TIME SERIES DATA PREDICTION OF NATURAL GAS CONSUMPTION USING ARIMA MODEL
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1 International Journal of Information Technology & Management Information System (IJITMIS) Volume 7, Issue 3, Sep-Dec-2016, pp , Article ID: IJITMIS_07_03_001 Available online at Journal Impact Factor (2016): (Calculated by GISI) ISSN Print: and ISSN Online: IAEME Publication TIME SERIES DATA PREDICTION OF NATURAL GAS CONSUMPTION USING ARIMA MODEL Prabodh Pradhan, Dr. Bhagirathi Nayak and Dr. Sunil Kumar Dhal Sri Sri University, Cuttuck, Odisha, India ABSTRACT Time series data modeling and prediction are used in various practical domains. Thus a lot of active research works is going on in this subject during several years. Several important models have been proposed in literature for accuracy and efficiency of time series modeling. The aim of this article is to present a statistical time series prediction using Autoregressive Integrated Moving Average (ARIMA) models. We have explained here different statistical methods of time series models. Here we have collected historical data of Natural Gas Consumption in India from year 2005 to 2014 of every quarter s data. Fitting a model to a dataset is used Goodness of fit statistic. Here the model used preliminary estimation: Yule-Walker prediction accuracy models fitted to a time series. We have shown the obtained prediction diagram, which graphically describes prediction of Natural Gas consumption in India. In this article, our observation about different methods of time series modeling and prediction are explained clearly. We have also shown that components such as trends and periodicity in the time series can be explicitly modeled, with the data being decomposed into trend, seasonal and residual components. Key words: Time Series, Prediction, Natural Gas, ARIMA Cite this Article Prabodh Pradhan, Dr. Bhagirathi Nayak and Dr. Sunil Kumar Dhal, Time Series Data Prediction of Natural Gas Consumption Using Arima Model. International Journal of Information Technology & Management Information System, 7(3), 2016, pp INTRODUCTION Time series modeling is a dynamic research area, which has attracted attentions of researchers. The main aim of time series modeling is to carefully collect and rigorously study the past observations of a time series to develop an appropriate model, which describes the inherent structure of the series. This model is then used to 1 editor@iaeme.com
2 Prabodh Pradhan, Dr. Bhagirathi Nayak and Dr. Sunil Kumar Dhal generate future values for the series, i.e. to make prediction. Time series data prediction can be termed as the act of predicting the future by understanding the past. Due to the indispensable importance of time series forecasting in numerous practical fields such as business, economics, finance, science and engineering, etc. proper care should be taken to fit an adequate model to the underlying time series. It is obvious that a successful time series forecasting depends on an appropriate model fitting. Over many years the researchers try to develop efficient models to improve the forecasting accuracy. As a result, various important time series forecasting models have been evolved in literature. Here we used ARIMA models in statistical model. The basic assumption made to implement this model is that the considered time series is linear and Goodness of fit statistical methods. In practice a suitable model is fitted to a given time series and the corresponding parameters are estimated using the known data values. The procedure of fitting a time series to a proper model is termed as Time Series Analysis. 2. TIME SERIES A time series containing records of a single variable is termed as unvaried. But if records of more than one variable are considered, it is termed as multivariate. A time series can be continuous or discrete. In a continuous time series observations are measured at every instance of time, whereas a discrete time series contains observations measured at discrete points of time. For example temperature readings, flow of a river, concentration of a chemical process etc. can be recorded as a continuous time series. On the other hand population of a particular city, production of a company, exchange rates between two different currencies may represent discrete time series. Usually in a discrete time series the consecutive observations are recorded at equally spaced time intervals such as hourly, daily, weekly, monthly or yearly time separations. The variable being observed in a discrete time series is assumed to measure as a continuous variable using the real number scale. Furthermore a continuous time series can be easily transformed to a discrete one by merging data together over a specified time interval. 3. ARIMA The two aspects of time series analysis and modeling can be combined in a more general, and often very effective, overall modeling framework. In its basic form approach is known as ARMA modeling (autoregressive moving average), or when differencing is included in the procedure, ARIMA or Box-Jenkins modeling. ARMA models combine autocorrelation methods (AR) and moving averages (MA) into a composite model of the time series. MA model can be written as: Where the β i terms are the weights applied to prior values in the time series, and it is normal to define β i =1, without loss of generality. So for a first order process, q=1 and we have the model: The autoregressive or AR component of an ARMA model can be written in the form: 2 editor@iaeme.com
3 Time Series Data Prediction of Natural Gas Consumption Using Arima Model Where the terms in α are autocorrelation coefficients at lags 1,2...p and z t is a residual error term. Note that this error term specifically relates to the current time period, t. So for a first order process, p=1 and we have the model: ARMA Models two subsections we introduced the MA mode of order q: The AR model of order p: We can combine these two models by simply adding them together as a model of order (p,q), where we have p AR terms and q MA terms: The ARIMA model can be viewed as a "cascade" of two models. The first is nonstationary: =(1 ) While the second is wide-sense stationary:1 =1 Now prediction can be made for the process Y t, using a generalization of the method of autoregressive prediction. 4. DATA COLLECTION The time series datasets, we have considered are taken from non-confidential sources and each of them is freely available on annual report of Petroleum Planning & Analysis Cell (PPAC). We have collected data from year 2005 to 2014, 10 years data of quarterly consumption of Natural Gas in India in Billion Cubic Meter (BCM). 5. METHODOLOGY Statisticians George Box and Gwilym Jenkins developed a practical approach to build ARIMA model, which best fit to a given time series and also satisfy the parsimony principle. Their concept has fundamental importance on the area of time series analysis and prediction. The Box-Jenkins methodology does not assume any particular pattern in the historical data of the series to be predicted. Rather, it uses a three step iterative approach of model identification, parameter estimation and diagnostic checking to determine the best parsimonious model from a general class of ARIMA models. Here in our article we used the ARIMA Models for prediction. One 3 editor@iaeme.com
4 Prabodh Pradhan, Dr. Bhagirathi Nayak and Dr. Sunil Kumar Dhal of the most popular and frequently used stochastic time series models is the Autoregressive Integrated Moving Average (ARIMA) model. The basic assumption made to implement this model is that the considered time series is linear and follows a particular known statistical distribution, such as the normal distribution. ARIMA model has subclasses of other models, such as the Autoregressive (AR), Moving Average (MA) and Autoregressive Moving Average (ARMA) models. For seasonal time series forecasting, Box and Jenkins had proposed a quite successful variation of ARIMA model, viz. the Seasonal ARIMA (SARIMA). The popularity of the ARIMA model is mainly due to its flexibility to represent several varieties of time series with simplicity as well as the associated Box-Jenkins methodology for optimal model building process. 6. ANALYSIS AND OBSERVATION We have presented the predict results of the experiments done by us. From the performance measures obtained for historical dataset, one can have a relative idea about the effectiveness and accuracy of the fitted models. Here we used ARIMA model of Goodness of fit statistical methods for prediction. The preliminary estimation: Yule-Walker prediction accuracy models are used for fitted to a time series data of Natural Gas consumption. The ARIMA or Box-Jenkins modeling are discussed in above paragraph. Summary statistics Variable Natural Gas Consumption Obser vation s Obs. with missing data Obs. without missing data Minimu m Maximu m Mea n Std. deviation Results of ARIMA modeling of the Natural Gas Consumption series: Preliminary estimation: Yule-Walker (Natural Gas Consumption): Goodness of fit statistics Observations 40 DF 37 SSE MSE RMSE WN Variance MAPE(Diff) MAPE Log(Like.) FPE AIC AICC SBC Iterations editor@iaeme.com
5 Time Series Data Prediction of Natural Gas Consumption Using Arima Model Table 1 Goodness of fit statistics Model parameters Parameter Value Constant Method Standard Lower bound error Upper bound Asympt Method Lower Upper Lower Upper. Parameter Value Standar bound bound bound bound Standar d error d error AR(1) Natural Gas Consumptionn in India Residuals Residual Time step Figure 1 Natural Gas Consumption Prediction of Natural Gas Consumption ARIMA (Natural Gas Consumption) Natural Gas Consumption Time step 45 Natural Gas Consumption ARIMA (Natural Gas Consumption) Validation Prediction Lower bound Upper bound Figure 2 Prediction of Natural Gas Consumption, ARIMA Model. 5 editor@iaeme.com
6 Prabodh Pradhan, Dr. Bhagirathi Nayak and Dr. Sunil Kumar Dhal Descriptive analysis of Natural Gas Consumption 1 Autocorrelogram Natural Gas Consumption Autocorrelation Lag Figure 3 Autocorrelogram of Natural Gas Consumption Partial autocorrelogram Natural Gas Consumption 1 Partial autocorrelation Lag Figure 3 Partial Autocorrelogram of Natural Gas Consumption Here we can observe the time series data has analyzed in statistical methods for predict of Natural Gas consumption of India. The method, which we are using in time series analysis, is Autoregressive Integrated Moving Average (ARIMA) model. After analysis of different ARIMA model we got the results, which are shows in different figures. The Summary of Statistics: Observation = 40 (Number of quarters in 10 years), Minimum = and Maximum = M BCM. Mean = 8.138, Standard Deviation= The goodness of fit statistics variable is shown in table 1. The output of Time series data prediction of Natural Gas Consumption in India is shown in figure 2. Here we can observe the prediction of every quarter for year The consumption is gradually increased from 7.34 Billion Cubic Meter (BCM) to 7.77 BCM. The blue colour graph is shown natural gas consumption and the red colour graph shown our ARIMA model of Natural Gas consumption. The green colour graph is shown ARIMA model Natural Gas prediction of four quarters of year CONCLUSIONS Prediction time series is a difficult problem. In this article we have used the ARIMA model of statistical analysis and algorithms for predicting the Natural Gas Consumption in India. We used data series of quarterly consumption (in Billion Cubic Meter)of ten years form 2005 to 2014.Here we used the Box-Jenkins or ARIMA models for linear time series prediction. 6 editor@iaeme.com
7 Time Series Data Prediction of Natural Gas Consumption Using Arima Model Preliminary Estimation is used Yule-Walker techniques, Optimize is Likelihood (Convergence = 1e-05 / Iterations = 500), Validation: 1, Confidence intervals (%): 95 and Prediction for 4 quarters of year In table 1, clearly define the Goodness of fit Statistics. The output of prediction is showing in figure 2, our analysis is robust and the prediction is also accurate. Our future research will try to collect the data monthly wise or day wise, so that our prediction will be more accuracy. REFERENCES [1] P. J. Brockwell and R. A. Davis (2002), Introduction to Time Series and Forecasting, Springer. [2] Mehdi Khashei, Mehdi Bijari, Gholam Ali Raissi Ardali, Hybridization of autoregressive integrated moving average (ARIMA) with probabilistic neural networks (PNNs), Computers & Industrial Engineering 63, pp , [3] R. Rojas, Neural Networks, Springer-Verlag, Berlin, [4] Tommaso Proietti, Helmut Lütkepohl, Does the Box Cox transformation help in forecasting macroeconomic time series?, International, Journal of Forecasting 29, pp , [5] Hong Tan, Neural Network for Stock Forecasting, Master of Science in Electrical Engineering Thesis, Faculty of Texas Tech University, [6] [7] G.P. Zhang, Time series forecasting using a hybrid ARIMA and neural network model, Neurocomputing 50 (2003), pp [8] John H. Cochrane, Time Series for Macroeconomics and Finance, Graduate School of Business, University of Chicago, Spring [9] Dr. S. Rajamohan, Operational Efficiency and Times Series Changes in Taico Bank Auto Regressive Integrated Moving Average (ARIMA) Model. International Journal of Management (IJM), 2(1), 2011, pp [10] M. Nirmala, S. M. Sundaram, Modeling and Predicting the Monthly Rainfall in Tamilnadu as A Seasonal Multivariate Arima Process. International Journal of Computer Engineering & Technology (IJCET), 1(1), 2010, pp [11] H. Park, Forecasting Three-Month Treasury Bills Using ARIMA and GARCH Models, Econ 930, Department of Economics, Kansas State University, [12] G.E.P. Box, G. Jenkins, Time Series Analysis, Forecasting and Control, Holden- Day, San Francisco, CA, editor@iaeme.com
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