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Mathematics
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Time Series Analysis
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Time Series Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (15 September 2023) | Viewed by 23678

Special Issue Editor

Prof. Dr. Paweł Kliber

E-Mail Website
Guest Editor
Department of Econometrics, Poznan University of Economics and Business, Poznan, Poland.
Interests: financial econometrics, time series econometrics, time series analysis

Special Issue Information

Dear Colleagues,

Time series data are probably among the most common forms of data, as they are connected to a systematic collection of observations over time. Time series analysis has two main fields of application. The first is the analysis of historical data. On the basis of these data, it is possible to draw specific conclusions about the data-generating process, which allows information about the system under study to be obtained (regardless of whether it is a machine, social or biological system). The second application is forecasting. Based on historical data and taking into account the nature of the data-generating process, it is possible to forecast the possible further development of the phenomenon under study. Application of the methodology developed by Box and Jenkins in the 1970s showed that simple models based on time series analysis often allow for more accurate predictions than those of complex cause and effect models.

This Special Issue aims to collect new achievements in the theory as well as in the applications of time series analysis. Engineering and social sciences (especially economics) are the main fields of applications of this type of analysis; however, there are many other fields of multidisciplinary applications.

Prof. Dr. Paweł Kliber
Guest Editor

Manuscript Submission Information

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Keywords

  • theoretical aspects of time series (stochastic processes with discrete time)
  • econometrical and technical applications
  • forecasting and assessment of forecasts
  • multiple time series and cointegration
  • time series with changes in regime
  • stationarity of time series and long-term memory
  • forecasting based on time series analysis
  • state-space models and kalman filters
  • filtering of stochastic processes
  • spectral analysis

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Published Papers (10 papers)

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Research

18 pages, 15610 KiB  
Article
Generalized Pandemic Model with COVID-19 for Early-Stage Infection Forecasting
by Mirna Patricia Ponce-Flores, Jesús David Terán-Villanueva, Salvador Ibarra-Martínez and José Antonio Castán-Rocha
Mathematics 2023, 11(18), 3924; https://doi.org/10.3390/math11183924 - 15 Sep 2023
Viewed by 1019
Abstract
In this paper, we tackle the problem of forecasting future pandemics by training models with a COVID-19 time series. We tested this approach by producing one model and using it to forecast a non-trained time series; however, we limited this paper to the [...] Read more.
In this paper, we tackle the problem of forecasting future pandemics by training models with a COVID-19 time series. We tested this approach by producing one model and using it to forecast a non-trained time series; however, we limited this paper to the eight states with the highest population density in Mexico. We propose a generalized pandemic forecasting framework that transforms the time series into a dataset via three different transformations using random forest and backward transformations. Additionally, we tested the impact of the horizon and dataset window sizes for the training phase. A Wilcoxon test showed that the best transformation technique statistically outperformed the other two transformations with 100% certainty. The best transformation included the accumulated efforts of the other two plus a normalization that helped rescale the non-trained time series, improving the sMAPE from the value of 25.48 attained for the second-best transformation to 13.53. The figures in the experimentation section show promising results regarding the possibility of forecasting the early stages of future pandemics with trained data from the COVID-19 time series. Full article
(This article belongs to the Special Issue Time Series Analysis)
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20 pages, 2704 KiB  
Article
Two-Threshold-Variable Integer-Valued Autoregressive Model
by Jiayue Zhang, Fukang Zhu and Huaping Chen
Mathematics 2023, 11(16), 3586; https://doi.org/10.3390/math11163586 - 18 Aug 2023
Cited by 3 | Viewed by 1365
Abstract
In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some [...] Read more.
In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model. Full article
(This article belongs to the Special Issue Time Series Analysis)
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19 pages, 725 KiB  
Article
Forecasting Day-Ahead Brent Crude Oil Prices Using Hybrid Combinations of Time Series Models
by Hasnain Iftikhar, Aimel Zafar, Josue E. Turpo-Chaparro, Paulo Canas Rodrigues and Javier Linkolk López-Gonzales
Mathematics 2023, 11(16), 3548; https://doi.org/10.3390/math11163548 - 16 Aug 2023
Cited by 33 | Viewed by 3921
Abstract
Crude oil price forecasting is an important research area in the international bulk commodity market. However, as risk factors diversify, price movements exhibit more complex nonlinear behavior. Hence, this study provides a comprehensive analysis of forecasting Brent crude oil prices by comparing various [...] Read more.
Crude oil price forecasting is an important research area in the international bulk commodity market. However, as risk factors diversify, price movements exhibit more complex nonlinear behavior. Hence, this study provides a comprehensive analysis of forecasting Brent crude oil prices by comparing various hybrid combinations of linear and nonlinear time series models. To this end, first, the logarithmic transformation is used to stabilize the variance of the crude oil prices time series; second, the original time series of log crude oil prices is decomposed into two new subseries, such as a long-run trend series and a stochastic series, using the Hodrick–Prescott filter; and third, two linear and two nonlinear time series models are considered to forecast the decomposed subseries. Finally, the forecast results for each subseries are combined to obtain the final day-ahead forecast result. The proposed modeling framework is applied to daily Brent spot prices from 1 January 2013 to 27 December 2022. Six different accuracy metrics, pictorial analysis, and a statistical test are performed to verify the proposed methodology’s performance. The experimental results (accuracy measures, pictorial analysis, and statistical test) show the efficiency and accuracy of the proposed hybrid forecasting methodology. Additionally, our forecasting results are comparatively better than the benchmark models. Finally, we believe that the proposed forecasting method can be used for other complex financial time data to obtain highly efficient and accurate forecasts. Full article
(This article belongs to the Special Issue Time Series Analysis)
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15 pages, 696 KiB  
Article
A Long-Term Prediction Method of Computer Parameter Degradation Based on Curriculum Learning and Transfer Learning
by Yuanhong Mao, Zhong Ma, Xi Liu, Pengchao He and Bo Chai
Mathematics 2023, 11(14), 3098; https://doi.org/10.3390/math11143098 - 13 Jul 2023
Cited by 2 | Viewed by 1391
Abstract
The long-term prediction of the degradation of key computer parameters improves maintenance performance. Traditional prediction methods may suffer from cumulative errors in iterative prediction, which affect the model’s long-term prediction accuracy. Our network adopts curriculum learning and transfer learning methods, which can effectively [...] Read more.
The long-term prediction of the degradation of key computer parameters improves maintenance performance. Traditional prediction methods may suffer from cumulative errors in iterative prediction, which affect the model’s long-term prediction accuracy. Our network adopts curriculum learning and transfer learning methods, which can effectively solve this problem. The training network uses a dual-branch Siamese network. One branch intermixes the predicted and annotated data as input and uses curriculum learning to train. The other branch uses the original annotated data for training. To further align the hidden distributions of the two branches, the transfer learning method calculates the covariance matrices of the time series of the two branches by correlation alignment loss. A single branch is used in the test for prediction without increasing the inference computation. Compared with the current mainstream networks, our method can effectively improve the accuracy of long-term prediction with the improvements above. Full article
(This article belongs to the Special Issue Time Series Analysis)
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16 pages, 514 KiB  
Article
An Excess Entropy Approach to Classify Long-Term and Short-Term Memory Stationary Time Series
by Xuyan Xiang and Jieming Zhou
Mathematics 2023, 11(11), 2448; https://doi.org/10.3390/math11112448 - 25 May 2023
Cited by 2 | Viewed by 1471
Abstract
Long-term memory behavior is one of the most important phenomena that has appeared in the time series analysis. Different from most definitions of second-order properties, an excess entropy approach is developed for stationary time series to classify long-term and short-term memory. A stationary [...] Read more.
Long-term memory behavior is one of the most important phenomena that has appeared in the time series analysis. Different from most definitions of second-order properties, an excess entropy approach is developed for stationary time series to classify long-term and short-term memory. A stationary sequence with finite block entropy is long-term memory if its excess entropy is infinite. The simulation results are graphically demonstrated after some theoretical results are simply presented by various stochastic sequences. Such an approach has advantages over the traditional ways that the excess entropy of stationary sequence with finite block entropy is invariant under instantaneous one-to-one transformation, and that it only requires very weak moment conditions rather than second-order moment conditions and thus can be applied to distinguish the LTM behavior of stationary sequences with unbounded second moment (e.g., heavy tail distribution). Finally, several applications on real data are exhibited. Full article
(This article belongs to the Special Issue Time Series Analysis)
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16 pages, 4291 KiB  
Article
Temperature Time Series Prediction Model Based on Time Series Decomposition and Bi-LSTM Network
by Kun Zhang, Xing Huo and Kun Shao
Mathematics 2023, 11(9), 2060; https://doi.org/10.3390/math11092060 - 26 Apr 2023
Cited by 8 | Viewed by 4013
Abstract
Utilizing a temperature time-series prediction model to achieve good results can help us to accurately sense the changes occurring in temperature levels in advance, which is important for human life. However, the random fluctuations occurring in a temperature time series can reduce the [...] Read more.
Utilizing a temperature time-series prediction model to achieve good results can help us to accurately sense the changes occurring in temperature levels in advance, which is important for human life. However, the random fluctuations occurring in a temperature time series can reduce the accuracy of the prediction model. Decomposing the time-series data prior to performing a prediction can effectively reduce the influence of random fluctuations in the data and consequently improve the prediction accuracy results. In the present study, we propose a temperature time-series prediction model that combines the seasonal-trend decomposition procedure based on the loess (STL) decomposition method, the jumps upon spectrum and trend (JUST) algorithm, and the bidirectional long short-term memory (Bi-LSTM) network. This model can achieve daily average temperature predictions for cities located in China. Firstly, we decompose the time series into trend, seasonal, and residual components using the JUST and STL algorithms. Then, the components determined by the two methods are combined. Secondly, the three components and original data are fed into the two-layer Bi-LSTM model for training purposes. Finally, the prediction results achieved for both the components and original data are merged by learnable weights and output as the final result. The experimental results show that the average root mean square and average absolute errors of our proposed model on the dataset are 0.2187 and 0.1737, respectively, which are less than the values 4.3997 and 3.3349 attained for the Bi-LSTM model, 2.5343 and 1.9265 for the EMD-LSTM model, and 0.9336 and 0.7066 for the STL-LSTM model. Full article
(This article belongs to the Special Issue Time Series Analysis)
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22 pages, 6975 KiB  
Article
Nonstationary Time Series Prediction Based on Deep Echo State Network Tuned by Bayesian Optimization
by Yu-Ting Bai, Wei Jia, Xue-Bo Jin, Ting-Li Su, Jian-Lei Kong and Zhi-Gang Shi
Mathematics 2023, 11(6), 1503; https://doi.org/10.3390/math11061503 - 20 Mar 2023
Cited by 6 | Viewed by 2788
Abstract
The predictions from time series data can help us sense development trends and make scientific decisions in advance. The commonly used forecasting methods with backpropagation consume a lot of computational resources. The deep echo state network (DeepESN) is an advanced prediction method with [...] Read more.
The predictions from time series data can help us sense development trends and make scientific decisions in advance. The commonly used forecasting methods with backpropagation consume a lot of computational resources. The deep echo state network (DeepESN) is an advanced prediction method with a deep neural network structure and training algorithm without backpropagation. In this paper, a Bayesian optimization algorithm (BOA) is proposed to optimize DeepESN to address the problem of increasing parameter scale. Firstly, the DeepESN was studied and constructed as the basic prediction model for the time series data. Secondly, the BOA was reconstructed, based on the DeepESN, for optimal parameter searching. The algorithm is proposed within the framework of the DeepESN. Thirdly, an experiment was conducted to verify the DeepESN with a BOA within three datasets: simulation data generated from computer programs, a real humidity dataset collected from Beijing, and a power load dataset obtained from America. Compared with the models of BP (backpropagation), LSTM (long short-term memory), GRU (gated recurrent unit), and ESN (echo state network), DeepESN obtained optimal results, which were 0.0719, 18.6707, and 764.5281 using RMSE evaluation. While getting better accuracy, the BOA optimization time was only 323.4 s, 563.2 s, and 9854 s for the three datasets. It is more efficient than grid search and grey wolf optimizer. Full article
(This article belongs to the Special Issue Time Series Analysis)
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18 pages, 977 KiB  
Article
Prediction of Infectious Disease to Reduce the Computation Stress on Medical and Health Care Facilitators
by Shalini Shekhawat, Akash Saxena, Ramadan A. Zeineldin and Ali Wagdy Mohamed
Mathematics 2023, 11(2), 490; https://doi.org/10.3390/math11020490 - 16 Jan 2023
Cited by 2 | Viewed by 1832
Abstract
Prediction of the infectious disease is a potential research area from the decades. With the progress in medical science, early anticipation of the disease spread becomes more meaningful when the resources are limited. Also spread prediction with limited data pose a deadly challenge [...] Read more.
Prediction of the infectious disease is a potential research area from the decades. With the progress in medical science, early anticipation of the disease spread becomes more meaningful when the resources are limited. Also spread prediction with limited data pose a deadly challenge to the practitioners. Hence, the paper presents a case study of the Corona virus (COVID-19). COVID-19 has hit the major parts of the world and implications of this virus, is life threatening. Research community has contributed significantly to understand the spread of virus with time, along with meteorological conditions and other parameters. Several forecasting techniques have already been deployed for this. Considering the fact, the paper presents a proposal of two Rolling horizon based Cubic Grey Models (RCGMs). First, the mathematical details of Cubic Polynomial based simple grey model is presented than two models based on time series rolling are proposed. The models are developed with the time series data of different locations, considering diverse overlap period and rolling values. It is observed that the proposed models yield satisfactory results as compared with the conventional and advanced grey models. The comparison of the performance has been carried out with calculation of standard error indices. At the end, some recommendations are also framed for the authorities, that can be helpful for decision making in tough time. Full article
(This article belongs to the Special Issue Time Series Analysis)
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24 pages, 470 KiB  
Article
Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes
by Muhammed Rasheed Irshad, Christophe Chesneau, Veena D’cruz, Naushad Mamode Khan and Radhakumari Maya
Mathematics 2022, 10(20), 3835; https://doi.org/10.3390/math10203835 - 17 Oct 2022
Cited by 1 | Viewed by 1564
Abstract
Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on [...] Read more.
Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These BINAR(1) processes are mainly focused on over-dispersion. This paper aims to propose new bivariate distributions and processes based on a recently proposed over-dispersed distribution: the Poisson 2S-Lindley distribution. The new bivariate distributions, denoted by the abbreviations BP2S-L(I) and BP2S-L(II), are then used as innovation distributions for the BINAR(1) process. Properties are investigated for both distributions as well as for the BINAR(1) processes. The distribution parameters are estimated using the maximum likelihood method, and the BINAR(1)BP2S-L(I) and BINAR(1)BP2S-L(II) process parameters are estimated using the conditional least squares and conditional maximum likelihood methods. Monte Carlo simulation experiments are conducted to study large and small sample performances and for the comparison of the estimation methods. The Pittsburgh crime series and candy sales datasets are then used to compare the new BINAR(1) processes to some other existing BINAR(1) processes in the literature. Full article
(This article belongs to the Special Issue Time Series Analysis)
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21 pages, 9662 KiB  
Article
Adaptive Broad Echo State Network for Nonstationary Time Series Forecasting
by Wen-Jie Liu, Yu-Ting Bai, Xue-Bo Jin, Ting-Li Su and Jian-Lei Kong
Mathematics 2022, 10(17), 3188; https://doi.org/10.3390/math10173188 - 3 Sep 2022
Cited by 5 | Viewed by 2060
Abstract
Time series forecasting provides a vital basis for the control and management of various systems. The time series data in the real world are usually strongly nonstationary and nonlinear, which increases the difficulty of reliable forecasting. To fully utilize the learning capability of [...] Read more.
Time series forecasting provides a vital basis for the control and management of various systems. The time series data in the real world are usually strongly nonstationary and nonlinear, which increases the difficulty of reliable forecasting. To fully utilize the learning capability of machine learning in time series forecasting, an adaptive broad echo state network (ABESN) is proposed in this paper. Firstly, the broad learning system (BLS) is used as a framework, and the reservoir pools in the echo state network (ESN) are introduced to form the broad echo state network (BESN). Secondly, for the problem of information redundancy in the reservoir structure in BESN, an adaptive optimization algorithm for the BESN structure based on the pruning algorithm is proposed. Thirdly, an adaptive optimization algorithm of hyperparameters based on the nonstationary test index is proposed. In brief, the structure and hyperparameter optimization algorithms are studied to form the ABESN based on the proposed BESN model in this paper. The ABESN is applied to the data forecasting of air humidity and electric load. The experiments show that the proposed ABESN has a better learning ability for nonstationary time series data and can achieve higher forecasting accuracy. Full article
(This article belongs to the Special Issue Time Series Analysis)
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