scholarly journals ASYMMETRIC ANOMALOUS DIFFUSION: AN EFFICIENT WAY TO DETECT MEMORY IN TIME SERIES

Fractals ◽  
2001 ◽  
Vol 09 (04) ◽  
pp. 439-449 ◽  
Author(s):  
PAOLO GRIGOLINI ◽  
LUIGI PALATELLA ◽  
GIACOMO RAFFAELLI
Keyword(s):  
Time Series ◽  
Diffusion Process ◽  
Rare Event ◽  
Real Data ◽  
Scaling Exponent ◽  
Constant Intensity ◽  
Scaling Parameter ◽  
Ballistic Motion ◽  
Maximum Value ◽  
Inverse Power Law

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where the waiting time distribution is an inverse power law with index μ. We focus our attention on μ<3, and we evaluate the scaling exponent δ of the time in the resulting diffusion process. We prove that δ gets its maximum value, δ=1, corresponding to the ballistic motion, at μ=2. We study the resulting diffusion process by means of joint use of the continuous time random walk and of the generalized central limit theorem (CLT), as well as adopting a numerical treatment. We show that rendering the diffusion process to be asymmetric yields the significant benefit of enhancing the value of the scaling parameter δ. Furthermore, this scaling parameter becomes sensitive to the power index μ in the whole region 1<μ<3. Finally, we show our method in action on real data concerning human heartbeat sequences.

On the pressure dependence of the thermodynamical scaling exponent γ

Soft Matter ◽  
2020 ◽  
Vol 16 (19) ◽  
pp. 4625-4631 ◽  
Author(s):  
R. Casalini ◽  
T. C. Ransom
Keyword(s):  
Pressure Dependence ◽  
Scaling Exponent ◽  
Scaling Parameter

In materials with a constant scaling parameter γS, the Isomorph γI is found to vary with pressure, demonstrating γS ≠ γI.

scholarly journals Calibrating the CreditRisk+ Model at Different Time Scales and in Presence of Temporal Autocorrelation †

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1679
Author(s):  
Jacopo Giacomelli ◽  
Luca Passalacqua
Keyword(s):  
Time Series ◽  
Default Risk ◽  
Real Life ◽  
Statistical Error ◽  
Real Data ◽  
Sampling Period ◽  
Calibration Procedure ◽  
Industry Standards ◽  
Default Rate

The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

Modeling of Psychomotor Reactions of a Person Based on Modification of the Tapping Test

2021 ◽  
pp. 190-200
Author(s):  
Lesia Mochurad ◽  
Yaroslav Hladun
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Time Series ◽  
Real Data ◽  
Finger Tapping ◽  
Similar Distribution ◽  
Model Learning ◽  
Machine Learning Model ◽  
Finger Tapping Test

The paper considers the method for analysis of a psychophysical state of a person on psychomotor indicators – finger tapping test. The app for mobile phone that generalizes the classic tapping test is developed for experiments. Developed tool allows collecting samples and analyzing them like individual experiments and like dataset as a whole. The data based on statistical methods and optimization of hyperparameters is investigated for anomalies, and an algorithm for reducing their number is developed. The machine learning model is used to predict different features of the dataset. These experiments demonstrate the data structure obtained using finger tapping test. As a result, we gained knowledge of how to conduct experiments for better generalization of the model in future. A method for removing anomalies is developed and it can be used in further research to increase an accuracy of the model. Developed model is a multilayer recurrent neural network that works well with the classification of time series. Error of model learning on a synthetic dataset is 1.5% and on a real data from similar distribution is 5%.

scholarly journals Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

Mathematics ◽  
2018 ◽  
Vol 6 (7) ◽  
pp. 124 ◽  
Author(s):  
Elena Barton ◽  
Basad Al-Sarray ◽  
Stéphane Chrétien ◽  
Kavya Jagan
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Data Analysis ◽  
Real Data ◽  
Real Data Analysis ◽  
Convex Optimisation ◽  
Dynamical Time

In this note, we present a component-wise algorithm combining several recent ideas from signal processing for simultaneous piecewise constants trend, seasonality, outliers, and noise decomposition of dynamical time series. Our approach is entirely based on convex optimisation, and our decomposition is guaranteed to be a global optimiser. We demonstrate the efficiency of the approach via simulations results and real data analysis.

scholarly journals Predicting Stock Market Index Using Hybrid Intelligence Model

2018 ◽  
Vol 7 (3.15) ◽  
pp. 36 ◽  
Author(s):  
Sarah Nadirah Mohd Johari ◽  
Fairuz Husna Muhamad Farid ◽  
Nur Afifah Enara Binti Nasrudin ◽  
Nur Sarah Liyana Bistamam ◽  
Nur Syamira Syamimi Muhammad Shuhaili
Keyword(s):  
Time Series ◽  
Stock Prices ◽  
Linear Models ◽  
Forecast Error ◽  
Arima Model ◽  
Real Data ◽  
Stock Index ◽  
Support Vector ◽  
Ann Model ◽  
Stock Market Index

Predicting financial market changes is an important issue in time series analysis, receiving an increasing attention due to financial crisis. Autoregressive integrated moving average (ARIMA) model has been one of the most widely used linear models in time series forecasting but ARIMA model cannot capture nonlinear patterns easily. Generalized autoregressive conditional heteroscedasticity (GARCH) model applied understanding of volatility depending to the estimation of previous forecast error and current volatility, improving ARIMA model. Support vector machine (SVM) and artificial neural network (ANN) have been successfully applied in solving nonlinear regression estimation problems. This study proposes hybrid methodology that exploits unique strength of GARCH + SVM model, and GARCH + ANN model in forecasting stock index. Real data sets of stock prices FTSE Bursa Malaysia KLCI were used to examine the forecasting accuracy of the proposed model. The results shows that the proposed hybrid model achieves best forecasting compared to other model.  

scholarly journals Analysis of Dynamical Behavior for Epidemic Disease COVID-19 with Application

2021 ◽  
Vol 12 (4) ◽  
pp. 568-577
Author(s):  
Dr. Maysoon M. Aziz, Et. al.
Keyword(s):  
Time Series ◽  
Linear System ◽  
Power Spectrum ◽  
Dynamical Behavior ◽  
Simulated Data ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Disease ◽  
The World ◽  
Non Linear System

In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application.  The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic and epidemic disease .

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

Are all the word ranking methods the same?

2021 ◽  
pp. 2150144
Author(s):  
Elham Najafi ◽  
Alireza Valizadeh ◽  
Amir H. Darooneh
Keyword(s):  
Complex System ◽  
Time Series ◽  
Spatial Distribution ◽  
Time Series Analysis ◽  
Complex Networks ◽  
Rank Correlation ◽  
Ranking Methods ◽  
Series Analysis ◽  
Maximum Value

Text as a complex system is commonly studied by various methods, like complex networks or time series analysis, in order to discover its properties. One of the most important properties of each text is its keywords, which are extracted by word ranking methods. There are various methods to rank words of a text. Each method differently ranks words according to their frequency, spatial distribution or other word properties. Here, we aimed to explore how similar various word ranking methods are. For this purpose, we studied the rank correlation of some important word ranking methods for number of sample texts with different subjects and text sizes. We found that by increasing text size the correlation between ranking methods grows. It means that as the text size increases, the associated word ranks calculated by different ranking methods converge. Also, we found out that the rank correlations of word ranking methods approach their maximum value in the case of large enough texts.

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

&lt;p&gt;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 &amp;#8211; 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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;

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