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Words 3732

Pages 15

Abstract

The purpose of this article is to compare and determine the most suitable technique for forecasting the Electricity Consumption Malaysia. The data was obtained from Statistical Department from January 2008 until December 2012. Five univariate modeling techniques were used include Naïve with Trend Model, Average Percent Change Model, Single Exponential Smoothing, Holt’s Method Model and Holt-winter’s. The data are divided into two parts which are model estimation (fitted) and model evaluation. The selection of the most suitable model was indicated by the smallest value of mean square error (MSE) and Mean Absolute Percentage Error (MAPE.) Based on the analysis, Holt’s Method Model is the most suitable model for forecasting electricity consumption since it has the smallest value of MSE and MAPE.

Keywords: Univariate Modelling Techniques; Forecast Model; Mean Absolute Percentage Error; Mean Square Error.

Introduction

Electricity is one of the most important and used form of energy. Nowadays, electricity is essential for economic development especially for industrial sector. Malaysia, as a developing country, the important of electricity cannot be denied especially in industrial sector. Malaysia’s National electricity utility company (TNB) is the largest in the industry, serving over six million customers throughout the country. TNB is responsible for transmission and distribution of electricity. Transmission activities include system planning, evaluating, implementing and maintaining the transmission assets. One of the requirements of the system planning is load forecasting.

Univariate Modelling Techniques are used for analyzing data on a single variable at a time. Examples of Univariate Modelling Techniques are the Naïve Models, Methods of Average, Exponential Smoothing Techniques and the Box-Jenkins Method. Single Exponential Smoothing, Holt’s Method and Hot-Winter’s illustrated in this study are classified in the Exponential Smoothing Techniques. Other models available in this same category are Double Exponential Smoothing and Single Adaptive Response Rate Exponential Smoothing (ARRES).

This paper is divided into several sections. First is introduction, second describes the definitions, objectives and literature review of the study, the third focuses on the methodology and some of the attempts made to move beyond the models. In this section, a same set of monthly electricity consumption data were tested using five different univariate forecasting models to obtain MSE and MAPE value. The fourth goes beyond the discussion of analysis and results while the last explores selection of models. The last section presents an evaluation of Holt’s Method and a brief conclusion.

Definition of Load Forecasting

Fadhilah et al. (2009) stated that load or consumption forecasting is the process of predicting the future load demands. It is important to ensure that they can cope with electricity demand year by year and ensure that there is no waste of electricity energy. Accurate load forecasting will lead to reduction of cost, better budget planning and maintenance scheduling.

Load forecasting can be divided into three categories which are short-term load forecasting (STLF), medium-term load forecasting (MTLF), and long-term load forecasts (LTLF). STLF, which is usually from one hour to one week, is concerned with forecast of hourly and daily peak system load. It is needed for control and scheduling of power system. Some of the techniques used for STLF are multiple linear regression, stochastic time series and artificial intelligence based approach. MTLF relates to a time frame from a week to a year and LTLF relates to more than a year. MTLF and LTLF are required for maintenance scheduling, fuel and hydro planning, and generation and transmission expansion planning.

Objective of the Study

The objective of the study is to compare and choose the most suitable model to forecast the electricity consumption in Malaysia. The output of the study will serve as a guide in selecting a model for future forecasting of electricity consumption. Forecasting on electricity consumption is one of the areas that should be developed in fulfilling the requirements at national and international levels.

Literature Review

Syariza, Norhafiza and Kamal (2005), forecast the monthly electricity demand in Perlis using three time series methods namely Box-Jenkins ARIMA, Multiplicative Holt-Winter Exponential Smoothing and Time Series Regression. The data was obtained from the review of sales report of monthly electricity consumption in Perlis. They compared mean squared error (MSE), root of mean squared error (RMSE), standard error value, mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean percentage error (MPE) and standard error in order to determine the best model to forecast load electricity. The result show that Seasonal Regression is the best method since it has the smallest value of measurement for forecasting. This study showed that the data series did not reveal any drastic changes of electricity consumption for the forecasted period. The forecast values followed the same trend every year, along with seasonal variation in data series. This study also found that Regression with seasonal element was the ‘best’ method for short term electricity forecasting in Perlis.

Hossein et al. (2011), forecast electricity usage in Washington. The data was obtained from 66 quarters (1980 until 1996) of electricity usage. These data were divided into two parts which are in-sample, used for parameters estimation and out-sample for forecasting evaluations. The objective of this study is to compare the seasonal time series models for forecasting electricity usage. In this study, they used five univariate forecasting methods which are naϊve, regression, decomposition addictive and multiplicative, exponential smoothing, and Box-Jenkins methods. Then, they were compared for quarterly electricity usage prediction using root mean of square error (RMSE) of out-sample data to evaluate performance for each method. The results showed that Winter’s method both additive and multiplicative methods are the best forecast estimator. Furthermore, Winter’s multiplicative method produced more accurate forecast than additive. On the other hand, the poorest result forecast was Box-Jenkin method since there was an outlier in out-sample data set. The outlier data will influence the accuracy of forecast.

Fadhilah et al. (2009),presents an attempt to find a good time series model to forecast the maximum demand. The methods considered in this study include the Naïve method, Exponential smoothing, Seasonal Holt-Winters, ARMA, ARAR algorithm, and Regression with ARMA Errors. The authors evaluated the performance of these different methods using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Relative Percentage Error (MARPE). The load data used in this research was a Power Load Profile for a utility company. The data represented monthly mean maximum demand measured in Megawatts (MW) in 52 months from September 2000 to December 2004. The data was analyzed using Interactive Time Series Modeling (ITSM). ITSM is a windows-based computer package for univariate and multivariate time series modeling and forecasting. From the result of estimation the model based on Maximum Likelihood, it showed that AR (2) has the minimum AICC value and can be considered as the most appropriate model if compared to the other models under ARMA. Besides that, from the validation tests that performed on the AR (2) show the model had the minimum value of AICC. Through the validation process, AR (2) model also show that the residuals were white noise. This study computed he forecasted values from January 2005 to May 2005. The difference between the forecast value and the actual value is less than 1%. From the forecasting measurement, the result shows that AR (2) under ARMA model computes the lowest The MARPE, MAE and RMSE. Thus, the result indicated that it is a better model for forecasting the maximum demand of electricity in a utility company.

Methodology

This section described briefly about the statistical techniques applied to analyze the data collected via statistical department website. Univariate Modelling Techniques were applied to predict future values of electricity consumption based on the past observations in a given time series, by fitting a model to the data. The monthly Electricity Consumption data from January 2008 until December 2012 were used to determine the suitable model. Time series forecasting analysis and forecast models were applied to predict the electricity consumption in Malaysia. Analysis was done using five types of forecast models which are Naïve with Trend Model, Average Percent Change Model, Single Exponential Smoothing, Holt’s Method and Holt-Winter’s method. Subsequently, predicted electricity consumption with the best model was compared with the actual electricity consumption obtained from the Statistical Department website to determine the accuracy of prediction. The statistical test and data analysis were done through Microsoft Excel.

a. Naïve with Trend Model

This model implies that all future forecast can be set to equal the actual observed value in the most recent time period plus the growth rate. The trend value is measured by. If yt is greater than yt-1 then the trend is on the upward and vice versa. The one step ahead forecast is represented as, .

where, yt : is the actual value in time, t. yt-1 : is the actual value in the preceding time period.

This model is highly sensitive to the changes in the actual values. A sudden drop or sharp increase in the values will severely affect the forecast. Furthermore, fitting this model type will result in the loss of the first two observations in the series. On the other hand, this model is only suitable to be used for short time series.

b. Average Percent Change Model

This model assumes that the forecast of the dependent variable equals to the actual level of that variable in the current time period plus the average of the percentage changes from one time period to the next.

Ft+m = yt + Average of Percent Changes

Where the Average of Percent Changes = x yt

This model stated that the forecast are generated based on percentage changes in historical data. This model is suitable for short data series.

c. Single Exponential Smoothing

This technique is the simplest form of model within the family of the exponential smoothing technique since it requires only one parameter, which is the smoothing constant, α, to generate the fitted values. The following notations are used:

Ft+m = αyt + (1-α)Ft

where,

Ft+m : is the single exponentially smoothed value in period t+m (m = 1, 2, 3, …, ) yt : is the actual value in time period t α : is the unknown smoothing constant (0 < α < 1)

Ft : is the forecast or smooth value for period t

There are several advantages that can be obtained when using single exponential smoothing technique:

a) Exponential smoothing models mesh very easily with computer system and hence, simple spreadsheet program such as Microsoft Excel can be used to generate new forecasts.

b) Data storage requirements are minimal when compared to other forecasting models.

c) It embodies the advantages of a weighted moving average since current observations are assigned larger weights.

d) Exponential smoothing models react more quickly to changes in data patterns than the moving average.

e) It does not require as much data as the Box-Jenkins methodology or the econometric modelling technique.

The main difficulty encountered when using this method is the determination of the value of α and initial value. The criterion is to choose α such that the MSE is minimum. However, by using the solver facility in Microsoft Excel, the value of α can easily determine. Whereas, the first value of data series act as the initial value of fitted data, since the main objective is to find the method that can fits well and forecasts well. Therefore, in order to determine the goodness of model, it depends on the value of α that minimizes the error.

d. Holt’s Method

Holt’s Method is a technique that takes into account to smooth the trend and the slope directly by using different smoothing constants. It also provides more flexibility in selecting the parameter value which the trend and slopes are tracked. Holt’s Method consists of three basic equations that define the exponential smoothed series and the trend estimate. The Holt’s Method equations are represented as follows:

Exponentially smoothed series:

St = αyt + (1-α)(St-1 + Tt-1)

Trend estimate:

Tt = β (St – St-1) + (1 – β) Tt-1

Therefore, the one step ahead forecast is:

FT+m = ST + TT x m

where,

S t : exponentially smoothed series

Y t : actual values

T t : trend estimate α : smoothing constant (0<α <1) β : smoothing constant for the trend estimate (0<β <1)

e) Holt-Winter’s Method

This is a technique that takes into account the trend and seasonality factors. It consists of three basic equations;

Level component:

Lt =

Trend component:

bt = β(Lt – Lt-1) + (1 – β)bt-1

Seasonality component:

St =

The m-step-ahead forecast:

Ft+m = (Lt + bt x m)St-s+m where, yt : the actual values which include seasonality

Lt : the level component of the series, comprising of the smoothed values but does not include the seasonal component bt : the estimate of the trend component

St : the estimate of the seasonality component s : the length of seasonality (number of month) α : the smoothing constant for level (0 < α < 1) β : the smoothing constant for the trend estimate (0 < β < 1) γ : the smoothing constant for seasonality estimate (0 < γ < 1) m : the number of step-ahead to be forecast

Ft+m : forecast for m-step-ahead

The initial value of L0, is determined by taken the average of the first 12 months.

Mean Squared Error (MSE)

MSE is the standard error measure for assessing the model’s fitness to a particular data and comparing the model’s forecasting performance. The MSE is given as

MSE =

which et = yt - ŷt

where, yt : is the actual observation at the time t. ŷt : is the fitted value in time t generated from the origin ( t =1,2,3,........,n ) n : is the number of out-of-sample error terms generated by the model.

Mean Absolute Percentage Error (MAPE)

MAPE =

When n denotes effective data points and is defined as the absolute percentage error calculated on the fitted value for a particular forecasting method.

The disadvantage of this measure lies in its relevancy as it is valid for ratio-scaled data. It is not suitable for in situation where denominator is small because they tend to grossly exaggerate errors in the forecasts.

Estimation and Evaluation Procedures

Basically, there are three stages involved:

i) In the first stage, the series is divided into two parts. The first part is called model estimation part (fitted part) and the second part is the evaluation part (holdout part), which will be used to evaluate the model’s forecasting performance.

ii) In the second stage, the models are tested using various forms of functional relationship and variable selections.

iii) In the third stage, the minimum value of α and β are determined by ‘Solver’ facility available in Microsoft Excel which derived parameter values from data series for the related model. Then, all the models with the smallest MSE and MAPE value are evaluated by comparing the MSE and MAPE value of each model.

Then the model that meets the entire requirement which has the smallest value of MSE and MAPE is selected as the most suitable model.

Analysis and Results

Figure 1 shows the graph and the trend line of the electricity consumption from January 2008 to December 2012. Values indicate that maximum and minimum electricity consumption is in November 2012 and February 2009 respectively. The overall trend line equation for monthly data is given by y = 32.191x + 7509.1. The trend line indicates that the underlying pattern of the data follows a relatively upward trend.

Figure 1: Monthly Electricity Consumption, Malaysia, 2008 to 2012

Univariate Modelling Techniques

The estimations were done with the objective of minimizing Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Results of the corresponding MSE and MAPE value for each model are shown below.

Naïve with Trend

Figure 2: Fitted Naive with Trend Model, Malaysia, 2008 - 2012

| Fitted Period (2008 - 2010) | Evaluation Period (2011 - 2012) | MSE | 386441.010 | 460959.983 | MAPE | 0.492 | 0.446 |

Average Percent Change Model

Figure 3: Fitted Average Percent Change Model, Malaysia, 2008 – 2012

| Fitted Period (2008 - 2010) | Evaluation Period (2011 - 2012) | MSE | 365912.500 | 408726.978 | MAPE | 0.386 | 0.483 |

Single Exponential Smoothing

Computation of the minimum value of α was determined by solver facility available in Microsoft Excel. Based on the solver result, the best α to use is 0.57 since it minimizes the error measure.

Figure 4: Fitted Single Exponential Smoothing Model, Malaysia, 2008 -2012

| Fitted Period (2008 - 2010) | Evaluation Period (2011 - 2012) | MSE | 124791.088 | 115230.076 | MAPE | 0.141 | 0.175 |

Holt’s Method

In this method, the value of α and β are set priori to 0.6 and 0.2 respectively.

Figure 5: Fitted Holt’s Method, Malaysia, 2008 - 2012

| Fitted Period (2008 - 2010) | Evaluation Period (2011 - 2012) | MSE | 20713.183 | 18614.148 | MAPE | 0.050 | 0.088 |

Holt-Winter’s Method

For this method, the values of α = 0.7, β = 0.2 and γ = 0.

Figure 6: Fitted Holt-Winter’s Method, Malaysia, 2008 - 2012

| Fitted Period (2008 - 2010) | Evaluation Period (2011 - 2012) | MSE | 109837.404 | 70174.523 | MAPE | 0.074 | 0.097 |

Selection of Model

Table 1 presents the summaries and comparison on MSE and MAPE figures for Naïve with Trend Model, Average Percent Change Model, Single Exponential Smoothing, Holt’s Method and Holt-Winter’s Method. Based on the value of MSE and MAPE calculated over the evaluation period, it can be concluded that the most suitable model to forecast the electricity consumption is Holt’s Method with α = 0.6 and β = 0.2 since it has the smallest value of MSE and MAPE compared to other forecasting techniques.

Table 1: The Value of MSE and MAPE for each Model.

Period | | Type of Model | | | Naïve with Trend | Average Percent Change Model | Single Exponential α = 0.57 | Holt's Method α = 0.6β = 0.2 | Holt-Winter's Methodα = 0.7β = 0.2γ = 0.0 | Fitted Period(2008 - 2010) | MSE | 386441.010 | 365912.500 | 124791.088 | 20713.183 | 109837.404 | | MAPE | 0.492 | 0.386 | 0.141 | 0.050 | 0.074 | Evaluation Period( 2011 - 2012) | MSE | 460959.983 | 408726.978 | 115230.076 | 18614.148 | 70174.523 | | MAPE | 0.446 | 0.483 | 0.175 | 0.088 | 0.097 |

As mentioned earlier, 24 data points from January 2011 to December 2012 are used as evaluation period for the purpose of model validation. Table 1 shows the Holt’s Method with α = 0.6 and β = 0.2 has minimum value of MSE and MAPE.

An Evaluation of Holt’s Method

The forecasting of electricity consumption has become one of the major fields of research in recent years. It serves as an important indicator in development planning and policy formulation.

MSE and MAPE were used to determine the suitable forecast model. From the results of the analysis, Holt’s Method with α=0.6 and β=0.2 and the resulting MSE = 18614.148 and MAPE = 0.088 seems to be the most reliable model in generating the forecast value of electricity consumption. It is because Holt’s method generated the smallest value of MSE and MAPE.

The advantage of using the Holt’s Method Model is not only smoothes the trend and the slope directly by using different smoothing constant but it also provides more flexibility in selecting the rates at which the trend and slopes are tracked.

Conclusion

From the result, Holt’s Method Model is the most suitable model for forecasting monthly electricity consumption since it generated the smallest value of MSE and MAPE compared to another models. Each model type has unique characteristic which fits to a particular data series. More forecasting techniques should be explored to ensure fitness to longer series of electricity consumption. Univariate Modelling Techniques are basically single variable models that use their past information as the basis to generate the forecast values. This is made on the assumption that the forecast values are dependent solely on the past pattern of the data series.

Short Description about the Writer

In this section I’m going to tell a little bit about myself. My name is Nurul Nadiah binti Abdul Halim. I’m from Terengganu. I’m the third from seven siblings. I have finished my secondary school on 2004 in Sekolah Menengah Sains Kuala Terengganu (SESTER). Then I have continued my study in UiTM Seri Iskandar, Perak for three years in Diploma of Quantitative Science. After that, I got and offer to further my study in Bachelor of Science (Hons.) Management Mathematics in UiTM Shah Alam, and currently is a full time student of Master of Quantitative Science in UiTM Shah Alam.

REFERENCES

Syariza, A.R., Norhafiza, M.N. & Kamal, K. (2005). Comparison Of Time Series Methods For Electricity Forecasting: A Case Study In Perlis. Icoqsia 2005,6 – 8 December, Penang, Malaysia. Retrieved on 28th March 2012 from http://repo.uum.edu.my/218/1/COMPARISON_OF_TIME_SERIES_METHOD FOR ELECTRICITY....pdf

Hossein, J., Muhammad, H.L & Suhartono (2011). An Evaluation of Some Classical Methods for Forecasting Electricity Usage on a Specific Problem. Journal of Statistical Modelling and Analytics, Vol.2 No 1, 1-10. Retrieved on 28th March 2012 from www.instatmy.org.my/downloads/e-jurnal%202/1.pdf

Fadhilah, A.R., Mahendran, S., Amir, H. & Izham, Z.A.(2009). Load Forecasting Using Time Series Models. Jurnal Kejuruteraan, 21, 53-62.Retrieved on 28th March 2012 from http://myais.fsktm.um.edu.my/11693/1/2009-6.pdf

A.A. Mati, M.Eng., B.G. Gajoga, B. Jimoh, A. Adegobye, & D.D. Dajab(2009). Electricity Demand Forecasting in Nigeria using Time Series Model. The Pacific Journal of Science and Technology, Volume 10, Number 2, 479 – 485. Retrieved on 28th March 2012 from www.akamaiuniversity.us/PJST10_2_479.pdf

VinkoLepojević & MarijaAnđelković-Pešić(2011). Forecasting Electricity Consumption By Using Holt-Winters And Seasonal Regression Models. Economics And Organization Vol. 8, No 4, Pp. 421 – 431. Retrieved on 28th March 2012 from http://facta.junis.ni.ac.rs/eao/eao201104/eao201104-09.pdf

Mohd, A.L.(2012). Introductory Business Forecasting – a practical approach, 3rd Edition, Kuala Lumpur : UiTM PRESS

Mining, Manufacturing and Electricity, Department of Statistics, Malaysia. (2012). Available from: www.statistics.gov.my

Department of Statistics, Malaysia (2011). Mining, Manufacturing and Electricity, Monthly Statistical Bulletin. Putrajaya.

Department of Statistics, Malaysia (2010). Mining, Manufacturing and Electricity, Monthly Statistical Bulletin. Putrajaya.

Department of Statistics, Malaysia (2009). Mining, Manufacturing and Electricity, Monthly Statistical Bulletin. Putrajaya.…...

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...------------------------------------------------- Electricity Lightning is one of the most dramatic effects of electricity. Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire. In addition, electricity encompasses less familiar concepts such as the electromagnetic field and electromagnetic induction. The word is from the New Latin ēlectricus, "amber-like"coined in the year 1600 from the Greek ήλεκτρον (electron) meaning amber(hardened plant resin), because static electricity effects were produced classically by rubbing amber. Usage In general usage, the word "electricity" adequately refers to a number of physical effects. In scientific usage, however, the term is vague, and these related, but distinct, concepts are better identified by more precise terms: * Electric charge: a property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields. * Electric current: a movement or flow of electrically charged particles, typically measured in amperes. * Electric field: an influence produced by an electric charge on other charges in its vicinity. * Electric potential: the capacity of an electric field to do work on an electric charge,......

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...4/13/2015 Forecasting Research Papers Hapikampr Login Join The Research Paper Factory Join Search Browse Saved Papers Search over 100,000 Essays Home Page » Business and Management Forecasting In: Business and Management Forecasting Forecasting HSM/260 University of Phoenix 06/20/2013 Exercise 9.1 The following data represent total personnel expenses for the Palmdale Human Service Agency for past four fiscal years: 20X1 $5,250,000 20X2 $5,500,000 20X3 $6,000,000 20X4 $6,750,000 Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted moving averages, exponential smoothing, and time series regression. For moving averages and weighted moving averages, use only the data for the past three fiscal years. For weighted moving averages, assign a value of 1 to the data for 20X2, a value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponential smoothing, assume that the last forecast for fiscal year 20X4 was $6,300,000. You decide on the alpha to be used for exponential smoothing. For time series regression, use the data for all four fiscal years. Which forecast will you use? Why Moving Averages Fiscal Year Expenses Please login to view the full essay... Essay's Statistics Submitted by: hapikampr Date shared: 08/07/2013 10:35 AM Words: 707 Pages: 3 20X2 $ 5,500,000 ......

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...Forecasting Tammy Powell HSM/260 December 19, 2014 Adrianne Franklin Exercise 9.3 Moving Averages 20X2-20X4 $18,250,000 / 3 = $6,083,333 Weighted Moving Averages 20X2 $5,500,000 1 $5,500,000 20X3 $6,000,000 2 $12,000,000 20X4 $6,750,000 3 $20,250,000 __ ___________ 6 $37,750,000 20X5 $37,750,000 /6 = $6,291,667 Exponential Smoothing NF = LF + a (LD – LF) NF = $6,300,000 + 0.95($6,750,000 - $6,300,000) = $6,300,000 + 0.95(45,000) = $6,300,000 + (42,750) = $6,342,750 Exercise 9.3 Moving Averages 20X2-20X4 $41,750,000 / 3 = $13,916,667 Weighted Moving Averages 20X2 $14,250,000 1 $14,250,000 20X3 $14,000,000 2 $28,000,000 20X4 $13,500,000 3 $40,500,000 __ ___________ 6 $82,750,000 20X5 $82,750,000/6 = $13,791,667 Exponential Smoothing NF = $13,000,000 + 0.95($13,500,000 - $13,000,000) = $13,000,000 + 0.95(500,000) = $13,000,000 + (475,000) = $13,475,000 Moving averages are the easiest to do without a computer and is fast, but less accurate. Add the three most recent years, and divide by three. Weighted moving averages are simple, but require more time. The most recent year gets the highest weight. The oldest data is one and one multiplies the total. The next year is two, and two multiplies the total. The most current data weight is three, and multiplied by three. Finally, use the total of all years, and dived by...

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