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Hybridization of hybrid structures for time series forecasting: a review

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Abstract

Achieving the desired accuracy in time series forecasting has become a binding domain, and developing a forecasting framework with a high degree of accuracy is one of the most challenging tasks in this area. Combining different forecasting methods to construct efficient hybrid models has been widely reported in the literature regarding this challenge. Various types of hybrid models have been developed and successfully employed to improve forecasting accuracy. The well-known hybrid models can be generally categorized into four classes: (1) preprocessing-based, (2) parameter optimization-based, (3) components combination-based, and (4) postprocessing-based hybrid models. Despite the significant successes of hybrid models, efforts to access more accurate results face continued growth. Hybridization of hybrid models is a novel idea proposed to obtain extreme accuracy in recent literature, in which two or more hybrid classes are combined instead of conjoining the conventional individual forecasting methods. Although, in many publications, the aforementioned classes of hybrid models have been reviewed and analyzed in a wide variety of forecasting fields; no study is conducted to review the hybridization of hybrid models. This paper’s main contribution is to fill this gap and provide classification and comprehensive review of the current endeavors done in the hybridization of hybrid models in time series forecasting areas. Our searches indicate that more than 250 papers have been published in recent years utilizing hybridization of hybrid models. In this paper, these published papers have been classified regarding their different used combination strategies into four main categories, including (1) Hybridization with preprocessing-based hybrid models (HPH), (2) Hybridization with parameter optimization-based hybrid models (HOH), (3) Hybridization with components combination-based hybrid models (HCH) and, (4) Hybridization with postprocessing-based hybrid models (HSH). Each hybridization of the hybrid class is evaluated regarding the usage frequency, specific merits, and limitations. It can be inferred from reviewing articles that the hybridization of the hybrid concept, as a recent advancement in time series forecasting, can significantly improve traditional hybrid models’ accuracy. Furthermore, each category’s research gaps and some future research directions are identified in this paper.

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Abbreviations

AACA:

Adaptive Ant Colony Algorithm

ABC:

Artificial Bee Colony

ACO:

Ant Colony Optimization

AFD:

Adaptive Fourier Decomposition

ALO:

Ant Lion Optimization

ANFIS:

Adaptive Neuro-Fuzzy Inference System

ANN:

Artificial Neural Network

APSOACO:

Adaptive Particle Swarm Optimization Ant Colony Optimization

AR-GARCH:

Auto-Regressive- Generalized Autoregressive Conditional Heteroskedasticity

ARIMA:

Autoregressive Integrated Moving Averages

ARMA:

Auto-Regressive Moving Average

BAG:

Bootstrap Aggregation

BASA:

Backtracking Search Algorithm

BCF:

Combined algorithm based on BA, CS and FA

BFGSA:

Broyden Fletcher Goldfarb Shanno Algorithm

BiGRU:

Bidirectional Gated Recurrent Unit

BOA:

Butterfly Optimization Algorithm

BPLS:

Back-Propagation and Least-Square

BPNN:

Back Propagation Neural Network

BSA:

Bird Swarm Algorithm

BSO:

Brain Storm Optimization

CA:

Crisscross Algorithm

CEEMDAN:

Complete Ensemble Empirical Mode Decomposition with Adaptive Noise

CGWO:

Chaotic Grey Wolf Optimization-Extreme

CKHA:

Chaotic Krill Herd Algorithm

CLSA:

Clonal Selection Algorithm

CLSFPA:

Chaotic Local Search Flower Pollination Algorithm

CNN:

Convolutional Neural Network

CNNSVM:

Convolutional Neural Network Support Vector Machine

CO:

Crisscross Optimization

COR:

Correlation

CPSO:

Chaotic Particle Swarm Optimization

CRSA:

Crow Search Algorithm

CSA:

Cuckoo Search Optimization

CSFPA:

Chaotic Self-adaptive Flower Pollination Algorithm

CSO:

Chicken Swarm Optimization

C-SSO:

Chaotic Shark Smell Optimization

CVMD:

Correntropy criterion into Variational Mode Decomposition

DA:

Dragonfly Algorithm

DAE:

Denoising Auto Encoders

DE:

Differential Evolution

DES:

Double Exponential Smoothing

DFS:

Date-Framework Strategy

DIFPSO:

Dynamic Inertia Factor Particle Swarm Optimization

DT:

Decision Tree

EBD:

Entropy-Based Discretization

EEMD:

Ensemble Empirical Mode Decomposition

ELM:

Extreme Learning Machine

EMD:

Empirical Mode Decomposition

ENN:

Elman Neural Network

EPSEMD:

EMD based on Extreme Point Span

ERNN:

Elman Recurrent Neural Network

EWT:

Empirical Wavelet Transform

FA:

Firefly Algorithm

FCM:

Fuzzy C-means Clustering

FCRBM:

Factored Conditional Restricted Boltzmann Machine

FEEMD:

Fast Ensemble Empirical Mode Decomposition

FFA:

Fruit Fly Algorithm

FFNN:

Feed Forward Neural Network

FFT:

Fast Fourier Transformation

FMRVR:

Fast Multi-output Relevance Vector Regression

FTS:

Fuzzy Time Series

GA:

Genetic Algorithm

GABICS:

Genetic Algorithm Binary Improved Cuckoo Search

GARCH-M:

Generalized Autoregressive Conditional Heteroskedasticity -in Mean

GBM:

Gradient Boosting Machine

GEP:

Gene Expression Programing

GMI:

Generalized Mutual Information

GOA:

Grasshopper Optimization Algorithm

GP:

Grid Partitioning

GPR:

Gaussian Process

GRNN:

Generalized Regression Neural Network

GRSA:

Group Search Algorithm

GRU:

Gated Recurrent Unit

GSA:

Gravitational Search Algorithm

GWDO:

Genetic Wind-driven Optimization Algorithm

GWO:

Gray Wolf Optimizer

HBASA:

Hybrid Backtracking Search Algorithm

HC:

Hierarchical Cluster

HGSA:

Hybrid Gravitation Search Algorithm

HGWO:

Hybridizing Grey Wolf Optimization

HHO:

Harris Hawks Optimization

HHOGWO:

Harris Hawks Optimization- Grey Wolf Optimizer

HSA:

Harmony Search Algorithm

IASA:

Improved Atomic Search Algorithm

IBOA:

Improved Butterfly Optimization Algorithm

ICA:

Independent Component Analysis

IEWT:

Improved Empirical Wavelet Transform

IGSA:

Improved Gravitational Search Algorithm

IHGWOSCA:

Improved Hybrid Grey Wolf Optimizer-Sine Cosine Algorithm

IHSA:

Improved Harmony Search Algorithm

IMF:

Intrinsic Mode Function

IMOSCA:

Improved Multi-objective Sine Cosine Algorithm

IPSO:

Improved Particle Swarm Optimization

iPSO:

Inertia weight PSO

IR:

Inconsistency Rate

ISFLA:

Improved Shuffled Frog Leaping Algorithm

ITA:

Innovative Trend Analysis

ITD:

Intrinsic Time-scale Decomposition

IVMD:

Improved Variational Mode Decomposition

IWOA:

Improved Whale Optimization Algorithm

KC:

K-means Clustering

KELM:

Kernel-based Extreme Learning Machine

KFCM:

Kernel-based Fuzzy C-means Clustering

KHM:

K-harmonic Mean

KLD:

Kullback-Leibler Divergence

KNEA:

Kernel-based Nonlinear Extension of the Arps

K-NN:

K-Nearest Neighbor

KPCA:

Kernel Principal Component Analysis

LR:

Logistic Regression

LSO:

Lion Swarm Optimizer

LSSVM:

Least Square Support Vector Machine

LSTM:

Long Short-Term Memory

MARS:

Multivariate Adaptive Regression Splines

MCSDE:

Modified Cuckoo Search and Differential Evolution Algorithm

MEMD:

Multivariate Empirical Mode Decomposition

MFO:

Moth-Flame Optimization

MGR-MR-IG:

Minimum Global Redundancy, Maximum Relevancy and Information Gain

MI:

Mutual Information

MKLSSVM:

Multi Kernel function Least Square Support Vector Machine

MLP:

Multi-Layer Perceptron

MLR:

Multiple Linear Regression

MMI:

Modified Mutual Information

MOBGWO:

Multi-Objective Binary Grey Wolf Optimizer

MOCSCA:

Multi-Objective Chaotic Sine Cosine Algorithm

MODA:

Multi-Objective Dragonfly Algorithm

MODWT:

Maximal Overlap Discrete Wavelet Transform

MOGOA:

Multi-Objective Grasshopper Optimization Algorithm

MOGWO:

Multi-Objective Grey Wolf Optimizer

MOICA:

Multi-Objective Imperialist Competitive Algorithm

MOMVO:

Multi-Objective Multi-universe Optimization

MOPSO:

Multi-Objective Particle Swarm Optimization

MOSBO:

Multi-Objective Satin Bowerbird Optimizer

MOSFA:

Multi-Objective Shuffled Frog-leaping Algorithm

MOSGA:

Multi-Objective Sine Cosine Algorithm

MOSSA:

Multi-Objective Salp Swarm Algorithm

MPSO:

Modified Particle Swarm Optimization

MSE:

Mean Squared Error

MVMD:

Multivariate Variational Mode Decomposition

MVO:

Multi-Verse Optimizer

MWOA:

Modified Whale Optimization Algorithm

NAR:

Nonlinear Autoregressive

NARX:

Nonlinear Auto-Regressive Network with Exogenous inputs

NB:

Naïve Bayes

NNGSA:

Neural Network Gravitational Search Algorithm

ORELM:

Outlier Robust Extreme Learning Machine

OSELM:

Online Sequential Extreme Learning Machine

OVMD:

Optimized Variational Mode Decomposition

PACF:

Partial Auto Correlation Function

PAM:

Physical Aging Model

PCA:

Principal component analysis

PSO:

Partial Swarm Optimization

PSRT:

Phase Space Reconstruction Technique

RBFNN:

Radial Basis Function Neural Network

RELM:

Regularized Extreme Learning Machine

RELM:

Robust Extreme Learning Machine

RF:

Random Forest

RGMDH-NN:

Architecture Group Method of Data Handling type Neural Network

RL:

Relief

RMO:

Radial Movement Optimization

RSAR:

Rough Sets Attribute Reduction

RVFL:

Random Vector Functional Link

RVM:

Relevance Vector Machine

SA:

Simulated Annealing

SARIMA:

Seasonal Autoregressive Integrated Moving Averages

SC:

Subtractive Clustering

SCA:

Sine Cosine Algorithm

SDA:

Similar Day Approach

SDCS:

Steepest Descent Cuckoo Search

SIE:

Seasonal Information Extraction

SLFN:

Single-hidden-Layer Feedforward Network

SOM:

Self-Organizing Map

WNN:

Wavelet Neural Network

WOA:

Whale Optimization Algorithm

WPA:

Wavelet Packet Analysis

WPD:

Wavelet Packet Decomposition

WRELM:

Weighted Regularized Extreme Learning Machine

WSTD:

Wavelet Soft Threshold Denoising

WT:

Wavelet Transform

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  1. Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Zahra Hajirahimi & Mehdi Khashei

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  1. Zahra Hajirahimi
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  2. Mehdi Khashei
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Correspondence to Mehdi Khashei.

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Hajirahimi, Z., Khashei, M. Hybridization of hybrid structures for time series forecasting: a review. Artif Intell Rev 56, 1201–1261 (2023). https://doi.org/10.1007/s10462-022-10199-0

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