TELECOMMUNICATION DATA FORECASTING BASED ON ARIMA MODEL

Transcription

1 TEECOMMUNICATION DATA FORECASTING BASED ON ARIMA MODE Anjuman Akbar Muani 1, Prof. Sachin Muraraka 2, Prof. K. Sujatha 3 1Student ME E&TC,Shree Ramchandra Coege of Engineering, onikand,pune,maharashtra 2,3Assistant Professor,Shree Ramchandra Coege of Engineering, onikand,pune,maharashtra ABSTRACT Forecasting of teecommunication data find difficut according to Internationa Teecommunication Union (ITU) recommendation due to uncertainty invoved and the continuous growth of data in teecommunication markets as it heps them in panning and determining their networks. So, there is a need of good forecasting mode to predict the future. In this paper, ARIMA is utiized for forecasting teecommunication data. This mode adaptivey uses auto regression, moving average or combined together if required. The three steps invoved in the ARIMA mode is identification, estimation and forecasting. The adaptive ARIMA mode is then appied to M3-Competition Data to do forecasting of teecommunication data. The performance of the mode is found out using the evauation metrics such as Root Mean Square Error, Sum otwf Squared Regression, Maximum Absoute Error, Mean Absoute Deviation, and Mean Absoute Percentage Error. The resuts proved that the ARIMA modes provide 7.6% improvement than the neura network method in forecasting performance. Keywords: ARIMA Mode, Forecasting, ITU Recommendations, Teecommunication, Time Series M3 Competition Data. I. INTRODUCTION Forecasting predicts what wi occur in the future. Forecasting is becoming important because of the high turbuence in teecommunications market because of rapid technoogica deveopment and iberaization. Teecommunications industries are growing very fast and the abiity to determine the future trends is an important task. Business peopes try to forecast with high accuracy, but it is difficut in today s fast-paced business word [12]. The boundaries of the teecommunication industries are increasing very fast and there is tremendous competition amongst them. Teecommunications companies are in need to impement new technoogies to meet the requirement of providing best services. Many industries depend on data monitoring to enhance their business by anayzing the market trends and marketing vaues for their products [8, 4]. However, there is a probem in bring the gap between the known data and probabe vaue in the future due to the ack of reiabe input data for forecasting and adequate mode. The forecastabiity of a time series data is an important factor for the forecasting practitioners. The forecasters can determine the outcome of any event with the prior knowedge about the event. Whie forecasting teecommunication data, many errors may occur and it motivates to find a better forecasting approach which 451 P a g e

2 minimizes the forecasting errors. If there is a probem in accuracy of forecasting data, then reducing the forecasting error wi be ineffective. So, it is necessary to impement new techniques to minimize the effects of poor forecasts [2]. The forecastabiity of a time series is dependent on the data reguarity. If the time series is ess reguar, then achieving good eve of forecasting accuracy is very difficut [3, 9-11]. In this paper, ARIMA mode for forecasting teecommunication data is proposed. M3-Competitive data is used here and the performance is measured in terms of Sum of Maximum Absoute Error (MAE), Mean Absoute Percentage Error (MAPE) Squared Regression (SSR), Root Mean Square Error (RMSE) and Mean Absoute Deviation (MAD). The paper is structured as foows. Section 2 provides the iterature review. Section 3 describes the M3-Competition teecommunication data. Section 4 describes about the ARIMA based forecast mode. Section 5 evauates performance of forecasting. Resuts of forecasting are given in section 6 and section 7 concudes the paper. II. ITERATURE REVIEW A forecasting system coects and processes data for thousands of items and deveops forecasts using forecasting methods such as ARIMA mode. It has an interactive management user interface which maintains a database of demands and has report fie-writing capabiities. Three panning horizons for forecasting exist. The short-term forecast covers a period beow three months. The medium-term forecast usuay covers a period of three months to two years. And, the ong-term forecast covers a period of more than two years. Generay, the short-term forecast is used for the routine operations and panning of a company. The ong-term forecast is used more for strategic panning [22]. Forecasting techniques can be categorized into quantitative techniques and quaitative techniques. The quaitative modes incude subjective or intuitive modes and the severa quantitative techniques are avaiabe for forecasting are Random wak (simpe forecasting method), exponentia smoothing methods such as simpe exponentia smoothing (SES), robust trend, Hot and Hot-winters etc. In the random wak mode, variabe vaues foow a random step for each time interva. It assumes the importance of current observation ony and the previous observations provide no information [15]. SES is a suitabe method for forecasting seasona data. But if there is a trend it s not suitabe [16]. An extended form of simpe exponentia smoothing method is HOT method and it aows forecasting data with trends. There can be improved to dea with both trend & seasona variations. By considering the seasona variations Hot-winter method overcomes Hot method [18]. Method suitabe for forecasting univariate time series data in the presence of outiers is robust trend. When using this method, incorrect abeing of sampes as outiers may occur. Mahsin used Box-Jenkins methodoogy for creating seasona ARIMA mode for monthy basis rainfa information taken for Dhaka station, Bangadesh, for amount during In their paper, ARIMA (0, 0, 1) (0, 1, 1) 12 mode was found adequate and aso the mode is used for forecasting the monthy rain [20]. Seyed et a. used time series methodoogy to mode weather parameter in Isamic, Abadeh Station in Iran and counseed ARIMA(0,0,1)(1,1,1) 12 because the best appropriate monthy rainfa information and ARIMA(2,1,0)(2,1,0) 12 for average temperature on monthy basis for Abadeh station. They modeed weather parameter using random methods (ARIMA Mode) [21]. 452 P a g e

3 III. M3-COMPETITION DATA As the forecastabiity is growing up, there is a great importance for checking the adequacy of forecasting methods. Makridakis and Hibon deveoped the M-Competition which is one of the important researches in this fied [5, 13]. M Competitions or M-Competitions is used for a series of competitions organized by teams ed by forecasting researcher Spyros Makridakis and intended to find out and compare the accuracy of various forecasting methods. Data used here are obtained from the Institute of Forecasters. The ast edition (M3) is referred to year 2000 and it incudes 3003 time series cassified in to various types such as micro (828), industry (519), macro (731), finance (308), demographic (413) and other (204) and the various time durations between the successive observations are gives by yeary, quartery, monthy and of unknown periodicity( others ). Minimum number of observations for each type of data is required to ensure that enough data can deveop an absoute forecasting mode. This minimum was set as 14 observations for yeary series, 16 for quartery, 48 for monthy and 60 for other series. Tabe 1 show the cassification of the 3003 series according to the two major grouping discussed above. The tabe shows the number of time series based on both time interva and domain. Tabe i: The cassification of the 3003 time series used in the m3-competition Time interva Types of time series data between successive observations Micro Industry Macro Finance Demographic Other Tota Yeary Quartery Monthy Other Tota IV. ARIMA-BASED FORECAST MODE Box and Jenkins introduced the Autoregressive integrated moving average (ARIMA) mode. It is used as one of the popuar method for forecasting time series data [6, 14]. Auto regression and Moving average can be used separatey and combined together if required. This method is considered as sophisticated method and required usuay arge dataset of past data. Major steps invoved in this process are identification, estimation and forecasting. ARIMA mode takes into account the past data and decomposes it into (i) an Autoregressive process (AR), where there is a memory of past events; (ii) an integrated (I) process, which makes the data stationary and ergodic making it easier to forecast; (iii) a moving average (MA) of the forecast errors, such that the forecast wi be accurate for onger historica data. ARIMA modes therefore have three mode parameters, one for the AR(p) process, one for the I(d) process and one for the MA(q) process, a combined into the ARIMA (p,d,q) mode. 453 P a g e

4 ARIMA mode is most commony used in time-series anaysis and mutivariate regressions. Because, the error residuas are correated with their own agged vaues and this seria correation vioates the standard assumption that disturbances are not correated with other disturbances. The ARIMA mode is used for time series forecasting where the variabes future vaue is a inear function of past vaues or observations and random errors and is expressed as, y y t 0 1 t1 y 2 t2 y p t p 2 t2 t 1 t1 q tq (1) Where, actua vaue y t and random error ε t at time t, and φ i (i = 1, 2,..., p) and θ j (j= 0, 1, 2,..., q) are the mode parameters. Integers, p and q are the order of the mode. The random errors, ε t are assumed to be independent and equay distributed with a zero mean a constant variance of σ 2 [7]. The steps in ARIMA mode can be summarized as foows (shown in Fig 1). Mode Identification: ARIMA mode assumes that the time series is stationary. So, data transformation is done to produce a stationary time series. For the stationary time series over the time the mean and autocorreation structure are constant. So, differentiation and power transformation are required to change the time series to stationary. To identify the appropriate mode form, partia autocorreation and autocorreation are cacuated from the data and it is compared to the theoretica autocorreation and partia autocorreation for different ARIMA modes. Steps (ii) and (iii) wi determine whether the mode is appropriate [1]. Pot series and obtain ACFs and PACFs Is mean stationary? Yes No Appy reguar and seasona Mode seection Estimate parameter vaues Modify mode No Are residuas uncorreated Yes No Are parameters significant? Yes Forecast Fig1. Steps of the ARIMA mode 454 P a g e

5 (ii) Parameter Estimation: The noninear east square procedure is used for parameter estimation in ARIMA Mode. (iii) Diagnostic Checking: Severa diagnostic statistics and pots such as Histogram, norma time sequence pot & probabiity pot are used to check the fitness of the mode estimated in step (i). Mode adequacy can be tested by Chi-square test. Once a satisfactory mode is obtained, the seected mode wi be used for forecasting. V. EVAUATION METRICS Forecast accuracy is measured using Sum of Squared Regression (SSR), Mean Absoute Deviation (MAD), Root Mean Square Error (RMSE), Mean Absoute Percentage Error (MAPE) and Maximum Absoute Error (MAE). (i) SSR: Sum of Squared Regression SSR 1 y y (2) where, y = origina data; y = predicted data; = number of sampes. (ii) MSE: (MSE) averages the squared prediction error at the same prediction horizon. A derivation of MSE is Root mean Square Error (RMSE). 1 MSE ( i) 1 i 2 (3) (iii) MAD: Mean Absoute Deviation (MAD) is the resistant estimator of the dispersion of the origina error from the prediction error. 1 AD( i) ( i) m (4) n 1 n 1 where, M median i and median is the th order statistic. 2 (iv) MAPE: MAPE averages the APE in the predictions of mutipe UUTd at the same prediction horizon.rather than the mean, Median absoute percentage error (MdAPE) can be computed by median in a simiar fashion. 1 MAPE ( i) r i i (5) v) MAE :The absoute prediction error is averaged by MAE for mutipe UUTs at the same prediction horizon. If we use median rather than mean gives absoute error (MdAE). MAE i 1 1 i 455 P a g e

6 VI. RESUTS AND DISCUSSION This section presents the performance evauation of the ARIMA mode in M3C data. Matab (R2013b) with a system configuration of 2GB RAM Inte processor and 32 bit OS is used for ARIMA mode impementation. In order to cacuate the forecastabiity of the ARIMA mode, it is appied to the yeary, quartery, monthy and other data. The autocorreation pots are used in the mode identification stage of the ARIMA time series modes. The randomness in a data set is checked by autocorreation pots. To find the randomness, autocorreations of data vaues at variabe time ags are cacuated. If we get autocorreation is near to zero for a the time-ag separations, then the data is random. The data is not random if the autocorreations are not zero. Partia autocorreation are used to find the order of the autoregressive mode. The time-series graph iustrates the data points at successive time intervas. The time is measured on the horizonta axis and the variabe is measured on the vertica axis. For comparing between the origina data observed and the observed forecasting data and respective performance measure for the yeary data, quartery data, monthy data and other data are shown in Fig 2, 3, 4 and 5 respectivey the time series graph is used. Fig 2. Yeary data Fig 3. Quartery data 456 P a g e

7 Fig 4. Monthy data Fig 5. Other data VII. CONCUSION In this study, we have appied the ARIMA mode for the M3-competition data set of 3003 time series to determine its forecastabiity. Better forecasting even when itte detai about the data is avaiabe is provided by ARIMA mode. The forecasting accuracy of the ARIMA mode is determined by parameters ike SSR, RMSE, MAD, MAPE, and MAE for the yeary, quartery monthy and other data and it is compared with the resuts given in [19]. It showed that the performance of ARIMA mode is better than the other modes. We therefore concude that the ARIMA mode gave 7.6% improvement than the neura network method in teecommunication data. REFERENCES [1] J. E. Hanke and D. W. Wichern, Business Forecasting, Prentice Ha, Engewood Ciffs, NJ, USA, [2] Koassa S., How to assess forecastabiity Foresight, the Internationa Journa of Appied Forecasting, 2009, pp [3] Tashman.J., Specia feature on forecastabiity: Preview, Foresight, The Internationa Journa of Appied Forecasting, vo. 23, [4] Gary Madden, Joachim Tan, Forecasting teecommunications data with inear modes, Teecommunications Poicy, vo. 31, pp , P a g e

8 [5] Makridakis S. and Hibon M., The M-3 Competition-Resuts, impications and concusions, IJOF 16, pages: , year [6] P. F. Pai and C. S. in, A hybrid ARIMA & SVM mode for stock prizing forecasting, Omega, voume 33, no-6, pages , year [7] G. P. Zhang, Time series forecasting using a hybrid ARIMA mode & neura network mode, Neurocomputing, vo. 50, pp , [8] Boyan J.E., Forecasting abiity definitions in more precise way, Foresight, IJAF, pages. 34 to 40, year [9] Coopy F. & Armstrong J, Empirica Comparison of Error Measures for generaizing forecast methods, IJOF, vo. 8, pp , [10] [10] Fides R., The Extrapoative Forecasting Methods Evauation, IJF, voume-8, pages. 81 to 98, year [11] Fides R., Makridakis S., Meade N. & Hibon M., Generaising about Univariate Forecasting Methods: Further Evidence for Empirica, IJOF, voume- 14, pp , [12] Grubesic T. & Murray A., Geographies for imperfection in teecom anaysis, Poicies of Teecom., voume. - 29, pages: 69 94, year [13] Makridakis S., Chatfied C., Mis T., Hibon M., awrence M., Ord K., The Makridakis & Hibon two competition: a rea-time judgmentay based forecasting study, IJOF, vo.-9, pp: 5 to 23, year [14] E. Parzen, ARIMA Modes about Time Series Anaysis and Forecasting, Journa of Forecasting, vo. 1, pages , [15] Simmons. F., M-Competition A coser [16] ook at Naıve2 & median APE: a note, IJOF, voume -4, pp , [17] Gardner E., Exponentia Smoothening: The state of the artpart ii, IJOF, voume-22, pages: , [18] Kotsiaos A., Papageorgiou M. & Pouimenos A., ong-term saes forecasting using Neura Network Methods & Hot-Winters, JOF, voume-24, pages: , year [19] Fides R. & Petropouos F., An Evauation of SFM Seection Rues (Working Paper on UMS 2013:2), The Department of Management Science, University ancaster. [20] Hibon M. & Makridakis S., Makridakis & Hibon-three competition resuts, concusion and impications, IJOF, voume-16, pp , [21] Mahsin M, Rainfa modeing in division Dhaka of Bangadesh using time series anaysis, JFMMAA, voume - 5, pages: 67-73, [22] Vahdat S.F., iaghat A., Shahida N., Sarraf A., & Shamsnia S.A., Weather Parameters Modeing Using Stochastic Methods (ARIMA Mode) (Study case: Iran, Abadeh Region), Internationa Conference on Environment and Industria Innovation, voume-12, pages: , year [23] Stephen A. Deurgio & Car D. Bhame, Forecasting systems for Operations Management, P a g e