Proposed Modification of Holt’s Method for Short Term Forecasting Md. Hasibul Haque Department of Mathematics Khulna University of Engineering & Technology Khulna-9203, Bangladesh A R M Jalal Uddin Jamali Department of Mathematics Khulna University of Engineering & Technology Khulna-9203, Bangladesh Mohammad Babul Hasan Department of Mathematics University of Dhaka Dhaka-1000, Bangladesh Abstract— Forecasting has long been our part of life. It was centered to weather forecasting only till 19 th century but in 20 th century it gets new dimension in the business planning. Since 1950’s a lot of research works has been carried out on business forecasting and is continuing today to improve the existing forecasting methods and develop a new method or model. This article deals with such an existing method namely Holt’s method (or sometimes called Holt-Winter’s method) to forecast the time series data containing trends or linear trends but no seasonality. It is noted that this method used only the observed (real) data to predict data for all the next periods ahead (3 to 5 ) but it does not take into consideration the most recent inter trends relation. We know that recent (last few periods) data have more significant effect rather than far old data on forecast. Exploiting this idea in this research works a modification is proposed to estimate future data. In the proposed modified approach, we take into account the recent available data (may be real or predicted) as weight parameter along with previous trend to forecast the next period outcome. We expect that our modified forecasts can be a better approximation or give the best upper or lower limit of the forecast depending on the nature of last few data. Keywords— Forecasting, Trends, seasonality, Holt’s method I. INTRODUCTION We all make and use forecasts every now and then, both in our jobs and everyday life. Armstrong [1] defined forecasting as the prediction of an actual value in a future time period. Makridakis et al. [2] stated that forecasting supplies information of what may occur in the future. And therefore, it is used to estimate when an event is likely to happen so that we can take necessary actions. In business, forecasting is the basis for budgeting, planning capacity, sales, production and inventory, personnel, purchasing etc. which affects decisions and activities throughout an organization [3]. Business forecasting is used not only in predicting demand but also that of profits, revenues, costs, productivity changes, raw materials, interest rates, movement of key economic indicators(e.g., GDP, inflation, government borrowing ) and prices of stocks and bonds. Though computers and sophisticated mathematical models are used in forecasting they are not exact science rather successful forecasting requires a proper blending of art and science. So in this modern age of business competitiveness is everywhere and to survive in such competitive world market business organization needs to predict the business involved future events as precisely as possible. To serve this purpose they have to use some mathematical model to predict the future outcomes based on the historical data available to them. The sequence of historical data collected at uniform time intervals is called time series [4]. The time intervals may be in hour(s), day(s), week(s), month(s), quarter year or year(s). Holt’s (linear exponential smoothing [5]) method performs well for the time series where only trends [6] exist but no seasonality. Its extended version called Holt-Winters’ method which is also a univariate method is used for the time series where trends and seasonality both exists [7]. Holt’s method is easy than some other method such as ARIMA [8]. II. EXISTING HOLT’S METHOD Exponential or single exponential [5] method does not work well if the time series data contains trends or seasonality. To overcome the In that case several methods were developed to overcome the difficulties involving errors in forecasting and usually they are referred to “double exponential smoothing method”. One of the methods is named "Holt-Winters double exponential smoothing" or only “Holt’s Method”. This method works as follows: We suppose that the raw data sequence of observations is represented by {X t}, beginning at time t = 0. We use {St} to represent the smoothed value for time t, and {Bt} is our best estimate of the trend at time t. The output of the algorithm is now written as Ft + m , an estimate of the value of Xt at time t+m, m>0 based on the raw data up to time t. Double exponential smoothing is given by the formulas: St = α Xt+(1- α)(St-1+Bt-1)  Bt = β (St-St-1) + (1- β) Bt-1  Where α and β are smoothing constants such that 0 < α, β < 1; Xt denotes observed data whereas Bt indicates tend value at time t and St be smoothed value at time t. Now we need the initial value of St, Bt and for t >1 they have the following form: S0=X0 and B0 = (Xn-X0)/n (3) And the h-step forecast by this method is given by the following equation: International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 http://www.ijert.org IJERTV6IS110225 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : www.ijert.org Vol. 6 Issue 11, November - 2017 496