Rob J Hyndman November 8, 2009 1 Forecasting, planning and goals
Forecasting is a common statistical task in business, where it helps inform decisions about scheduling of production, transportation and personnel, and provides a guide to long-term strategic planning. However, business forecasting is often done poorly and is frequently confused with planning and goals. They are three diﬀerent things. Forecasting is about predicting the future as accurately as possible, given all the information available including historical data and knowledge of any future events that might impact the forecasts. Goals are what you would like to happen. Goals should be linked to forecasts and plans, but this does not always occur. Too often, goals are set without any plan for how to achieve them, and no forecasts for whether they are realistic. Planning is a response to forecasts and goals. Planning involves determining the appropriate actions that are required to make your forecasts match your goals. Forecasting should be an integral part of the decision-making activities of management, as it can play an important role in many areas of a company. Modern organizations require short-, medium- and long-term forecasts, depending on the speciﬁc application. Short-term forecasts are needed for scheduling of personnel, production and transportation. As part of the scheduling process, forecasts of demand are often also required. Medium-term forecasts are needed to determine future resource requirements in order to purchase raw materials, hire personnel, or buy machinery and equipment. Long-term forecasts are used in strategic planning. Such decisions must take account of market opportunities, environmental factors and internal resources. An organization needs to develop a forecasting system involving several approaches to predicting uncertain events. Such forecasting systems require the development of expertise in identifying forecasting problems, applying a range of forecasting methods, selecting appropriate methods for each problem, and evaluating and reﬁning forecasting methods over time. It is also important to have strong organizational support for the use of formal forecasting methods if they are to be used successfully.
Commonly used methods
Typically, businesses use relatively simple forecasting methods that are often not based on statistical modelling. However, the use of statistical forecasting is growing and some of the most commonly used methods are listed below. 1
Time series methods
Let the historical time series data be denoted by y1 , . . . , yn , and the forecast of yn+h be given by ˆ yn+h|n , h > 0. • Na¨ve forecasting is where the forecast of all future values of a time series are set to be ı ˆ equal to the last observed value: yn+h|n = yn , h = 1, 2, . . . . If the data follow a random walk process (yt = yt−1 + et , where et is white noise — a series of iid random variables with zero mean), then this is the optimal method of forecasting. Consequently, it is popular for stock price and stock index forecasting, and for other time series that measure the behaviour of a market that can be assumed to be eﬃcient. • Simple exponential smoothing was developed in the 1950s (Brown 1959) and has been widely used ever since. Forecasts can be computed recursively as each new data point is observed: ˆ ˆ yt+1|t = αyt + (1 − α)yt|t−1 , ˆ ˆ where 0 < α < 1. (Longer-term forecasts are constant: yt+h|t = yt+1|t , h ≥ 2.) Consequently, only the most recent data point and most recent forecast need to be stored. This was an attractive feature of the method when computer storage was expensive. The method has proved remarkably robust to a wide range of time series, and is optimal for several processes including the ARIMA(0,1,1) process (Chatﬁeld et al. 2001). • Holt’s linear method (Holt 1957) is an extension of simple exponential forecasting that ˆ allows a locally linear trend to be...