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- Time series forecasting of styrene price using a hybrid ARIMA and neural network model
- International Journal of Computational Intelligence Systems
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- Time series forecasting of styrene price using a hybrid ARIMA and neural network model

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## Time series forecasting of styrene price using a hybrid ARIMA and neural network model

Drought is a water shortage that is caused by an imbalance between supply and demand. As one of the most severe natural disasters, drought exerts relatively widespread effects on human society that usually last for several months or even a few years, causing huge economic loss, reductions in food yield, starvation, and land degradation Piao et al.

China is located in the East Asian monsoon region, with complex geographical conditions, complex climate changes, and frequent climate disasters. As climate warming and drying become increasingly apparent, the occurrence of natural disasters has increased significantly. Affected by specific climatic conditions, topographical features, and water resources, China is one of the countries with the most frequent and severe drought in the world.

Local or regional drought occurs almost every year Chen and Sun ; Wang et al. Global warming and excessive carbon emissions will lead to the continued warming of agricultural lands in the future Allen and Ingram Global food production, including in China, has been seriously threatened. Therefore, quantitative studies on drought could facilitate research regarding the spatiotemporal changes in drought characteristics, improve drought monitoring ability, aid in the performance of drought forecasting work, and help identify drought management and coping strategies.

It has important significance for future agricultural production, drought prevention, and drought resistance in China.

Droughts are generally categorized into five types: meteorological droughts, agricultural droughts, hydrological droughts, socioeconomical droughts, and droughts that impact stream health Esfahanian et al.

Because of the wide range of applications of drought indicators and the variation in the understanding of drought across different professions and disciplines, various drought indicators have emerged. More than drought definitions and indicators exist worldwide.

Different angle definitions and the use of different criteria to measure drought will result in variation in the understanding of drought. There are many meteorological drought indices Tarpley et al. Among them, the PDSI is calculated with monthly temperature and precipitation data and soil water-holding capacity information, and the main application is to identify droughts that affect agriculture Belayneh et al.

Similarly, the SPEI requires the inclusion of temperature and precipitation data so that the index can take into account the effect of temperature on drought development, but compared to the SPI, it is more computationally expensive and is not widely applicable. The SPI drought index, which was first proposed by McKee in the study of drought in Colorado, United States, is the quantile of the standard normal distribution transformed from the precipitation distribution function, and it can be used to characterize the probability of precipitation occurring during a certain period of time.

The SPI is a powerful, flexible index that is sample to calculate. In fact, precipitation is the only required input parameter. Huang et al. To provide an overall view of drought conditions across the Loess Plateau of China, Liu et al. Therefore, the SPI drought index was chosen to forecast drought in this study. It is important to strengthen research on drought prediction to prevent drought disasters and reduce the loss caused by drought disasters.

To date, the most commonly used methods to assess and predict drought are data-driven methods. Data-driven models have rapid development times and have traditionally been used for drought forecasting Adamowski ; Karthika et al.

Fung et al. The principal objective of the Karthika et al. The results showed that the best ARIMA models are compared with the observed data for model validation purposes in which the predicted data show reasonably good agreement with the actual data. The results reveal that all developed ARIMA models demonstrate the potential ability to forecast drought over different time scales. Stochastic models are linear models with limited ability to predict nonlinear data.

To effectively predict nonlinear data, an increasing number of researchers have begun to use artificial neural networks ANNs to predict hydrological data in the past decade Kousari et al. Artificial neural networks have been used as drought prediction tools in many studies Seibert et al. Support vector machines SVMs , such as the ANN model, are machine-learning techniques that have been successfully applied in classification, regression, and forecasting in the field of hydrology Tabari et al.

Support vector machines can be divided into support vector classification SVC and support vector regression SVR , which solve classification and regression problems, respectively. Borji et al. The results showed, that the SVR approach showed a better efficiency in the forecast of long-term droughts compared to the ANN.

When predicting the drought conditions in the Awash River basin of Ethiopia, Belayneh et al. To improve prediction accuracy in time series forecasting, Choubin et al. A study by Soh et al. A study by Fung et al. Using similar methods, Fung et al. The similarity between this study and Soh et al. The purpose of this paper is to propose a hybrid model to improve the application of a single linear or nonlinear model in drought prediction. Taking Henan Province as an example, based on the SPI values of 19 meteorological stations from to , this study compares the effectiveness of two models in forecasting drought conditions in Henan Province.

Because ArcGIS has a powerful function in spatial analysis, the kriging interpolation method is commonly used for interpolation analysis of drought index and rainfall Cai et al.

When Afzali et al. Karavitis et al. Similar research has also used Cai et al. This paper will describe the use of the kriging interpolation method in the ArcGIS software to conduct a visual analysis of the SPI3 observed values and fitted values of the two models in As a province located in the middle and lower reaches of the Yellow River, a midlatitude zone in China, Henan Province is an important food-crop-producing area and a major agricultural province.

It plays a vital role in ensuring national food security Shi et al. As a province situated in the warm temperate and subtropical region, Henan is characterized by a dry spring with frequent wind, a hot summer with abundant rainfall, a clear autumn with plenty of sunshine, and a cold winter with light snow. However, due to its special topography and geographical location, meteorological disasters are frequent occurrences; drought is one of the most frequent natural disasters, with a long duration, including spring droughts and summer droughts, as well as spring and summer or summer and autumn droughts.

Due to the large area of Henan Province, the terrain features are high in the west and low in the east. This paper uses daily precipitation data from 19 national meteorological stations Fig. Citation: Journal of Applied Meteorology and Climatology 59, 7; The results of his work were first presented at the Eighth Congress of Applied Climatology in January The index is based on the relationships between drought and frequency, duration, and time scale.

The SPI can be applied to all climatic conditions, and the calculated SPI values indicating large climactic differences can be compared and analyzed. Because of the flexibility of the SPI, it can be calculated using data missing from the recording cycle at a given location. Typically calculated on a month time scale, the index is flexible and can be used for a variety of purposes, including for events affecting agriculture, water resources and other industries.

Usually, SPI values of less than 3 months may be used for basic drought monitoring, while SPI values of less than 6 months may be used for monitoring agricultural impacts, and SPI values of more than 12 months may be used for hydrological impacts Tsakiris and Vangelis ; Mishra and Desai ; Cacciamani et al. The use of precipitation data is the greatest advantage of the SPI because it makes it extremely easy to use and calculate Cacciamani et al.

The classification of dry and wet spells resulting from the values of the SPI is shown in Table 1. The ARIMA model is the stochastic model and has been widely used in hydrologic forecasting over recent decades according to the well-known Box—Jenkins methodology Kisi et al. The modeling process is first to judge the smoothness of the model, then to use the difference method to smooth the nonstationary time series, and then to select AR p and MA q to classify the model; the number of differences is recorded as d , which will be determined.

The ARIMA q, d, p —selected time segments are used as training sets and test sets for predictive analysis. Equation 5 is the MA formula; MA is constructed with the weighted average of u t itself and q lag terms of u t ,. The formula is as follows:.

The basic idea of the SVM is to construct a hyperplane in a high-dimensional space used for classification or regression. Its characteristic is to transform the nonlinear classification problem or original sample attribute space into a linear convex quadratic programming problem of high-dimensional space by introducing the kernel function mapping method.

This method guarantees the uniqueness and global optimality of the understanding and solves the local extremum problem, which is difficult to avoid in the neural network method, and the algorithm complexity is independent of the sample dimension. The core of the SVM method is to find the classification surface in the case of a linear separable.

The SVM model uses a small number of support vectors to represent the decision function, which has sparse characteristics. When extending the SVM method to the regression problem—namely, SVR—it is necessary to introduce a loss function to maintain this important property. The relationship between sigma and gamma in the radial basis function RBF formula is as follows:. The relationship between sigma and gamma in the RBF is calculated as follows:.

It was assumed that the time series Y t can be regarded as a combination of the linear autocorrelation part L t and the nonlinear residual N t. First, the ARIMA model was used to predict the SPI values, and then the result was subtracted from the actual value to obtain the residual, which was recorded as a nonlinear part.

Second, the residual was brought into the SVR model for prediction. Last, the two prediction results were added to obtain the combined result:. RMSE is used to measure the deviation between the observed value and the real value. MAE is the mean value of the absolute error, which can better reflect the actual situation of the error of the predicted value. The R 2 method is typically used in regression models to evaluate the degree to which a predicted value matches the actual value, using the mean value as the error baseline to determine whether the prediction error is greater than or less than the mean.

The interval is usually 0, 1 ; 0 means not predictable at all, directly taking the mean, and 1 means that all forecasts match the real result perfectly. The NSE method is typically used in hydrological simulation of hydrology, as well as in the test of model simulation effect of studying the relationship between climate, environment, soil, ecology, and hydrological process. The formulas are as follows Belayneh et al. SSE is given by. The coefficient of determination is.

The matplotlib visualization library in Python 3. Because there were too many meteorological station sites, this paper selects five meteorological stations in east, west, south, north, and middle of Henan Province as examples to carry out the calculation and demonstration of multiscale SPI, as shown in Fig. Using augmented Dickey—Fuller ADF to test the stationarity of time series and analysis is conducted according to the Box—Jenkins method the same way as in this paper.

The ADF test was adopted in this paper to evaluate the stationarity of the time series. In the ADF test, the original hypothesis was that of a nonstationary time series, and there was a unit root.

Given a significance level of 0. If the P value is greater than 0. Therefore, the difference for the stationary time series, after adopting the Ljung—Box test white noise inspection procedure, smoothed the white noise sequence, and then the autocorrelation function ACF and partial autocorrelation function PACF were used to classify the ARIMA p , d , q model.

Unit root test of five example meteorological stations at four time scales of the SPI original sequence.

## International Journal of Computational Intelligence Systems

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Zhang Published Computer Science Neurocomputing. Abstract Autoregressive integrated moving average ARIMA is one of the popular linear models in time series forecasting during the past three decades.

Artificial neural networks ANNs are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. This is the reason that hybrid methodologies combining linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. Despite of all advantages of the traditional methodologies for combining ARIMA and ANNs, they have some assumptions that will degenerate their performance if the opposite situation occurs. In this paper, a new methodology is proposed in order to combine the ANNs with ARIMA in order to overcome the limitations of traditional hybrid methodologies and yield more general and more accurate hybrid models.

## We apologize for the inconvenience...

This paper proposes a novel hybrid forecasting model combining autoregressive integrated moving average ARIMA and artificial neural network ANN with incorporating moving average and the annual seasonal index for Thailand's cassava export i. The comprehensive experiments are conducted to investigate the appropriate parameters of the proposed model as well as other forecasting models compared. Therefore, the proposed model can be used as an alternative forecasting method for stakeholders making a decision in cassava international trading to obtain better accuracy in predicting future export of native starch and modified starch which are the majority of the total export. Time series forecasting is an important research area which has attracted a lot of attention from research communities in numerous practical fields including statistics, business, econometrics, finance, weather forecasting, earthquake prediction, etc.

*Authors: Fengxia Zheng , Shouming Zhong. ANNARIMA that combines both autoregressive integrated moving average ARIMA model and artificial neural network ANN model is a valuable tool for modeling and forecasting nonlinear time series, yet the over-fitting problem is more likely to occur in neural network models.*

### Time series forecasting of styrene price using a hybrid ARIMA and neural network model

Linear forecasting models have played major roles in many applications for over a century. If error terms in models are normally distributed, linear models are capable of producing the most accurate forecasting results. The central limit theorem CLT provides theoretical support in applying linear models. During the last two decades, nonlinear models such as neural network models have gradually emerged as alternatives in modeling and forecasting real processes.

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Drought is a water shortage that is caused by an imbalance between supply and demand.