Comparative Study of ANFIS and ARIMA Model for Weather Forecasting in Dhaka

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1 Comparative Study of ANFIS and ARIMA Model for Weather Forecasting in Dhaka Mahmudur Rahman, A.H.M. Saiful Islam, Shah Yaser Maqnoon Nadvi, Rashedur M Rahman Department of Electrical Engineering and Computer Science, North South University, Dhaka 1229, Bangladesh babu_2008nsu@yahoo.com, tamim_saif@yahoo.com, symnadvi@yahoo.com, rashedur@northsouth.edu Abstract Significant amount of research have been carried out and various models have been developed by the researchers for weather forecasting. In this paper we present a comparative study of ARIMA (Auto-Regressive Integrated Moving Average) and ANFIS (Adaptive Network Based Fuzzy Inference System) models for forecasting the weather conditions in Dhaka, Bangladesh. Ten years weather data (from year 2000 to 2009), i.e., Maximum Temperature, Minimum Temperature, Humidity and Air Pressure are used in this research. We have compared the models with difference performance metric, for example, with Mean Absolute Error (MAE), Root Mean Square Error (RMSE), R-square error and the Sum of Square Error (SSE). Experimental results demonstrate that ARIMA has better performance compared to ANFIS. In this study, SPSS is used to carry out experiments on ARIMA model and Fuzzy Logic Toolbox in Matlab is used for ANFIS model. Keywords- ANFIS; fuzzy logic; ARIMA; fuzzy inference system; weather forecasting. I. INTRODUCTION Weather forecast systems are among the most complex systems that computers need to solve [1]. Weather prediction can have many different forms, depending on the required applications [2]. For example, in the seaport we need to know the future weather condition for a week or more. On the other hand, in the airport it is more important to know about the climate visibility a few hours ahead rather than the temperature. Whereas, in buildings weather predictions can play an important role in saving the energy [2]. Weather forecasts give an idea about future weather. There are various techniques involved in weather forecasting, from relatively simple observation of the sky to highly complex computerized mathematical models [1]. However, Meteorological data are uncertain (fuzzy) in nature, and Information on weather is vaguely defined [3]. Weather data can have the noises and outliers, therefore, the analysis may not be accurate. Noise is a random error or parasite that comes from the sensor network, error handwriting and so on. On the other hand, an outlier is an observation of the data that deviates from other observations so much [2]. Therefore, we need preprocessing of the weather data to improve the quality of data for precise weather prediction. The data are collected from the Bangladesh Meteorological Department which is the head office of the all weather stations in Bangladesh. In the data set, there are five parameters: Maximum Temperature, Minimum Temperature, Humidity and Air Pressure, and this data are only on Dhaka s weather condition. For analysis and forecast, we applied ANFIS and ARIMA on this data; finally they are evaluated and compared. In this paper, ARIMA model is used in SPSS software for weather forecast. SPSS which stands for Statistical Package for the Social Sciences encapsulates advanced mathematical and statistical expertise to extract predictive knowledge that when deployed into existing processes makes them adaptive to improve outcomes [4]. Thus, together with these advantages offered by this software, we can predict the outcomes before they occur. ANFIS model is used from ANFIS Editor GUI in the Fuzzy Logic Toolbox. These tools apply fuzzy inference techniques to data modeling. The ANFIS toolbox function constructs a fuzzy inference system (FIS) whose membership function parameters are tuned (adjusted) using either a back propagation algorithm alone, or in combination with the least squares methods. This allows our fuzzy systems to learn from the data they are modeling [5]. The rest of the paper is organized as follows: Section 2 describes the related works on our topic. Section 3 is used for methodologies and data representation, the models that are investigated are also described in Section 3 and Sectio 4. Section presents and analyzes the results. Finally we summarize and give future direction of research in Section 6. II. LITERATURE REVIEW ON RELATED WORK History of numerical weather prediction has been since the groundbreaking work of V. Bjerknes (1904) and LF. Richardson (1922), the challenge of weather forecasting has been related to an initial value problem of mathematical physics (based on the non-linear equations governing fluid flow) and has been approached using numerical means [2]. In [2], the authors proposed a new method by using fuzzy c-mean and type-2 fuzzy logic. They presented a comparative study of different methods of weather forecasting. For example, they used Numerical Weather Prediction (NWP), Markov-Fourier Gray Model, Artificial Neural Networks (ANNs), Neuro-Fuzzy Logic System, Fuzzy logic and Clustering Analysis. Those methods were used for comparison and the results found were discussed with their strengths and weaknesses. This paper also illustrated different data preprocessing techniques /13/$ IEEE

2 In [6], the authors used ARIMA and ANFIS model for forecasting Wi-max traffic. Final results show that ANFIS has more accuracy than ARIMA, though ARIMA has less execution time than ANFIS. The best use of ANFIS model for weather forecasting can be found in [7]. The authors used ANIFS model for predicting rainfall based on other weather data. In this study, they applied multi parameter Adaptive Neuro Fuzzy Inference System (ANFIS) for daily rainfall prediction in a location of PT Timika, Indonesia, and used series data of relative humidity, temperature, pressure and rainfall. In conclusion, they said that they performed a study on multivariate ANFIS application in predicting daily rainfall values. The study focused on the influence of training data length. They also found that ANFIS was sensitive to different magnitudes and scale sizes and not an appropriate tool for a stochastic process like rainfall [7]. Reference [8] is on radiation fog forecasting using fuzzy logic rule based approach. Weather forecasts will be most important when the situation is irregular or disordered. Under such situations, existing Numerical Weather Prediction (NWP) approach does not produce satisfactory results. To cope up with vague and/or abnormal (chaotic) meteorological information, a weather forecasting approach using fuzzy logic based approximate reasoning is considered [8]. This paper compares the numerical method and fuzzy logic. The authors developed different fuzzy if-then rules for predicting the condition. In summary, the research addresses the issue of fuzzy rule-based modelling of available data and indicates a solution for predicting the probability of the formation of fog by formulating the problem within a fuzzy framework [8]. There is another work on ANFIS model in [9]. The authors present a time series prediction model for daylight interior luminance obtained using Adaptive Neuro Fuzzy Inference System (ANFIS). The authors show that ANFIS has automated identification algorithm and has easier design compared to neural networks with respect to less number of parameters and faster adaptation. In conclusion they said that the most important advantage of such model is the ability to predict natural system s behavior at a future time, which can be used for lighting control. In [15], the authors show that ANFIS model has better performance than ANN ( Artificial Neural Network ). They forecast rainfall for Klang River in Malaysia on a monthly basis. For performance comparison, five criterias are used such as Root Mean Square Error (RMSE), Correlation Coefficient (R 2 ) and Nash Sutcliffe coefficient (NE), Gamma Coefficent (GC), Spearman correlation coefficient (SCC). In summary, the authors show that ANFIS method is superior to the ANN method in forecasting monthly rainfall [15]. III. THE ANFIS MODEL Roger Jang proposed Adaptive Neuro Fuzzy Inference system (ANFIS) in ANFIS can provide as a basis for constructing a set of fuzzy if-then rules with appropriate membership functions to generate the stipulated input output pairs [10]. A. ANFIS model description ANFIS model is based on the Sugeno Model. If there are two inputs x and y and one output z, then the first-order Sugeno model can be described by the rules as follows (Fig. 1): Rule1: If x is A1 and y is B1, then f1 = p1x + q1y + r1 Rule2: If x is A2 and y is B2, then f2 = p2x + q2y + r2 Figure 1. Sugeno Fuzzy Inference Model. ANFIS is the combination of fuzzy logic and neural network. In ANFIS model, crisp input series are converted to fuzzy inputs by developing membership function for each input series [1]. The membership function can be any shape but it depends on the data set. In our data set we used Gaussian shape for membership function. Therefore, the overall architecture of ANFIS is given in Fig. 2. Layer1 Layer2 Layer3 Layer4 Layer5 Figure 2. ANFIS architecture. Here, we have five layers of ANFIS and each layer has different operation. The nodes in the same layer of ANFIS are of the same functional family and are arranged as follows [10]: Layer 1: In this layer, every node generates the membership grades of a linguistic label. So any mode of this layer performs the membership function. For example, if the input is x then it puts x into the membership function μa (x) where A is the linguistic value to associate with each node. The set of parameters {a, b, c} is used to adjust the shape of the membership function. Layer 2: The firing strength of each rule is calculated by multiplication. (1)

Layer 3: The i th node of this layer calculates the ratio of the i th rule s firing strength to the sum of all rule s firing strengths: w1 W = (2) w + w 1 2 Layer 4: In this layer, the operation is

Figure 3. Membership functions of ANFS model. Layer 5: This is the final layer. It gives the output by the summation of all incoming signals: Overall output= f (4) w i B.

3 Layer 3: The i th node of this layer calculates the ratio of the i th rule s firing strength to the sum of all rule s firing strengths: w1 W = (2) w + w 1 2 Layer 4: In this layer, the operation is that it multiplies the output of layer3 and Sugeno model output : ( px + qy rz) w f = w + (3) Where (p, q, r) is the parameter set. These parameters will be referred to as consequent parameters. Figure 3. Membership functions of ANFS model. Layer 5: This is the final layer. It gives the output by the summation of all incoming signals: Overall output= f (4) w i B. Using ANFIS for Time-Series Prediction According to the reference [13], weather time series is completely chaotic, and there is no clearly defined period. Generally, in time-series prediction, we would like to use known values of the time series up to the point in time, let t, to predict the value at some point in the future, say, (t + P). The standard method for this type of prediction is to create a mapping from D sample data points, sampled every unit in time, (x (t-(d-1) Δ)... x (t-δ), x (t)), to a predicted future value x (t + P). Following the conventional settings for predicting the weather time series, we set D = 4 and Δ = P = 6. For each t, the input training data for ANFIS is a fourdimensional vector of the following form: Figure 4. ANFIS Structure (5) The output training data corresponds to the trajectory prediction: 6 (6) For each t, ranging in values from 118 to 1117, the training input/output data will be a structure whose first component is the four-dimensional input w, and whose second component is the output, S. After applying the ANFIS model with data; Number of nodes: 193, Number of linear parameters: 81, Number of nonlinear parameters: 24, Total number of parameters: 105, Number of training data pairs: 1586, Number of checking data pairs: 0, Number of fuzzy rules: 81. Figure 5. Step Size error of 20 epochs

Figure 6. : Real and ANFIS system output Figure 8. Error output of the model. IV. THE ARIMA MODEL In real world application, much process can be represented using the time series as follows [1]:.

Linear prediction, where the estimate is based on a linear combination of N past samples [1], can be represented as below: X 1 a i., (8) Where prediction coefficient is a i,i=0, 1, 2 N-1. Figure 7.

It uses auto-regressive, integrated, moving-average (ARIMA) models for time series data. We know that a time series is a set of observations ordered according to the time they were observed.

4 Figure 6. : Real and ANFIS system output Figure 8. Error output of the model. IV. THE ARIMA MODEL In real world application, much process can be represented using the time series as follows [1]:. 2, 1, (7) There are many numerical methods for time series prediction. For prediction we need to use previous sample data. Linear prediction, where the estimate is based on a linear combination of N past samples [1], can be represented as below: X 1 a i., (8) Where prediction coefficient is a i,i=0, 1, 2 N-1. Figure 7. : Regression results ARIMA stands for Auto-Regressive Integrated Moving Average. ARIMA model is popularized by Box and Jenkins (1976). It is a combination of three mathematical models. It uses auto-regressive, integrated, moving-average (ARIMA) models for time series data. We know that a time series is a set of observations ordered according to the time they were observed. For the reason that the value observed at time t may depend on values observed at previous time points, time series data may violate independence assumptions [14]. An ARIMA (p, d, and q) model can account for temporal dependence in several ways. First, the time series is deference to render it stationary, by taking d differences.. If d = 0, the observations are modelled directly, and If d = 1, the differences between consecutive observations are modelled.

Second, the time dependence of the stationary process is modelled, by including p auto-regressive. The equation for p is that: Estimated Std Error Regression Coefficients V1 0.000 0.

It takes the observation of previous errors. The equation is:, (10) Where, is the parameter of the model, is the error term. Finally, combining these three models we get ARIMA model.

5 Second, the time dependence of the stationary process is modelled, by including p auto-regressive. The equation for p is that: Estimated Std Error Regression Coefficients V , (9) Constant Where, a is the constant, is the parameter of the model, is the value that observed at t and stands for random error. a. Output of SPSS s package Third, q is the moving-average terms, in addition to any time-varying covariates. It takes the observation of previous errors. The equation is:, (10) Where, is the parameter of the model, is the error term. Finally, combining these three models we get ARIMA model. So the general form of the ARIMA models is given by: Figure 9. The data plot with predicted values. Y., (11) Where Y, a stationary is a stochastic process, is the constant, is the error or white noise disturbance term, means auto-regression coefficient and is the moving average coefficient. For a cyclical time series, these steps can be repeated according to the period of the cycle, whether quarterly or monthly or other time interval. ARIMA models are extremely flexible for continuous data [14]. For computing ARIMA model we use SPSS s package program. We take ARIMA (2, 0, 1) model (Fig. 9). For accuracy of the ARIMA (2, 0, 1), we need to plot Autocorrelation Function (ACF) and Partial autocorrelation (PACF). From ACF, we obtain Moving Average terms, and from PACF, we find Auto-Regressive terms. Fig. 10 and Fig. 11 shows the ACF and the PACF graphs respectively. The result of parameters of the ARIMA (2, 0, 1) is obtained from the output of SPSS s package as follows: Figure 10. ACF for ARIMA (2, 0, 1). TABLE I. PARAMETER ESTIMATION Estimated Std Error Non-seasonal Lags AR1 AR2 MA Figure 11. : PACF for ARIMA (2, 0, 1).

6 The error of the ARIMA (2, 0, 1) model is plotted in the Fig. 12. VI. CONCLUSION In this research, the performances of ANFIS and ARIMA are compared. ARIMA can more efficiently capture the dynamic behavior of the weather property, say, temperature compared to ANFIS. However we could not explore all the features of ANFIS due to the time limitation. Therefore, the decision about the performance of ANFIS model is not complete and final. We need to investigate more in this direction. Our preliminary findings show that ARIMA is better than ANFIS. In the future, we plan to develop our own fuzzy logic and curve fitting techniques for weather forecasting. Finally, we want to compare those four techniques along with artificial neural network to find the best one. Figure 12. Error of the prediction. V. DISCUSSION AND THE RESULT ANALYSIS In our study, all data, recorded in the Bangladesh Meteorological Department, is used for the analysis in this comparison study. We collected the ten years data from 2000 to 2009, and then did the data pre-processing to clean data such as missing data and inconsistent data. We used ANFIS model for four inputs and one output. We also used 95% temparture data to train this model, and rest 5% data for testing the model. We used the same data for ARIMA (2, 0, 1 ) model. In our project, we did not test the model with other weather data, for example, humidity or air pressure due to time limitation. The performance comparisons of ANFIS and ARIMA (2, 0, 1) due to MAE, SSE, RMSE and R 2 are shown below: TABLE II. PERFORMANCE COMPARISON Performance criteria ANFIS ARIMA 1. SSE R RMSE MAE From this, we can say that ARIMA has better performance than ANFIS model. REFERENCES [1] M. Tektas, Weather Forecasting Using ANFIS and ARIMA- A Case Study for Istanbul,. Environmental Research, Engineering and Management, vol. 1 (51), pp. 5 10, [2] A. Shahi, R. Atan, M. N. Sulaiman, An Effective Fuzzy C-Mean and Type-2 Logic for Weather Forecasting,. Journal of Theoretical and Applied Information, vol. 5 (5), pp , [3] H. Bjarne, A fuzzy expert system For critiquing marine forecasts,. The Maritimes Weather Centre of Environment Canada in Bedford, Nova Scotia, vol. 11, pp , [4] SPSS, accessed on August [5] Fuzzy Logic Toolbox: For Use with MATLAB, User s Guide, Version 2, The MathWorks. [6] P. Francisco, A. Cesar, S. Hernandez, J. Octavio, P. Salcedo, Comparative Analysis of Time Series Techniques ARIMA and ANFIS of Forecast Wimax Traffic,. ACM, New York, NY, USA, pp ,2009. [7] A. Edvin, D. Yudha Setiawan, Application of Multivariate Anfis for Daily Rainfall Prediction: Influences of Training Data Size, Makara, Sains, Vol. 12 ( 1), pp. 7-14, April [8] B. Rajarshi, T. P. Singh, Forecasting of Radiation Fog: A Fuzzy Logic Rule Based Approach, Symbiosis International University,Pune, unpublished. [9] K. Ciji Pearl, V. I. George, B. Jayadev, A. Radhakrishna, Anfis Model for the Time Series Prediction of Interior Daylight Illuminance,. AIML Journal, vol. 6 (3), September [10] L. H. Tsoukalas, R. E. Uhrig, Fuzzy and Neural Approaches in Engineering. A Wiley-Interscience Publication, [11] H. Jiawei, M. Kamber, Data Mining: Concepts and Techniques. The Morgan Kaufman Series in Data Management Systems, University of Illinois at Urbana-Champaign: Diane Cerra, 2006 [12] J.S.R. Jang, ANFIS : Adaptive-Network-Based Fuzzy Inference System,. IEEE transactions on systems, Man and Cybern., vol. 23(3), pp , Jun1993. [13] Tutorial (Fuzzy toolbox), Matlab 7. [14] J. Grimmer, Arima Models for Time Series Data. Zelig: Everyone s Statistical Software, [15] A. El-Shafie, O. Jaafer, A. Seyed Ahmad, Adaptive Neuro-fuzzy Inference System based Model for Rainfall Forecasting in Klang River, Malaysia,. International Journal of the Physical Sciences, vol. 6 (12), pp ,june2011.

Comparative Analysis of ANFIS, ARIMA and Polynomial Curve Fitting for Weather Forecasting

Indian Journal of Science and Technology, Vol 9(15), DOI: 10.17485/ijst/2016/v9i15/89814, April 2016 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 Comparative Analysis of ANFIS, ARIMA and Polynomial