasets. Also, the BPNN method showed that effective and easy to use. In other words, BPNN method is capable to producing good value of forecasting.Keywords - BPNN; foreign tourists; BPS; MSEPemanfaatan backpropagation neural network (BPNN) dengan data deret waktu telah digunakan dalam paper ini. Metode BPNN telah digunakan untuk memprediksi data kedatangan turis asing ke Indonesia, dimana data turis tersebut diambil dari badan pusat statistik Indonesia (BPS). Hasil pengujian menunjukkan bahwa metode BPNN dengan dua lapisan tersembunyi mampu memodelkan dan meramalkan data kedatangan turis asing ke Indonesia yang diindikasikan dengan nilai mean square error (MSE). Penelitian ini merekomendasikan bahwa metode BPNN mampu menjadi alternative metode dalam memprediksi data yang berjenis deret waktu karena metode BPNN efektif dan lebih mudah digunakan serta mampu menghasilkan akurasi nilai peramalan yang baik.

scholarly journals A Comparison Study on Fuzzy Time Series and Holt-Winter Model in Forecasting Tourist Arrival in Langkawi, Kedah

2020 ◽  
Vol 5 (1) ◽  
pp. 34-43
Author(s):  
Nur Fatihah Fauzi ◽  
Nurul Shahiera Ahmadi ◽  
Nor Hayati Shafii ◽  
Huda Zuhrah Ab Halim
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Tourism Industry ◽  
Fuzzy Time Series ◽  
Mean Square ◽  
Comparison Study ◽  
Microsoft Excel ◽  
A Value ◽  
The Mean ◽  
Major Donors

The tourism industry in Malaysia has been growing significantly over the years. Tourism has been one of the major donors to Malaysia’s economy. Based on the report from the Department of Statistics, a total of domestic visitors in Malaysia were recorded at about 221.3 million in 2018 with an increase of 7.7% alongside a higher record in visitor arrivals and tourism expenditure.  This study aims to make a comparison between two methods, which are Fuzzy Time Series and Holt-Winter in forecasting the number of tourist arrival in Langkawi based on the monthly tourist arrival data from January 2015 to December 2019. Both models were generated using Microsoft Excel in obtaining the forecast value.  The Mean Square Error (MSE) has been calculated in this study to get the best model by looking at the lowest value. The result found that Holt-Winter has the lowest value that is 713524285 compared to the Fuzzy Time Series with a value of 2625517469. Thus, the Holt-Winter model is the best method and has been used to forecast the tourist arrival for the next 2 years. The forecast value for the years 2020 and 2021 are displayed by month.

scholarly journals AUTOREGRESSION MODELS OF SPACE OBJECTS MOVEMENT REPRESENTED BY TLE ELEMENTS

2020 ◽  
Vol 2 (127) ◽  
pp. 103-116
Author(s):  
Aleksandr Sarichev ◽  
Bogdan Perviy
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Autoregressive Model ◽  
Autoregressive Models ◽  
Mean Square ◽  
Element Determination ◽  
Training Samples ◽  
Space Objects ◽  
The Mean

The developed method, which is a modification of the previously developed methods for constructing autoregressive models, is used to simulate the motion of space objects in the time series of their TLE elements. The modeling system has been developed that includes: determining the optimal volume of training samples in modeling time series of TLE elements; determination of the autoregression order for each variable (TLE element); determination of the optimal structure and identification of the parameters of the autoregressive model for each variable; identification of patterns of evolution of the mean square error of autoregressive models in time based on the modeling of time series of TLE elements according to the principle of "moving interval".

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