Genetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecasting

I J C T A, 9(26) 2016, pp Iteratioal Sciece Press Geetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecastig B. Arputhamary 1, Z. Asha farhath 2 ad L. Arockiam 3 ABSTRACT The
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I J C T A, 9(26) 2016, pp Iteratioal Sciece Press Geetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecastig B. Arputhamary 1, Z. Asha farhath 2 ad L. Arockiam 3 ABSTRACT The model of predictio ad forecastig has existed from time traditioal. Oly most recetly scietific methods have bee ivolved i the process i time series models. Such forecastig whe doe through the moder techiques like ARIMA aturally improves the accuracy which is the primary focus of this study. I this work, a fuzzy based time series model Geetic ARIMA is proposed to compare with the ARIMA model ad the results show that the proposed model (Geetic ARIMA) performs better tha the existig ARIMA Model. This elaborates o the choices to be made for the appropriate dataset ad also foud that error rates are cosiderably less whe compared with the earlier models. Keywords: ARIMA Models, Forecastig, Fuzzy, Predictio, Time Series Models. 1. INTRODUCTION Time-series methods make forecasts or predictios based o the historical patters foud i the recorded data i the past. Such time-series methods utilizes the time as a idepedet variable while the factors are i the y plae. For ay time series, such y measuremets are take at successive poits (itervals) or over successive periods of time may be equal or o-equal. Such as the regardig measuremets may be take every hour, day, week, moth, year or ay other regular or irregular iterval of time. Therefore the first step i usig such time-series approaches is to gather the historical data of the object i focus. This historical data is represetative of the coditios expected i the future. Time series models are sufficiet to forecastig if demad it has show a cosistet patter i the past that is expected to occur i the future. Such as, ew homebuilders i US may see variatio i sales from moth to moth, but aalysis of past years data may expose that the sales of ew homes are icreased gradually over the period of time. I this case tred is icreased i ew home sales. Time series models are categorized ito four compoets; they are cyclical compoet, tred compoet, seasoal compoet ad irregular compoet. Tred is importat characteristics of time series models. Eve if times series may display tred, there might be data poits lyig above or below tred lie. Ay recurrig sequece of poits are above ad below the tred lie that last for more tha a year is cosidered to represet the cyclical compoet of the time series that is these observatios i the time series deviate from the tred due to fluctuatios. The compoet of the time series data that captures the chageability i the data due to seasoal fluctuatio is called the seasoal compoet. The seasoal compoet is similar to the cyclical compoet i that they both refer to some regular fluctuatio i a time series. Seasoal compoets are capturig the regular patter of variability i the time series with i oe-year periods. Seasoal commodities are best example for seasoal compoets. Radom variatio i 1 Research Scholar, Departmet of Computer Sciece, Mother Teresa Wome s Uiversity, Kodaikaal, Idia. 2 Research Scholar, Departmet of Computer Sciece, Bishop Heber College, Tiruchirappalli, Idia. 3 Associate Professor, Departmet of Computer Applicatios, St. Joseph s College, Tiruchirappalli, Idia. 418 B. Arputhamary, Z. Asha farhath ad L. Arockiam the times series are represeted by the irregular compoet. The irregular compoet of the time series caot be predicted i advace. The radom variatio i the time series is caused by short term, uexpected ad o recurrig factors that affect the time series. The focus is here to propose popular time series model Geetic ARIMA based o fuzzy for the same dataset ad the measures the parameters like predictio accuracy, time cosumed, ad overheads. The Geetic model s predictio is more accurate tha the ormal ARIMA model. I that the limitatio of the requiremets of huge historical data i a short spa of time is overcome by combiig the geetic model which utilizes the fuzzy regressio model i combiatio with a ARIMA model to work with little historical data. Combiatio of these two models the practical limitatio of requirig huge historical data is overcome ad also the overheads are sigificatly less aturally with icreased speed ad accuracy. 2. RELATED WORKS Johsto ad Harriso [1] foud forecast variaces for the simple ad Holt expoetial smoothig methods for state space models with multiple sources of errors. W. Jacobs et al [2] artificial eural etwork models ad compare the results to the idividual models, exemplify the combied forecast for the productio plaig. Styliaos I. Vagropoulos et al [3] i compares four practical methods for electricity geeratio forecastig of grid-coected Photovoltaic (PV) plats, that is Seasoal Autoregressive Itegrated Movig Average (SARIMA) model, SARIMAX model (SARIMA modelig with exogeous factor),modified SARIMA model, as a result of a a posteriori modificatio of the SARIMA model, ad ANN-based modelig. Rodrigo N. Calheiros et al [4] preseted the realizatio of a cloud workload predictio module for SaaS provider based o the autoregressive itegrated movig average (ARIMA) model. Lig Wag et al [5] proposed a simple ad effective predictio method for metro wheel wear based o the time series modelig ARIMA (p, d, q) model i Wear predictio of metro wheels based o the ARIMA model.takaomi HIRATA et al [6] a ovel predictio method which composes ot oly a kid of DBN with RBM ad MLP but also ARIMA to study of oliear pheomeo. Guoqiag Liu [7] proposed a hybrid model which cosists of two methods, Sigular Spectrum Aalysis (SSA) ad Auto Regressive Itegrated Movig Average (ARIMA) for forecastig medium ad log-term software failure time. Sorpo Wichaidit et al [8] predicted short-term stock prices of SET50 of Stock Exchage of Thailad usig CARIMA (Cross Correlatio Autoregressive Itegrated Movig Average) ad the results of CARIMA model yield better price treds.vaccaro et al [9] Local Learig-ARIMA adaptive hybrid architecture for hourly electricity price forecastig i proposed hybrid architecture for electricity price forecastig. The proposed architecture combies the advatages of the easy-to-use ad relatively easy-to-tue Autoregressive Itegrated Movig Average (ARIMA) models ad the approximatio power of local learig techiques. Shazhi Li et al [10] proposed hybrid model which combie a Autoregressive Itegrated Movig Average (ARIMA) model ad a Radial Basis Fuctio Neural Network (RBFNN) model where the result of fuzzy-eural etwork combiatio method reduce both mea square ad mea absolute errors. 3. PROPOSED MODEL The proposed model of geetic fuzzy ARIMA is implemeted o the basis of calculatig the forecast values by takig the umber of steps to be predicted. I this sectio the Geetic ARIMA (GA) is proposed to cosider the least amout of data s will be predicted ad produce the future accuracy values. It takes fuzzy logic ad it should be predicted the lower boud ad upper boud liear values. I geetic arima to reduce the time take, overheads, RMSE (Root Mea Square Error), MAPE (Mea Absolute Percetage Error) is Geetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecastig 419 compared to the Arima. Further the RMSE ad MAPE values for the airlie passeger dataset are computed for both the models ad displayed provig the latter model to accurately. The output graph shows the plot movig average or movig variace ad it will visible, if it varies with time. We will take the average/ variace of the last year that is last 12 moths. This is oe of the statistical tests for checkig statioary. The membership fuctios of the dataset that represets predictio or target parameters which is at the ceter of the umber where a high ad low are captured while a average is take. The weight of the predicted value depeds o the relatio of time lag ad the preset observatio. Fittig the ARIMA (p, d, q) by usig the available iformatio of observatios, i.e., iput data is the optimum solutio of the parameters ad residuals. The umber of costrait fuctios is the same as the umber of observatios. Next delete the data aroud the model s upper boud ad lower boud whe the Geetic ARIMA (fuzzy) model has outliers with a wide spread. Fially, delete the data aroud the model s upper ad lower boud whe the fuzzy ARIMA model has outliers with a wide spread. After forecast the values have bee geerated, the error rates for mea absolute percetage error, root mea square value are calculated from the forecasted values, which are tabulated ad graphed. Geetic ARIMA is compared to ARIMA it requires the accurate value of the forecasted data. It also calculated the error rates are better tha ARIMA model. A. The Arima Model does the Followig I ARIMA (p, d, q )p is the umber of autoregressive terms. d is the umber of o-seasoal differeces eeded for statioary. q is the umber of lagged forecast errors i the predictio equatio. To idetify the appropriate ARIMA model for Y, begi by determiig the order of differecig (d) eedig to statioeries the series ad remove the gross features of seasoality, perhaps i cojuctio with a variace-stabilize trasformatio such as loggig or deflatig. If stop this poit ad predict the differeced series are costat, have oly fitted a radom walk or radom tred model. However, the statioarized series may still have auto correlated errors, suggestig that some umber of AR terms (p 1) ad some umber MA terms (q 1) are also eeded i the forecastig equatio. B. Geetic Fuzzy Arima Algorithm Step 1: Iput N Dataset Step 2: Fid Itervals for i periods Step 3: Clease If iterval ivalid Remove data poit dp Else if iterval valid ad o data value Add data di based o historical data Step 4: Iput to Fuzzy F for i poits (x) = 1/(1 + e^ x) (x) + ( x) = 1 ( (x) + ( x)) * ( (y) + ( y)) * ( (z) + ( z)) = 1 Where x is for data poits across y time period i 420 B. Arputhamary, Z. Asha farhath ad L. Arockiam Step 5: Fuzzy set (..., x x, f ( x), x x 1, y 1,...) iterpolates the iterval [x, x +1 ] with a liear coectig the poits (x, f (x )) ad (x +1, y +1 ) Step 6: Take average values ad forecast. Step 7: Fid the error rates, Step 8: 1 MAPE Actual Forecast RMSE Step 9: Forecast with Actual Error Percetages. C. Algorithm Steps t 1 ( x x ) 1, t 2, t First the iput dataset is loaded ad it is fit ito the ARIMA model where the oise is idetified ad cleared. Next the icomplete dataset is filled up usig fuzzy logic. This leads to dataset values of itervals with upper ad lower boud values. The upper boud ad the actual values averages are got. Next the upper wide area is cleared, similarly for the lower wide area. This area is deleted ad the middle value is got ad the regressio model is the applied with ARIMA model by takig the average values. This yields the forecast of the period required. Next calculate the error percet usig MAPE ad RMSE. D. Cofiguratio Setup for Geetic Arima 2 Figure1: Proposed methodology of Geetic ARIMA Geetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecastig 421 Figure 2: Graphs shows the performace of the Geetic ARIMA is better tha ARIMA. Figure 3: Predictio for ARIMA forecastig model 4. EVALUATION AND DISCUSSION The predictive ability of the fuzzy ARIMA is rather ecouragig ad the possible iterval of the Geetic ARIMA is arrower tha 95% of the cofidece iterval of ormal ARIMA. It has the tedecy to icrease i the cofidece iterval. The time take for the algorithm to complete the forecastig is calculated based o the System. Nao method i millisecods which are recorded both before ad after the process is completed. This millisecod is divided by 1000 to get the secods take ad the the values are plotted o a graph. I this figure represet to predict the forecastig values of airlie passeger dataset usig ARIMA model ad calculate the MAPE (Mea Absolute Percetage Error), RMSE (Root Mea Squared Error). I this figure represet to predict the future accurate forecastig values usig fuzzy ad it fids the Error rates also. 422 B. Arputhamary, Z. Asha farhath ad L. Arockiam Figure 4: Predictio for Geetic ARIMA forecastig model (fuzzy) Table 1 Compariso of ARIMA Geetic ARIMA Error rates Error Rate RMSE MAPE Arima Geetic Arima Arima Geetic Arima MAPE (Mea Absolute Percetage Error) = 1 Actual Forecast. It calculates the Mea Absolute Percetage Error with the actual ad forecasted values. RMSE (Root Mea Squared Error) = t 1 ( x x ) 1, t 2, t 2. It calculates the Root Mea Squared Error with forecasted predictio values, ad it gives the accurate values of the Error rate. Geetic ARIMA (GARIMA): A Fuzzy based ARIMA Model for Time Series Forecastig CONCLUSIONS The proposed model requires cosiderably lesser observed historical data tha the ARIMA model. I additio to the umerous advatages outlied above the proposed model gives both scearios i.e. the best ad the worst etc. Also with a less observatios the predictio accuracy is high while the time cosumed ad overheads are sigificatly less compared to the traditioal ARIMA model, because of the icreased cofidece provided. The forecast values are also iterpolated with the error rates i.e. Root Mea Squared Error (RMSE) ad Mea Absolute Percetage (MAPE) ad it is foud that proposed model is havig the least error differetial rate whe compared with earlier models. REFERENCES Figure 5: Error rates for the ARIMA ad Geetic ARIMA. 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Aitouche, Wid Speed Forecastig Based o Fuzzy-Neural Network Combiatio Method, The 27 th Chiese Cotrol ad Decisio Coferece (2015 CCDC), Qigdao, , 2015.
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