Submit to Mathematics Review for Mathematics Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Complex Network Analysis of Nonlinear Time Series

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Published Papers

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (20 October 2023) | Viewed by 20755

Share This Special Issue

Special Issue Editor

Dr. Darko Vukovic

E-Mail Website
Guest Editor

1. Head of International Laboratory for Finance and Financial Markets, Faculty of Economics, People’s Friendship University of Russia (RUDN University), st. Miklukho-Maklaya 6, 117198 Moscow, Russia
2. Head of Department of regional economics and economic geography, Geographical Institute “Jovan Cvijic”, Serbian Academy of Sciences and Arts, Djure Jaksica 9, 11000 Belgrade, Serbia
Interests: neural networks; financial times-series management; nonlinear models; portfolio management; market efficiency; random walk
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

In the last two decades, the analysis and testing of time series models has led to the development of a number of complex methodologies. Time series contain data of mostly a nonstationary nature and with chaotic, dynamic, and nonlinear characteristics. The largest number of time series models is applied from various financial data, but also data from many other areas (for example, engineering science, medicine, COVID-19 studies, physics, social science, and more). Consequently, classical regression models often cannot efficiently analyze complex and dynamical networks of such data.

Numerous studies in the literature have confirmed this statement and offer complex models with strong links to nonlinear dynamics. The most used models are machine learning methods (neural network, support vector regression, long short-term memory, Markov switching models, regression tree, gradient boosting, Bayesian sequential estimation, random forest, and more) and different threshold and regression models (dynamic panel threshold regression model, smooth transition model, Fourier ADF unit root test, etc.). The significance of these models is even greater because most authors use them for predictions of time series data (especially machine learning methods).

The goal of this Special Issue is the interpretation and theoretical and practical implication of existing approaches of complex network analysis of nonlinear time series. The Special Issue will also consider manuscripts that analyze models of time series forecasting, with emphasis on recent developments. Manuscripts should be focused on theoretical-methodological analysis, practical application of complex network methods, and/or future insights of complex nonlinear models.

Dr. Darko Vukovic
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

complex network
nonlinear models
dynamic regression
financial time series management
polynomial function forecasting
learning machine
kernel-based models
nonlinear models of time series forecasting
LSTM, SVM, GMDH, MSA, auto-encoder networks, recurrent neural network
network optimization
multilayer perceptions
exponential smoothing
newbolt/granger grouping scheme
auto-encoder networks
MSA bivariate copula model
chaotic, dynamic, and nonlinear time series data management
threshold regression models
applicative testing of complex nonlinear models in COVID-19 studies, physics, crisis events and different social science cases
theoretical insights of complex nonlinear methodologies

Published Papers (10 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

21 pages, 712 KiB

Open AccessArticle

Network Evolution Model with Preferential Attachment at Triadic Formation Step

by Sergei Sidorov, Timofei Emelianov, Sergei Mironov, Elena Sidorova, Yuri Kostyukhin, Alexandr Volkov, Anna Ostrovskaya and Lyudmila Polezharova

Mathematics 2024, 12(5), 643; https://doi.org/10.3390/math12050643 - 22 Feb 2024

Viewed by 570

Abstract

It is recognized that most real systems and networks exhibit a much higher clustering with comparison to a random null model, which can be explained by a higher probability of the triad formation—a pair of nodes with a mutual neighbor have a greater possibility of having a link between them. To catch the more substantial clustering of real-world networks, the model based on the triadic closure mechanism was introduced by P. Holme and B. J. Kim in 2002. It includes a “triad formation step” in which a newly added node links both to a preferentially chosen node and to its randomly chosen neighbor, therefore forming a triad. In this study, we propose a new model of network evolution in which the triad formation mechanism is essentially changed in comparison to the model of P. Holme and B. J. Kim. In our proposed model, the second node is also chosen preferentially, i.e., the probability of its selection is proportional to its degree with respect to the sum of the degrees of the neighbors of the first selected node. The main goal of this paper is to study the properties of networks generated by this model. Using both analytical and empirical methods, we show that the networks are scale-free with power-law degree distributions, but their exponent

γ

is tunable which is distinguishable from the networks generated by the model of P. Holme and B. J. Kim. Moreover, we show that the degree dynamics of individual nodes are described by a power law. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

18 pages, 527 KiB

Open AccessArticle

Stability Analysis of Recurrent-Neural-Based Controllers Using Dissipativity Domain

by Reza Jafari

Mathematics 2023, 11(14), 3050; https://doi.org/10.3390/math11143050 - 10 Jul 2023

Cited by 1 | Viewed by 740

Abstract

This paper proposes a method for the stability analysis of dynamic neural networks. The stability analysis of dynamic neural networks is a challenging task due to internal feedback connections. In this research work, we propose an algorithm based on the Reduction of Dissipativity Domain (RODD) algorithm. The RODD algorithm is a numerical technique for the detection of the stability of nonlinear dynamic systems. The method works by using an approximation of the reachable set. This paper proposes linear and quadratic approximations of reachable sets. RODD-LB uses a linear approximation, RODD-EB uses a quadratic approximation, and the RODD-Hybrid algorithm uses a combination of the linear and quadratic approximations. The accuracy and convergence of these algorithms were derived through numerical dynamic systems. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

17 pages, 8579 KiB

Open AccessArticle

Spatial–Temporal Dynamic Graph Differential Equation Network for Traffic Flow Forecasting

by Junwei Zhou, Xizhong Qin, Yuanfeng Ding and Haodong Ma

Mathematics 2023, 11(13), 2867; https://doi.org/10.3390/math11132867 - 26 Jun 2023

Cited by 2 | Viewed by 1477

Abstract

Traffic flow forecasting is the foundation of intelligent transportation systems. Accurate traffic forecasting is crucial for intelligent traffic management and urban development. However, achieving highly accurate traffic flow prediction is challenging due to road networks’ complex dynamic spatial and temporal dependencies. Previous work using predefined static adjacency matrices in graph convolutional networks needs to be revised to reflect the dynamic spatial dependencies in the traffic system. In addition, most current methods ignore the hidden dynamic spatial–temporal correlations between road network nodes as they evolve. We propose a spatial–temporal dynamic graph differential equation network (ST-DGDE) for traffic prediction to address the above problems. First, the model captures the dynamic changes between spatial nodes over time through a dynamic graph learning network. Then, dynamic graph differential equations (DGDE) are used to learn the spatial–temporal dynamic relationships in the global space that change continuously over time. Finally, static adjacency matrices are constructed by static node embedding. The generated dynamic and predefined static graphs are fused and input into a gated temporal causal convolutional network to jointly capture the fixed long-term spatial association patterns and achieve a global receiver domain that facilitates long-term prediction. Experiments of our model on two natural traffic flow datasets show that ST-DGDE outperforms other baselines. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

14 pages, 1006 KiB

Open AccessArticle

Tourism Employment and Economic Growth: Dynamic Panel Threshold Analysis

by Darko B. Vuković, Moinak Maiti and Marko D. Petrović

Mathematics 2023, 11(5), 1112; https://doi.org/10.3390/math11051112 - 23 Feb 2023

Cited by 2 | Viewed by 1521

Abstract

The manuscript reports on findings on the interconnection between tourism employment and economic growth for the selected OECD member states. The dynamic panel threshold regression method was used to analyze the data, where the threshold variable was tourism employment, and the growth of gross national income and value added by activity services were dependent variables in the corresponding models. The dataset covered the period between 2008 and 2020. Both marginal effects indicated positive implications of tourism employment on economic growth. A percent rise in tourism employment leads to an increase in gross national income by 0.15% (in the low regime) and 0.61% (in the high regime). Yet, the results revealed a negative marginal effect of tourism employment on value added by activity services. The outcomes explain that a percent rise in tourism employment in the average country will lead to a decrease in the value added by activity services, as a percentage of value added, by 0.07% (low regime) and 0.09% (high regime). Therefore, the applications of this study are twofold—the first one is its contribution to existing theoretical knowledge through the filling of the literature gaps, and the second one is related to advances in the standing policies. The main limitations and the proposal for future research are the application of random effects and smooth transition threshold models as an alternative to the indicator functions. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

20 pages, 4679 KiB

Open AccessArticle

Application of Solar Activity Time Series in Machine Learning Predictive Modeling of Precipitation-Induced Floods

by Slavica Malinović-Milićević, Milan M. Radovanović, Sonja D. Radenković, Yaroslav Vyklyuk, Boško Milovanović, Ana Milanović Pešić, Milan Milenković, Vladimir Popović, Marko Petrović, Petro Sydor and Mirjana Gajić

Mathematics 2023, 11(4), 795; https://doi.org/10.3390/math11040795 - 04 Feb 2023

Cited by 3 | Viewed by 2747

Abstract

This research is devoted to the determination of hidden dependencies between the flow of particles that come from the Sun and precipitation-induced floods in the United Kingdom (UK). The analysis covers 20 flood events during the period from October 2001 to December 2019. The parameters of solar activity were used as model input data, while precipitations data in the period 10 days before and during each flood event were used as model output. The time lag of 0–9 days was taken into account in the research. Correlation analysis was conducted to determine the degree of randomness for the time series of input and output parameters. For establishing a potential causative link, machine learning classification predictive modeling was applied. Two approaches, the decision tree, and the random forest were used. We analyzed the accuracy of classification models forecast from 0 to 9 days in advance. It was found that the most important factors for flood forecasting are proton density with a time lag of 9, differential proton flux in the range of 310–580 keV, and ion temperature. Research in this paper has shown that the decision tree model is more accurate and adequate in predicting the appearance of precipitation-induced floods up to 9 days ahead with an accuracy of 91%. The results of this study confirmed that by increasing technical capabilities, using improved machine learning techniques and large data sets, it is possible to improve the understanding of the physical link between the solar wind and tropospheric weather and help improve severe weather forecasting. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

24 pages, 1016 KiB

Open AccessArticle

A Multi Parameter Forecasting for Stock Time Series Data Using LSTM and Deep Learning Model

by Shahzad Zaheer, Nadeem Anjum, Saddam Hussain, Abeer D. Algarni, Jawaid Iqbal, Sami Bourouis and Syed Sajid Ullah

Mathematics 2023, 11(3), 590; https://doi.org/10.3390/math11030590 - 22 Jan 2023

Cited by 26 | Viewed by 5675

Abstract

Financial data are a type of historical time series data that provide a large amount of information that is frequently employed in data analysis tasks. The question of how to forecast stock prices continues to be a topic of interest for both investors and financial professionals. Stock price forecasting is quite challenging because of the significant noise, non-linearity, and volatility of time series data on stock prices. The previous studies focus on a single stock parameter such as close price. A hybrid deep-learning, forecasting model is proposed. The model takes the input stock data and forecasts two stock parameters close price and high price for the next day. The experiments are conducted on the Shanghai Composite Index (000001), and the comparisons have been performed by existing methods. These existing methods are CNN, RNN, LSTM, CNN-RNN, and CNN-LSTM. The generated result shows that CNN performs worst, LSTM outperforms CNN-LSTM, CNN-RNN outperforms CNN-LSTM, CNN-RNN outperforms LSTM, and the suggested single Layer RNN model beats all other models. The proposed single Layer RNN model improves by 2.2%, 0.4%, 0.3%, 0.2%, and 0.1%. The experimental results validate the effectiveness of the proposed model, which will assist investors in increasing their profits by making good decisions. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

24 pages, 1669 KiB

Open AccessArticle

by Mustafa Özer, Serap Kamisli, Fatih Temizel and Melik Kamisli

Mathematics 2023, 11(1), 196; https://doi.org/10.3390/math11010196 - 30 Dec 2022

Viewed by 2004

Abstract

The aim of this study was to investigate the causal relations between COVID-19 economic supports and Bitcoin markets. For this purpose, we first determined the degree of the integration of variables by implementing Fourier Augmented Dickey–Fuller unit root tests. Then, we carried out both linear (Bootstrap Toda–Yamamoto) and non-linear (Fractional Frequency Flexible Fourier form Toda–Yamamoto) causality tests to consider the nonlinearities in variables, to determine if the effects of multiple structural breaks were temporary or permanent, and to evaluate the unidirectional causality running from COVID-19-related economic supports and the price, volatility, and trading volume of Bitcoin. Our study included 158 countries, and we used daily data over the period from 1 January 2020 and 10 March 2022. The findings of this study provide evidence of unidirectional causalities running from COVID-19-related economic supports to the price, volatility, and trading volume of Bitcoin in most of the countries in the sample. The application of non-linear causality tests helped us obtain more evidence about these causalities. Some of these causalities were found to be permanent, and some of them were found to be temporary. The results of the study indicate that COVID-19-related economic supports can be considered a major driver of the surge in the Bitcoin market during the pandemic. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

17 pages, 1220 KiB

Open AccessArticle

The Dollar Exchange Rate, Adjustment to the Purchasing Power Parity, and the Interest Rate Differential

by Michael Frömmel, Darko B. Vukovic and Jinyuan Wu

Mathematics 2022, 10(23), 4504; https://doi.org/10.3390/math10234504 - 29 Nov 2022

Viewed by 1464

Abstract

This study applies a Markov switching error correction model to describe the single most important real exchange rate (Deutsche mark versus US dollar) over the flexible exchange rates period from 1973 to 2004. We show an alternative way of modelling non-linear adjustment to the purchasing power parity (PPP) besides standard threshold models. The model merges the two possible sources of non-linearity by additionally allowing the probability of a mean-reverting regime to increase with the distance from PPP. The interest rate differential as an additional determinant of real exchange rate behaviour in a Markov switching framework is introduced in the model. The study finds that the real dollar exchange rate during the post-Bretton Woods era is well described by a Markov switching error correction model with (PPP) as long-run equilibrium. There is one mean reversion regime where PPP and the interest parity condition are valid. Contrary, the second regime is characterised by persistent mean aversion, where a regime switch does not become more likely with increasing distance from PPP. The unconditional half-life of shocks is about 1.5 years. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

14 pages, 1562 KiB

Open AccessArticle

Two-Dimensional Correlation Analysis of Periodicity in Noisy Series: Case of VLF Signal Amplitude Variations in the Time Vicinity of an Earthquake

by Andjelka B. Kovačević, Aleksandra Nina, Luka Č. Popović and Milan Radovanović

Mathematics 2022, 10(22), 4278; https://doi.org/10.3390/math10224278 - 15 Nov 2022

Cited by 2 | Viewed by 1057

Abstract

Extraction of information in the form of oscillations from noisy data of natural phenomena such as sounds, earthquakes, ionospheric and brain activity, and various emissions from cosmic objects is extremely difficult. As a method for finding periodicity in such challenging data sets, the 2D Hybrid approach, which employs wavelets, is presented. Our technique produces a wavelet transform correlation intensity contour map for two (or one) time series on a period plane defined by two independent period axes. Notably, by spreading peaks across the second dimension, our method improves the apparent resolution of detected oscillations in the period plane and identifies the direction of signal changes using correlation coefficients. We demonstrate the performance of the 2D Hybrid technique on a very low frequency (VLF) signal emitted in Italy and recorded in Serbia in time vicinity of the occurrence of an earthquake on 3 November 2010, near Kraljevo, Serbia. We identified a distinct signal in the range of 120–130 s that appears only in association with the considered earthquake. Other wavelets, such as Superlets, which may detect fast transient oscillations, will be employed in future analysis. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

26 pages, 6946 KiB

Open AccessArticle

Dynamic Connectedness among Vaccine Companies’ Stock Prices: Before and after Vaccines Released

by Kazi Sohag, Anna Gainetdinova, Shawkat Hammoudeh and Riad Shams

Mathematics 2022, 10(15), 2812; https://doi.org/10.3390/math10152812 - 08 Aug 2022

Cited by 2 | Viewed by 1993

Abstract

This study investigates the interconnectedness among the stocks of the publicly listed vaccine-producing companies before and after vaccine releases in 2020/21. In doing so, the study utilizes the daily frequency equity returns of the major vaccine producers, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. First, the investigation applies the TVP-VAR Dynamic Connectedness approach to explore the time–frequency connectedness between the stocks of those vaccine producers. The empirical findings demonstrate that Moderna performs as the most prominent net volatility contributor, whereas Sinopharm is the highest net volatility receiver. Interestingly, the vaccine release significantly increases the stock market connectedness among our sampled vaccine companies. Second, the cross-quantile dependency framework allows for the observation of the interconnectedness under the bearish and bullish stock market conditions by splitting any paired variables into 19 quantiles when considering short-, medium- and long-memories. The results also show that a high level of connectivity among the vaccine producers exists under bullish stock market conditions. Notably, Moderna transmits significant volatility spillovers to Sinopharm, Johnson & Johnson and AstraZeneca under both the bearish and bullish conditions, though the volatility transmission from Moderna to Pfizer is less pronounced. The policy implication proposes that the vaccine release allows companies to increase their stock returns and induce substantial volatility spillovers from company to company. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Journal Menu

Journal Browser

Complex Network Analysis of Nonlinear Time Series

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (10 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI