论文信息 - Intuitionistic Fuzzy Time Series: An Approach for Handling Nondeterminism in Time Series Forecasting

2011 - Neurocomputing

A novel neural network ensemble architecture for time series forecasting

We propose a novel homogeneous neural network ensemble approach called Generalized Regression Neural Network (GEFTS-GRNN) Ensemble for Forecasting Time Series, which is a concatenation of existing machine learning algorithms. GEFTS uses a dynamic nonlinear weighting system wherein the outputs from several base-level GRNNs are combined using a combiner GRNN to produce the final output. We compare GEFTS with the 11 most used algorithms on 30 real datasets. The proposed algorithm appears to be more powerful than existing ones. Unlike conventional algorithms, GEFTS is effective in forecasting time series with seasonal patterns.

2012 - Appl. Soft Comput.

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.

2000

Multivariate Analysis in Vector Time Series

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Pena and Box (1987) and Pena and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.

2006 - African Journal of Ecology

Assessing fragmentation and disturbance of west Kenyan rainforests by means of remotely sensed time series data and landscape metrics

Biodiversity in tropical rainforests is heavily influenced by land use/cover change (LUCC), but so far there have been few LUCC studies conducted in Africa. We present several methods that make use of remotely sensed data and landscape metrics and allow for assessment of the development of land cover and thus forest fragmentation and disturbance over a substantial period of time. The study covers Kakamega Forest and its associated forest areas in western Kenya, over the last 30 years. The accuracy of a supervised multispectral classification of Landsat time series data encompassing seven time steps between 1972 and 2001 is numerically assessed using ground truth reference data considering the 2001 time step. Here, buffering the forest areas by 1 km, highest user's accuracies for the forest classes ‘near natural + old secondary forest’ (87.50%), ‘secondary forest’ (80.00%) and ‘bushland/shrubs’ (81.08%) are revealed. Images of a spatially distributed fragmentation index derived from the land cover time series by applying a three by 3 pixel-sized moving window to determine forest pixels’ adjacency, highlight trends in forest fragmentation, e.g. the splitting into two separate forests along the Yala/Ikuywa corridor. Calculations of mean fragmentation indices for the Biodiversity Monitoring Transect Analysis in Eastern Africa (BIOTA-East Africa) focus research areas are used to evaluate the fragmentation index and to demonstrate its potential to extrapolate (e.g. biological) field findings in space and time. Here we argue for a correlation of the fragmentation indices results not only with forest management regimes, but with population distribution and accessibility (e.g. by roads). A cluster analysis applying the isodata-algorithm on the classification results of all seven times steps allows for a rapid visual assessment of the distinct pattern of typical land cover development trends since 1972. This reveals that parts of Kakamega Forest have experienced severe forest loss while others, especially in the north-east, show signs of succession. Resume La biodiversite des forets pluviales tropicales est fort influencee par les changements d'utilisation et de couverture du sol (land use/cover change– LUCC), mais il y a eu jusqu’a present fort peu d’etudes des LUCC en Afrique. Nous presentons plusieurs methodes qui utilisent des donnees de teledetection et d’ecologie spatiale et permettent d’evaluer le developpement du couvert forestier et donc de la fragmentation et des perturbations durant une periode substantielle. L’etude concerne la foret de Kakamega et toute les zones forestieres qui lui sont associees dans l'ouest du Kenya, au cours des 30 dernieres annees. L'exactitude d'une classification multispectrale de donnees sur des series temporelles Landsat, qui regroupent sept etapes chronologiques entre 1972 et 2001, est evaluee numeriquement en utilisant les donnees reelles de «verite terrain» correspondant a l’etape de 2001. En quadrillant la foret en unites d'un km de cote, l'utilisateur obtient les plus grandes precisions pour les classes de forets «presque naturelle + ancienne foret secondaire» (87,50%), «forets secondaires» (80,00%) et «Brousse/buissons» (81,08%). Des images de l'index de fragmentation spatialement distribue, derivees de series temporelles de la couverture du sol en appliquant une fenetre glissante de trois pixels sur trois pour determiner l'adjacence des pixels, mettent en evidence les tendances de la fragmentation de la foret, par exemple la separation en deux forets separees le long du corridor Yala/Ikuywa. Les calculs des indices de fragmentation moyens pour les zones centrales de recherche de BIOTA-est servent aevaluer l'indice de fragmentation et a demontrer son potentiel pour extrapoler des decouvertes (ex. biologiques) de terrain dans l'espace et le temps. Nous defendons ici une correlation des resultats des indices de fragmentation non seulement avec les regimes de gestion forestiere, mais aussi avec la distribution de la population et l'accessibilite (routes). Une analyse d'ensemble appliquant l'algorithme de seuillage aux resultats de l'application des sept etapes permet une evaluation visuelle rapide du pattern distinct des tendances typiques du developpement de la couverture vegetale depuis 1972. Ceci revele que des parties de la foret de Kakamega ont connu de graves pertes forestieres alors que d'autres, specialement au nord-est, presentent des signes de succession.

2010 - IEEE Transactions on Power Systems

Notice of Violation of IEEE Publication PrinciplesA Hybrid ARIMA and Neural Network Model for Short-Term Price Forecasting in Deregulated Market

In the framework of competitive electricity markets, power producers and consumers need accurate price forecasting tools. Price forecasts embody crucial information for producers and consumers when planning bidding strategies in order to maximize their benefits and utilities, respectively. The choice of the forecasting model becomes the important influence factor on how to improve price forecasting accuracy. This paper provides a hybrid methodology that combines both autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) models for predicting short-term electricity prices. This method is examined by using the data of Australian national electricity market, New South Wales, in the year 2006. Comparison of forecasting performance with the proposed ARIMA, ANN, and hybrid models are presented. Empirical results indicate that a hybrid ARIMA-ANN model can improve the price forecasting accuracy.

1995

The Impact of Empirical Accuracy Studies On Time Series Analysis and Forecasting

Cet article concerne un domaine important de statistique : l'application de l'analyse de series chronologiques a la prevision, notamment dans l'economie et les affaires. Ce domaine est inhabituel en sciences sociales car il permet l'experimentation objective, replicable et controlee par des etudes empiriques qui utilisent des donnees de la vie courante. Dans cet article nous examinons l'importante recherche empirique qui a ete faite dans ce domaine depuis deux decennies et nous comparons les principaux resultats d'une telle recherche avec ce a quoi nous pourrions nous attendre si le paradigme statistique restait le meme. Ainsi nous remarquons plusieurs anomalies qui ne peuvent pas etre expliquees facilement. En utilisant l'analyse de citation, nous montrons qu'il y a eu peu de travail theoretique qui a pris de tels resultats en compte. En consequence il y a eu peu ou meme pas de progres du tout pour redefinir le paradigme dominant en statistique des series chronologiques et faire avancer le domaine de recherche dans la direction de la precision amelioree de la prevision des valeurs futures. Que l'objectif soit la precision de la prevision des valeurs futures ou bien la validation du modele, il faut reexaminer l'hypothese qui est faite d'habitude dans le domaine de la prevision de series chronologiques, que les donnees aient une structure constante ou stationnaire. Ceux qui travaillent dans le domaine de la recherche appliquee ou empirique ont besoin d'un cadre theorique dans lequel ils peuvent developper des methodes de prevision ameliorees et etablir un critere de selection efficace. Nous decrivons plusieurs domaines de priorite pour la recherche, y compris le modelisme robuste et l'utilisation de la connaissance des informations dans leur contexte particulier pour identifier un modele. L'article se termine par un defi pour les statisticiens de series chronologiques theoretiques et les chercheurs empiriques : en travaillant ensemble, peuvent-ils apprendre les uns des autres ? S'ils reussissent, leurs conclusions devraient permettre d'avancer dans le domaine afin de mieux servir ceux qui sont engages dans la prise de decisions ou d'orientations politiques d'une facon qui les aidera a beneficier de predictions plus precises. Il est egalement important que les competitions de previsions puissent fournir aux chercheurs un banc d'essai qui puisse diriger l'evolution de leur discipline et la rendre plus utile et pertinente aux applications de la vie courante.

2020 - J. Mach. Learn. Res.

Tslearn, A Machine Learning Toolkit for Time Series Data

tslearn is a general-purpose Python machine learning library for time series that offers tools for pre-processing and feature extraction as well as dedicated models for clustering, classification and regression. It follows scikit-learn's Application Programming Interface for transformers and estimators, allowing the use of standard pipelines and model selection tools on top of tslearn objects. It is distributed under the BSD-2-Clause license, and its source code is available at https://github.com/tslearn-team/tslearn.

2015 - IIE Transactions

Time series forecasting for nonlinear and non-stationary processes: a review and comparative study

Forecasting the evolution of complex systems is noted as one of the 10 grand challenges of modern science. Time series data from complex systems capture the dynamic behaviors and causalities of the underlying processes and provide a tractable means to predict and monitor system state evolution. However, the nonlinear and non-stationary dynamics of the underlying processes pose a major challenge for accurate forecasting. For most real-world systems, the vector field of state dynamics is a nonlinear function of the state variables; i.e., the relationship connecting intrinsic state variables with their autoregressive terms and exogenous variables is nonlinear. Time series emerging from such complex systems exhibit aperiodic (chaotic) patterns even under steady state. Also, since real-world systems often evolve under transient conditions, the signals obtained therefrom tend to exhibit myriad forms of non-stationarity. Nonetheless, methods reported in the literature focus mostly on forecasting linear and stationary processes. This article presents a review of these advancements in nonlinear and non-stationary time series forecasting models and a comparison of their performances in certain real-world manufacturing and health informatics applications. Conventional approaches do not adequately capture the system evolution (from the standpoint of forecasting accuracy, computational effort, and sensitivity to quantity and quality of a priori information) in these applications.

2019 - IEEE Access

DeepAnT: A Deep Learning Approach for Unsupervised Anomaly Detection in Time Series

Traditional distance and density-based anomaly detection techniques are unable to detect periodic and seasonality related point anomalies which occur commonly in streaming data, leaving a big gap in time series anomaly detection in the current era of the IoT. To address this problem, we present a novel deep learning-based anomaly detection approach (DeepAnT) for time series data, which is equally applicable to the non-streaming cases. DeepAnT is capable of detecting a wide range of anomalies, i.e., point anomalies, contextual anomalies, and discords in time series data. In contrast to the anomaly detection methods where anomalies are learned, DeepAnT uses unlabeled data to capture and learn the data distribution that is used to forecast the normal behavior of a time series. DeepAnT consists of two modules: time series predictor and anomaly detector. The time series predictor module uses deep convolutional neural network (CNN) to predict the next time stamp on the defined horizon. This module takes a window of time series (used as a context) and attempts to predict the next time stamp. The predicted value is then passed to the anomaly detector module, which is responsible for tagging the corresponding time stamp as normal or abnormal. DeepAnT can be trained even without removing the anomalies from the given data set. Generally, in deep learning-based approaches, a lot of data are required to train a model. Whereas in DeepAnT, a model can be trained on relatively small data set while achieving good generalization capabilities due to the effective parameter sharing of the CNN. As the anomaly detection in DeepAnT is unsupervised, it does not rely on anomaly labels at the time of model generation. Therefore, this approach can be directly applied to real-life scenarios where it is practically impossible to label a big stream of data coming from heterogeneous sensors comprising of both normal as well as anomalous points. We have performed a detailed evaluation of 15 algorithms on 10 anomaly detection benchmarks, which contain a total of 433 real and synthetic time series. Experiments show that DeepAnT outperforms the state-of-the-art anomaly detection methods in most of the cases, while performing on par with others.

2008 - Neurocomputing

Forecasting models for interval-valued time series

This paper presents approaches to interval-valued time series forecasting. The first and second approaches are based on the autoregressive (AR) and autoregressive integrated moving average (ARIMA) models, respectively. The third approach is based on an artificial neural network (ANN) model and the last is based on a hybrid methodology that combines both ARIMA and ANN models. Each approach fits, respectively, two models on the mid-point and range of the interval values assumed by the interval-valued time series in the learning set. The forecasting of the lower and upper bounds of the interval value of the time series is accomplished through a combination of forecasts from the mid-point and range of the interval values. The evaluation of the models presented is based on the estimation of the average behavior of the mean absolute error and mean squared error in the framework of a Monte Carlo experiment. The results demonstrate that the approaches are useful in forecasting alternatives for interval-valued time series and indicate that the hybrid model is an effective way to improve the forecasting accuracy achieved by any one of the models separately.

2005 - International Journal of Systems Science

Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making

Intuitionistic fuzzy sets are extensions of fuzzy sets. Their elements have two degrees – a degree of membership and a degree of non-membership so that their sum is smaller or equal to 1. Intuitionistic fuzzy interpretations of the processes of multi-person and of multi-measurement tool multi-criteria decision makings are discussed in this paper.

1989 - Econometric Theory

Testing for Unit Roots in Time Series Data

Let Yt satisfy the stochastic difference equation for t = 1,2,…, where et are independent and identically distributed random variables with mean zero and variance σ2 and the initial conditions (Y−p+1,…, Y0) are fixed constants. It is assumed that the process is invertible and that the true, but unknown, roots m1,m2,…,mp of satisfy the hypothesis Hd: m1 = … = md = 1 and |mj| < 1 for j = d + 1,…,p. We present a reparameterization of the model for Yt that is convenient for testing the hypothesis Hd. We consider the asymptotic properties of (i) a likelihood ratio type “F-statistic” for testing the hypothesis Hd, (ii) a likelihood ratio type t-statistic for testing the hypothesis Hd against the alternative Hd−1. Using these asymptotic results, we obtain two sequential testing procedures that are asymptotically consistent.

2004 - Journal of Heuristics

Evolving Time Series Forecasting ARMA Models

Time Series Forecasting (TSF) allows the modeling of complex systems as “black-boxes”, being a focus of attention in several research arenas such as Operational Research, Statistics or Computer Science. Alternative TSF approaches emerged from the Artificial Intelligence arena, where optimization algorithms inspired on natural selection processes, such as Evolutionary Algorithms (EAs), are popular. The present work reports on a two-level architecture, where a (meta-level) binary EA will search for the best ARMA model, being the parameters optimized by a (low-level) EA, which encodes real values. The handicap of this approach is compared with conventional forecasting methods, being competitive.

2020 - Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining

Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

2010 - Expert Syst. Appl.

Forecasting TAIFEX based on fuzzy time series and particle swarm optimization

The TAIFEX (Taiwan Stock Index Futures) forecasting problem has attracted some researchers' attention in the past decades. Several forecast methods for the TAIFEX forecasting based either on the statistic theorems have been proposed, but their results are not satisfied. Fuzzy time series is used to doing forecasting but the forecasted accuracy still needs to be improved. In this paper we present a new hybrid forecast method to solve the TAIFEX forecasting problem based on fuzzy time series and particle swarm optimization. The experimental results show that the new proposed forecast model is better than any existing fuzzy forecast models and is more precise than four famous statistic forecast models.

2016 - Inf. Sci.

Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures

In this paper, we propose a new fuzzy time series forecasting method for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series, fuzzy logical relationships, particle swarm optimization techniques, the K-means clustering algorithm, and similarity measures between the subscript of the fuzzy set of the fuzzified historical testing datum on the previous trading day and the subscripts of the fuzzy sets appearing in the current states of the fuzzy logical relationships in the chosen fuzzy logical relationship group. The particle swarm optimization techniques are used to get the optimal partition of the intervals in the universe of discourse. The K-means clustering algorithm is used to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups. The experimental results show that the proposed fuzzy forecasting method gets higher forecasting accuracy rates than the existing methods. The advantages of the proposed fuzzy forecasting method is that it uses the particle swarm optimization techniques to get the optimal partition of the intervals in the universe of discourse and uses the K-means clustering algorithm to cluster the subscripts of the fuzzy sets of the current states of the fuzzy logical relationships to get the cluster center of each cluster and to divide the constructed fuzzy logical relationships into fuzzy logical relationship groups for increasing the forecasting accuracy rates.

2012 - KDD : proceedings. International Conference on Knowledge Discovery & Data Mining

Searching and Mining Trillions of Time Series Subsequences under Dynamic Time Warping

Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms. The difficulty of scaling search to large datasets largely explains why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine truly massive time series for the first time. We demonstrate the following extremely unintuitive fact; in large datasets we can exactly search under DTW much more quickly than the current state-of-the-art Euclidean distance search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We show that our ideas allow us to solve higher-level time series data mining problem such as motif discovery and clustering at scales that would otherwise be untenable. In addition to mining massive datasets, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.

2011 - Expert Syst. Appl.

The adaptive fuzzy time series model with an application to Taiwan's tourism demand

In this study, an adaptive fuzzy time series model for forecasting Taiwan's tourism demand is proposed to further enhance the predicted accuracy. We first transfer fuzzy time series data to the fuzzy logic group, assign weights to each period, and then use the proposed adaptive fuzzy time series model for forecasting in which an enrollment forecasting values is applied to obtain the smallest forecasting error. Finally, an illustrated example for forecasting Taiwan's tourism demand is used to verify the effectiveness of proposed model and confirmed the potential benefits of the proposed approach with a very small forecasting error MAPE and RMSE.

2013 - ArXiv

An Introductory Study on Time Series Modeling and Forecasting

Modeling and forecasting of time series data has fundamental importance in various practical domains. The aim of this book is to present a concise description of some popular time series forecasting models with their salient features. Three important classes of time series models, viz. stochastic, neural networks and support vector machines are studied together with their inherent forecasting strengths and weaknesses. The book also meticulously discusses about several basic issues related to time series analysis, such as stationarity, parsimony, overfitting, etc. Our study is enriched by presenting the empirical forecasting results, conducted on six real-world time series datasets. Five performance measures are used to evaluate the forecasting accuracies of different models as well as to compare the models. For each of the six time series datasets, we further show the obtained forecast diagram which graphically depicts the closeness between the original and predicted observations.

2008 - World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering

Multivariate High Order Fuzzy Time Series Forecasting for Car Road Accidents

In this paper, we have presented a new multivariate fuzzy time series forecasting method. This method assumes mfactors with one main factor of interest. History of past three years is used for making new forecasts. This new method is applied in forecasting total number of car accidents in Belgium using four secondary factors. We also make comparison of our proposed method with existing methods of fuzzy time series forecasting. Experimentally, it is shown that our proposed method perform better than existing fuzzy time series forecasting methods. Practically, actuaries are interested in analysis of the patterns of causalities in road accidents. Thus using fuzzy time series, actuaries can define fuzzy premium and fuzzy underwriting of car insurance and life insurance for car insurance. National Institute of Statistics, Belgium provides region of risk classification for each road. Thus using this risk classification, we can predict premium rate and underwriting of insurance policy holders. Keywords—Average forecasting error rate (AFER), Fuzziness of fuzzy sets Fuzzy, If-Then rules, Multivariate fuzzy time series.

Intuitionistic Fuzzy Time Series: An Approach for Handling Nondeterminism in Time Series Forecasting

Fuzzy time series forecasting method based on hesitant fuzzy sets

Hesitant probabilistic fuzzy set based time series forecasting method

Time series forecasting based on complex network in weighted node similarity

A Novel Fuzzy Time Series Forecasting Model Based on Multiple Linear Regression and Time Series Clustering

Handling higher order time series forecasting approach in intuitionistic fuzzy environment

A Refined Approach for Forecasting Based on Neutrosophic Time Series

A Semiparametric Model for Time Series Based on Fuzzy Data

A Novel Single Valued Neutrosophic Hesitant Fuzzy Time Series Model: Applications in Indonesian and Argentinian Stock Index Forecasting

A novel equilibrium solution concept for intuitionistic fuzzy bi-matrix games considering proportion mix of possibility and necessity expectations

Comparing Performance Potentials of Classical and Intuitionistic Fuzzy Systems in Terms of Sculpting the State Space

A non-parametric model for fuzzy forecasting time series data

MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

Internet Performance Prediction Framework Based on PingER Dataset

A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets

An Efficient Network Method for Time Series Forecasting Based on the DC Algorithm and Visibility Relation

A Non-Probabilistic Neutrosophic Entropy-Based Method For High-Order Fuzzy Time-Series Forecasting

Hesitant fuzzy set based computational method for financial time series forecasting

Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony

A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series

A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation