Keywords

1 Introduction

A time series, viewed as a sequence of data points that are collected over a period of time, has wide range of many different domain scientific fields from economics to engineering. In the engineering literature, state-space methods have been developed for the sequential analysis of data [1]. Time series analysis involves to extract the meaningful information or patterns or characteristics from the given raw data to understand the behavior. On the other hand, time series predictions are involved in building a model that can forecast into the future based on available observed data. The fundamental time series model is the regression analysis, which constructs a model by considering one or more independent variables to predict the outcome on continuous variables. The analysis of time series has some pattens involved, which can be discovered. Time series analysis can be further classified into univariate and multivariate based on the number of variables available for observation.

The univariate time series consists of a single observation over a time period. The multivariate time series consists of more than one observations collected over time.

Multivariate time series analysis research is more challenging compared to univariate time series analysis. To design and correlation of multivariate across hierarchical levels vary from “system-to-system”. To handle multivariate time series, uses factor analysis which reduces the attribute space from large numbers to smaller numbers of factors. Various prediction and forecasting machine learning models have been proposed in [2,3,4,5,6].

2 State-of-the-Art in Time Series on Various Domains

This section describes the detailed survey of various time series methods proposed by research communities that forecasting various application domains. More than two decades, the BOX-Jenkins method for time series forecasting using ARIMA model treated as benchmark to evaluate some of new methods.

The nonlinear Taylor rule-based exchange rate system has been analyzed by [7], complementing latest studies that discovered that the linear variant of this system outperforms a random walk method. It is found that, with respect to several macroeconomic determinants, the evidence of nonlinearities in the exchange rate suggests that the Taylor rule exchange rate models can in some cases be improved by considering regime changes. Future study in this region might consider alternative nonlinear modeling methods and a broader range of prospective factors for transformation.

Multiple sophisticated time series models have been suggested to forecast forex up to 30 pairs by [8]. Based on the Augmented-Dickey Fuller Test (ADF-test), each forex was converted to be stationary. It is discovered that the enormous benefit of using BCVAR and TVP-BCVAR to estimate EUR-DKK for all forecasting activities compared to the typical Bayesian Auto Regression (AR)(4).

Veraart [9] proposed a new methodology to investigate the connection between the amount of limited order entries and deletions in a limited order book relies on a blended moving average method powered by Levy Noise, called a trawl method. The methodology can be extended to four dimensions to get more accurate predictions.

Phan et al. [10] proposed a new method for filling missing values in the time series which resulted a better prediction accuracy.

The GRU-D model of [11] proved that the model with trainable decays has same time and space complexity to the existing RNN models, but is ahead of non-deep learning methods.

The MTS Networks proposed by [12] facilitates an easy interpretation of dynamics of multivariate time series.

The SFM recurrent neural network developed by [13] is tested on real-time trading data and the accuracy of trading patterns predicted is better than AR model and LSTM.

Ma et al. [14] proposed a new approach for predicting solar flares based on the past data available. Though the approach requires expensive clustering time, guarantees satisfiable prediction accuracy.

Nayak [15] has developed a hybrid system by considering the base system of four higher order neural networks. The performance of these hybrid designs is assessed by predicting some actual stock market’s one-step-ahead exchange prices. The efficiency and superiority of the models are established by comparing the results with other models.

Dasgupta and Osogami [16] extended to Gaussian DyBM the dynamic Boltzman Machine (DyBM), which deals with true valued information. The design has also been expanded to a recurrent neural network (RNN) that regulates the DyBM units preference entry. Experiments with synthesized datasets demonstrate that the RNN-Gussian DyBM increases predictive precision by up to 35 percent with normal VAR.

The adaptive inferential model learning design of neuro-complex fuzzy has been expanded by [17] to the multivariate time series data. The writers explored the scheme with design variants of single-input-single-output, multi-input-single-output, and multi-input-multiple-output, testing its efficiency on four multivariate trigger levels. It was evident that the drawings on these datasets are inferior to the published results, and at least as precise as filters based on kernel-based forecasting methods.

The IFS-based technique suggested by [18] utilizes a straightforward max-min synthesis operator for IFSs, making the technique easy and less complicated. Not only does the suggested technique outperform the techniques proposed by different scientists, but it is also sufficiently effective to predict in near line with real-time series data in the hesitation environment.

According to [19], the performance of Functional Link Radial Basis Function method seems better compared to Functional Link method and Radial Basis Function alone.

Opare [20] studied the mortality rate under 5 years using ARIMA model. The study used time series data from 1961 to 2012. The dataset is partitioned into train data from 1961 to 2000 and test data from 2001 to 2012 for each model.

Aboagye-Sarfo et al. [21] presented a paper on the comparison of time series models of univariate and multivarite. The paper demonstrated the comparative performance of VARMA and ARMA models applied to predict the demand for strategic planning and resource allocation from the Emergency Department (ED). The study concluded the superiority of VARMA model.

A mixed regression model for mortality data was proposed by [22].

A hybrid prediction method for the Foreign Exchange Market was proposed by [23]. The findings show that the hybrid technique described is a very helpful and efficient technique for forecasting economic prices and extracting economic patterns.

Adhikari and Agrawal [24] proposed a combined approach to exploit the strengths of the systems Random Walk (RW) and Artificial Neural Network (ANN). The strategy utilizes the RW system to process the linear part of a monetary dataset and the remaining discrete residuals are handled with neural models. Predictive capacity of suggested system is examined in light of three common error stats on four real-world economic time series. The findings acquired obviously show that the combined technique achieves predictive accuracies fairly better than each of the designs RW, FANN, and EANN.

Khashei and Bijari [25] submitted a new hybrid model for time series which is tested on three real datasets. The final extracted results indicate that the model proposed produces higher prediction accuracy.

The authors [26] have proposed an ANN-based naive method to forecast the financial time series.

The time series prediction of electric prices based on asymmetric subset hood product fuzzy neural inference system was proposed by [27]. Authors suggested a better approach for predicting the time series into future with neuro-fuzzy inference system.

Authors proposed in [28], a hybrid approach that combines linear ARMA and Artificial Neural Networks. To reduce the error rate the proposed method used artificial neural network to forecast the time series. This hybrid approach achieves less error rate for real datasets and synthetic time series.

Summary of all the research papaers studied is given in Table 1.

Table 1 Summary of time series analysis and fore casting models state of the art
Full size table

3 Conclusion

The growth of the time series applications enables many services in real time. As the time series data increases, it leads to many challenges. In order to guarantee the accurate forecast need an efficient mechanisms for time series analysis. Even though the AR, MA, ARMA, and ARIMA methods have their advantages and disadvantages that impact to analyze the time series, they can only be applied on univariate time series data.

This paper provides a study of projections of univariate and multivariate time series that closely defines current methods. A comprehensive literature assessment was given, highlighting each study’s accomplishments and its primary objectives. Researchers have a strong stake in analyzing the literature proof in time series forecasting over the previous few years, driven by the difficulties generated by the new algorithms. In addition, the evolution of time series demonstrates a growing interest for univariate and multivariate factors. Furthermore, the research continues to explore time series information using sophisticated processes to correctly predict profound training in real time.

4 Suggested Future Research

The comprehensive review suggests the below methods as future research directions.

  • It is possible to explore the hybridization of Fuzzy regression and fuzzy support vector regression to see if the stronger time series prediction can be achieved.

  • The hybrids incorporating Support Vector Machine (SVM) and Evolutionary Computation (EC) can be employed in the future.

  • The soft computing constituencies involving Fuzzy Logic (FL) and Evolutionary Computation (EC) need to be investigated to see their efficiency for time series data.

  • The evolutionary computation techniques other than Genetic Algorithms (GA) and Particle Swam Optimization (PSO) such as Differential Evolution (DE) in the financial time series analysis context to form new set of hybrid forecasting models.

  • Due to their superior exploring capabilities, Quantum-inspired Evolutionary algorithms demonstrated their worth in classification and prediction. A little or no research on the forecast of financial time series is recorded in this area.

  • In this context of forecasting financial time series, Deep learning architectures that displayed enormous potential in Image Processing need to be studied and implemented.

  • The application of Hidden Markov Model (HMM) is not found in all of the papers that are reviewed. Therefore, the hybrids involving HMM-based models can be developed for forecasting.

  • The Quantile Regression (QR)-based hybrids are another alternate method that needs to focus on time series applications.

  • The impact of external variables such as sentiment analysis, factors that affect the price of stock need to be properly incorporated into the time series forecasting models.