Handling forecasting problems using fuzzy time series

In [6–9], Song et al. proposed fuzzy time-series models to deal with forecasting problems. In [10], Sullivan and Woodall reviewed the first-order time-invariant fuzzy time series model and the first-order time-variant model proposed by Song and Chissom [6–8], where the models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. In this paper, we propose a new method to forecast university enrollments, where the historical enrollments of the University of Alabama shown in [7,8] are used to illustrate the forecasting process. The average forecasting errors and the time complexity of these methods are compared. The proposed method is more efficient than the ones presented in [7, 8, 10] due to the fact that the proposed method simplifies the arithmetic operation process. Furthermore, the average forecasting error of the proposed method is smaller than the ones presented in [2, 7, 8].     

Stock market forecasting by using a hybrid model of exponential fuzzy time series

The initial aim of this study is to propose a hybrid method based on exponential fuzzy time series and learning automata based optimization for stock market forecasting. For doing so, a two-phase approach is introduced. In the first phase, the optimal lengths of intervals are obtained by applying a conventional fuzzy time series together with learning automata swarm intelligence algorithm to tune the length of intervals properly. Subsequently, the obtained optimal lengths are applied to generate a new fuzzy time series, proposed in this study, named exponential fuzzy time series. In this final phase, due to the nature of exponential fuzzy time series, another round of optimization is required to estimate certain method parameters. Finally, this model is used for future forecasts. In order to validate the proposed hybrid method, forty-six case studies from five stock index databases are employed and the findings are compared with well-known fuzzy time series models and classic methods for time series. The proposed model has outperformed its counterparts in terms of accuracy.     

An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers

One of the major drawbacks of the existing fuzzy time series forecasting models is the fact that they only provide a single-point forecasted value just like the output of the traditional time series methods. Hence, they cannot provide a decision analyst more useful information. The aim of this present research is to design an improved fuzzy time series forecasting method in which the forecasted value will be a trapezoidal fuzzy number instead of a single-point value. Furthermore, the proposed method may also increase the forecasting accuracy. Two numerical data sets were used to illustrate the proposed method and compare the forecasting accuracy with three fuzzy time series methods. The results of the comparison indicate that the proposed method can generate forecasting values that are more accurate.     

Using interval information granules to improve forecasting in fuzzy time series

In the process of modeling and forecasting of fuzzy time series, an issue on how to partition the universe of discourse impacts the quality of the forecasting performance of the constructed fuzzy time series model. In this paper, a novel method of partitioning the universe of discourse of time series based on interval information granules is proposed for improving forecasting accuracy of model. In the method, the universe of discourse of time series is first pre-divided into some intervals according to the predefined number of intervals to be partitioned, and then information granules are constructed in the amplitude-change space on the basis of data of time series belonging to each of intervals and their corresponding change (trends). In the sequel, optimal intervals are formed by continually adjusting width of these intervals to make information granules which associate with the corresponding intervals become most “informative”. Three benchmark time series are used to perform experiments to validate the feasibility and effectiveness of proposed method. The experimental results clearly show that the proposed method produces more reasonable intervals exhibiting sound semantics. When using the proposed partitioning method to determine intervals for modeling of fuzzy time series, forecasting accuracy of the constructed model are prominently enhanced.     

我国水路货运量短期预测模型

本文对我国逐月水路货运量进行了趋势、季节分析，并利用时间序列分析方法建立了简单、实用的短期预测模型。     

An investigation of model selection criteria for neural network time series forecasting

Artificial neural networks (ANNs) have received more and more attention in time series forecasting in recent years. One major disadvantage of neural networks is that there is no formal systematic model building approach. In this paper, we expose problems of the commonly used information-based in-sample model selection criteria in selecting neural networks for financial time series forecasting. Specifically, Akaike’s information criterion (AIC) and Bayesian information criterion (BIC) as well as several extensions have been examined through three real time series of Standard and Poor’s 500 index (S&P 500 index), exchange rate, and interest rate. In addition, the relationship between in-sample model fitting and out-of-sample forecasting performance with commonly used performance measures is also studied. Results indicate that the in-sample model selection criteria we investigated are not able to provide a reliable guide to out-of-sample performance and there is no apparent connection between in-sample model fit and out-of-sample forecasting performance.     

Evolutionary learning of fuzzy grey cognitive maps for the forecasting of multivariate,interval-valued time series

Time series are built as a result of real-valued observations ordered in time; however, in some cases, the values of the observed variables change significantly, and those changes do not produce useful information. Therefore, within defined periods of time, only those bounds in which the variables change are considered. The temporal sequence of vectors with the interval-valued elements is called a ‘multivariate interval-valued time series.’ In this paper, the problem of forecasting such data is addressed. It is proposed to use fuzzy grey cognitive maps (FGCMs) as a nonlinear predictive model. Using interval arithmetic, an evolutionary algorithm for learning FGCMs is developed, and it is shown how the new algorithm can be applied to learn FGCMs on the basis of historical time series data. Experiments with real meteorological data provided evidence that, for properly-adjusted learning and prediction horizons, the proposed approach can be used effectively to the forecasting of multivariate, interval-valued time series. The domain-specific interpretability of the FGCM-based model that was obtained also is confirmed.     

A case-based fuzzy multicriteria decision support model for tropical cyclone forecasting

This paper proposes a multi-stage framework for intelligent decision support. The proposed framework integrates case-based reasoning and fuzzy multicriteria decision making techniques. It potentially leads to more accurate, flexible and efficient retrieval of alternatives that are most similar and most useful to the current decision situation. Additionally, the framework provides intelligent assistance in articulating domain expert's preferences through outranking relations. We illustrated the proposed approach in the context of tropical cyclone prediction. Ten years of historical observation data about tropical cyclones was represented within fuzzy multicriteria decision-making problem. We describe a prototype intelligent decision support system, which helps the forecaster in retrieving best-fitted solutions in terms of both usefulness and similarity to the current observed case.     

Neural network forecasting for seasonal and trend time series

Neural networks have been widely used as a promising method for time series forecasting. However, limited empirical studies on seasonal time series forecasting with neural networks yield mixed results. While some find that neural networks are able to model seasonality directly and prior deseasonalization is not necessary, others conclude just the opposite. In this paper, we investigate the issue of how to effectively model time series with both seasonal and trend patterns. In particular, we study the effectiveness of data preprocessing, including deseasonalization and detrending, on neural network modeling and forecasting performance. Both simulation and real data are examined and results are compared to those obtained from the Box–Jenkins seasonal autoregressive integrated moving average models. We find that neural networks are not able to capture seasonal or trend variations effectively with the unpreprocessed raw data and either detrending or deseasonalization can dramatically reduce forecasting errors. Moreover, a combined detrending and deseasonalization is found to be the most effective data preprocessing approach.     

A better project performance prediction model using fuzzy time series and data envelopment analysis

Earned value management (EVM) is a critical project management methodology that evaluates and predicts project performance from cost and schedule perspectives. The novel theoretical framework presented in this paper estimates future performance of a project based on the past performance data. The model benefits from a fuzzy time series forecasting model in the estimation process. Furthermore, fuzzy-based estimation is developed using linguistic terms to interpret different possible conditions of projects. Eventually, data envelopment analysis is applied to determine the superior model for forecasting of project performance. Multiple illustrative cases and simulated data have been used for comparative analysis and to illustrate the applicability of theoretical model to real situations. Contrary to EVM-based approach, which assumes the future performance is the same as the past, the proposed model can greatly assist project managers in more realistically assessing prospective performance of projects and thereby taking necessary and on-time appropriate actions.     

A novel signal extraction approach for filtering and forecasting noisy exponential series

The coefficients of Linear Recurrent Relations (LRR) play a pivotal role in many forecasting techniques. Precise and closed form of the LRR coefficients enables one to achieve more accurate forecasts. On account to the fact that, in real-world situations, a time series data is contaminated with noise, extracting the noiseless series is of great importance. This paper seeks to obtain a closed form, with less noise level, of LRR coefficients for noisy exponential time series. Improving the filtering performance through employing noiseless eigenvectors of the covariance matrix is another novelty of this study. Our simulation results confirm that the proposed approach enhances filtering and forecasting results.     

Improved time-variant fuzzy time series forecast

Since Song and Chissom (Fuzzy Set Syst 54:1–9, 1993a) first proposed the structure of fuzzy time series forecast, researchers have devoted themselves to related studies. Among these studies, Hwang et al. (Fuzzy Set Syst 100:217–228, 1998) revised Song and Chissom’s method, and generated better forecasted results. In their method, however, several factors that affect the accuracy of forecast are not taken into consideration, such as levels of window base, length of interval, degrees of membership values, and the existence of outliers. Focusing on these factors, this study proposes an improved fuzzy time series forecasting method. The improved method can provide decision-makers with more precise forecasted values. Two numerical examples are employed to illustrate the proposed method, as well as to compare the forecasting accuracy of the proposed method with that of two fuzzy forecasting methods. The results of the comparison indicate that the proposed method produces more accurate forecasting results.     

A new forecasting method for time continuous model of dynamic system

Usually a linear differential equation is used to represent continuous dynamic systems, but a linear difference equation is used to represent discrete dynamic systems. AGO is one of the most important characteristics of grey theory, and its main purpose is to reduce the randomness of data. A linear differential equation, instead of a linear difference equation, is used to replace the grey differential equation to analyze discrete systems in this paper. Approximating a k-order derivative by operating after spline curve fitting of 1-AGO data, a model is directly established by means of the least square method. ARIMA models are used to analyze the leading indicator in advance, and the Fourier series with suitably chosen values of parameters is used in the fitting of leading indicator. This model is called the GDM(2, 2, 1) model.     

A novel grey forecasting model and its optimization

Although the grey forecasting model has been successfully employed in many fields and demonstrated promising results, its prediction results may be inaccurate sometimes. For the purposes of enhancing the predictive performance of grey forecasting model and enlarging its suitable ranges, this paper puts forward a novel grey forecasting model termed NGM model and its optimized model, develops a calculative formula for solving the parameters of the novel NGM model through the least squares method, and obtains the time response sequence of NGM model by using differential equation as a procedure for reasoning. It performs a numerical demonstration on the prediction accuracy of NGM model and its optimized models. As shown in the results, the proposed model and it optimized model can enhance the prediction accuracy. Numerical results illustrate that the proposed NGM model and its optimized model are effective. They are suitable for predicting the data sequence with the characteristics of non-homogeneous exponential law. This work makes important contribution to the enrichment of grey prediction theory.     

MODWT-ARMA model for time series prediction

Many time series in the applied sciences display a time-varying second order structure and long-range dependence (LRD). In this paper, we present a hybrid MODWT-ARMA model by combining the maximal overlap discrete wavelet transform (MODWT) and the ARMA model to deal with the non-stationary and LRD time series. We prove theoretically that the details series obtained by MODWT are stationary and short-range dependent (SRD). Then we derive the general form of MODWT-ARMA model. In the experimental study, the daily rainfall and Mackey–Glass time series are used to assess the performance of the hybrid model. Finally, the normalized error comparison with DWT-ARMA, EMD-ARMA and ARIMA model indicates that this combined model is an effective way to improve forecasting accuracy.     

An introduction to forecasting with time series models

The use of ARIMA time series models in forecasting is reviewed. In connection with this, some important points about forecasting are discussed, including: (1) difficulties in forecasting by fitting and extrapolating a deterministic function of time; (2) the importance of providing reasonable measures of forecast accuracy; and (3) the need to incorporate subject matter knowledge with time series models when forecasting.     

Parsimonious modelling and forecasting of seasonal time series

Some seasonal time series models are considered which are appropriate for the univariate modelling and forecasting of many time series. The equivalent ARIMA forms of these models provide the basis for a critical examination of the Box-Jenkins approach to seasonal model-building. It is concluded that this approach is unsatisfactory and in particular can often result in over-differencing and the adoption of an inappropriate model. Two main reasons for this are discussed: (a) the inadequate class of models considered which rests on a restricted view of parsimony, and (b) the shortcomings of the basic approach to model identification.