FORECASTING (overview)

The history of forecasting The development of business forecasting in the 17th century was a major innovation [Bernstein P. (1996)] Along with the development of data-based methods, forecasting has grown significantly over the last 50 years Without any data history, human judgement may be the only way to make predictions about the future If data are available, forecasts can be produced by quantitative techniques Lack of managerial oversight and improper use of forecasting techniques can lead costly decisions

Is forecasting neccessary? How can an operations manager realistically set production schedule without some estimates of future sales.. How can a company determine staffing for its call centers without some guess of future demand for service Everyone requires forecasts The need for forecasts cuts across all functional lines as well as types of organizations

Types of forecasts- quantitative or qualitative A purely qualitative technique is one requiring no manipulation of data judgement of the forecaster is used A purely quantitative technique need no judgement mechanical procedures that produce quantitative results are used Effective management of modern organizations need judgement and common sense along with mechanical and data-manipulative procedures

Choosing a forecasting method Rarely (practically never)does one method work for all cases While choosing the forecasting method, organization’s manager must consider: Different products New versus established Characteristics of data Stationary or unstationary Has trend / seasonality /or wavelike fluctuation Goals simple prediction versus need for future values Constraints cost, required expertise, immediacy Several methods can be tried in a given situation The methodology producing the most accurate forecasts in one case may not be the best methodology in another situation

Forecasting steps Problem formulation and data collection The problem determines the appropriate data Often accessing and assembling appropriate data is challenging and time-consuming task If appropriae data are not available, the problem may have to be redefined Data manipulation and cleaning Some data may not be relevant to problem Some data may have missing values that must be estimated Model building and evaluation Involves fitting the collected data into a forecasting model that minimizes forecasting error Model implementation Generation of the actual model once the appropriate data have collected Forecast evaluation Involves comparing forecast values with actual historical values

Exploring time series data pattern Horizontal pattern When data collected over time fluctuate around a constant level or mean, horizontal pattern exists. This type of series is said to be stationary in mean Ex. Monthly sales for a food product that do not increase or decrease consistently over an extended period Trend pattern When data grow or decline over several time periods, trend pattern exists Ex. Population growth, price, inflation, technological change, consumer preferences, productivity increases..

Exploring time series data pattern Cyclical pattern Is the wavelike fluctuation around the trend Are usually affected by economic conditions Cyclical peak in figure shows economic expansion Cyclical vallye shows economic contradiction Seasonal pattern When observations are influenced by seasonal factors a seasonal pattern exists It refers to a pattern of change that repeats itself year after year Water power residential customers is highest in the first quarter, winter months Seasonal variation may reflect weather conditions, school schedules, holidays

Measuring Forecast Error Basic Forecasting Notation 𝑌 𝑡 :𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑎 𝑡𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑌 𝑡 :𝑡ℎ𝑒 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑌 𝑡 A residual Is the difference between on actual observed value and its forecast value

Measuring Forecast Error Mean absolute deviation: 𝑀𝐴𝐷= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 Mean Squared error 𝑀𝑆𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 2 Root mean squared error 𝑅𝑀𝑆𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 2 Mean absolute percentage error 𝑀𝐴𝑃𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 𝑌 𝑡 Mean percentage error 𝑀𝑃𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 𝑌 𝑡

Naive models Often young businesses face the dilemma of trying to forecast with very small data sets This situation creates a real problem, since many forecasting techniques require large amounts of data These methods assume that recent periods are the best predictors of future Ex. Tomorrow’s weather will be much likely today’s weather 𝑌 𝑡+1 = 𝑌 𝑡 When data values increase over time, they are said to be non-stationary in level or to have a trend If the above equation is used the projections-estimations will be consistently low. Technique can be adjusted to take trend into the consideration by adding the differences between last two periods. Then the adjusted equation is: 𝑌 𝑡+1 = 𝑌 𝑡 + 𝑌 𝑡 − 𝑌 𝑡−1

Methods Based on Averaging Some quick, inexpensive, very simple short-term forecasting tools are needed when management faces with hundreds or thousands of items Simple Averages Decision is made to use the first t data points as the initialization parta and remaining data point as the test part 𝑌 𝑡+1 = 1 𝑡 𝑖=1 𝑡 𝑌 𝑖

Moving Averages What if the analyst is more concerned with recent observations We use moving averages. 𝑌 𝑡+1 = 𝑌 𝑡 + 𝑌 𝑡−1 +…+ 𝑌 𝑡−𝑘+1 𝑘 where 𝑌 𝑡+1 : the forecast value for the next period 𝑌 𝑡 : the actual value at period t k: the number of terms in the moving average

Weighted Moving Average Takes only the most recent observation into account, But the weights of observations are not equal. Gives higher weights most recent data.

Exercise month yield January 9.29 February 9.99 March 10.16 April 10.25 May 10.61 June 11.07 July 11.52 August 11.09 September 10.80 October 10.50 November 10.96 December 9.97 The yield on a general obligation bond for the city of Davenport fluctuates with the market. The monthly quotations for 2014 are given as:

Exercise Find the forecast value of the yield for the obligation bonds for each month, starting with April, using a trend adjusted naive method Find the forecast value of the yield for the obligation bonds for each month, starting with April, using a two-month moving average Find the forecast value of the yield for the obligation bonds for each month, starting with June, using a five-month moving average Evaluate the performance of the methods using MAD Evaluate the performance of the methods using MSE Forecast the yield for January 2007 using the better technique