FORECASTING CH 1 PART 2
The Five Steps to Forecasting
Step 1: Problem definition
• Defining the problem carefully requires an understanding of:
1. the way the forecasts will be used,
2. who requires the forecasts,
3. and how the forecasting function fits within the organization requiring the forecasts.
• A forecaster needs to spend time talking to everyone who will be involved in
collecting data, maintaining databases, and using the forecasts for future
planning.
Step 1: Problem definition
• Consider the following statement by the manager of a paper
products manufacturing company:
• We have a computerized inventory control system and we can get daily,
weekly, and monthly reports at the drop of a hat. But our inventory situation
is bad. We have too much inventory at the factories, in the warehouses, and
in the pipeline. Can we get better forecasts of future production and
demand so we can reduce our inventory and save storage costs?
Step 1: Problem definition
• A forecaster has a great deal of work to do to properly define the forecasting
problem, before any answers can be provided. For example, we need to know
exactly what products are stored, who uses them, how long it takes to produce
each item, what level of unsatisfied demand the company is prepared to bear,
and so on.
Step 2: Gathering information
• There are always at least two kinds of information required: (a) statistical data,
and (b) the accumulated expertise of the people who collect the data and use
the forecasts.
• Often, it will be difficult to obtain enough historical data to be able to fit a good
statistical model. However, occasionally, very old data will be less useful due
to changes in the system being forecast.
Step 2: Gathering information
• In the case of the paper products inventory, the data collected may consist of
monthly demand and production for each item of interest over the previous
three years.
• Other relevant data such as the timing and length of any significant production
downtime due to equipment failure or industrial disputes may also need to be
collected.
Step 3: Preliminary (exploratory) analysis
• Always start by graphing the data.
1. Are there consistent patterns?
2. Is there a significant trend?
3. Is seasonality important?
4. Is there evidence of the presence of business cycles?
5. Are there any outliers in the data that need to be explained by those with expert
knowledge?
6. How strong are the relationships among the variables available for analysis?
Step 3: Preliminary (exploratory) analysis
• Then we compute some simple descriptive statistics (e.g., mean, standard
deviation, minimum, maximum, percentiles) associated with each set of data.
• Where more than one series of historical data is available and relevant, we can produce
scatter plots of each pair of series and related descriptive statistics (e.g., correlations).
• Another useful tool is decomposition analysis to check the relative strengths of trend,
seasonality, cycles, and to identify unusual data points.
• Such preliminary analyses will help suggest a class of quantitative models that
might be useful in the forecasting assignment.
Step 4: Choosing and fitting models
• This step involves choosing and fitting several quantitative forecasting models.
The preliminary analysis (step 3, above) serves to limit the search for an
appropriate forecasting model and we would pursue one or two leading
contenders for subsequent analysis.
Step 4: Choosing and fitting models
• Each model is itself an artificial construct. It is based on a set of assumptions
(explicit and implicit) and usually involves one or more parameters which must
be “fitted” using the known historical data
• Note that when forecasting the long-term, a less formal approach is often
better. This can involve identifying and extrapolating mega trends going back
in time, using analogies, and constructing scenarios to consider future
possibilities.
Step 5: Using and evaluating a forecasting model.
• Once a model has been selected judiciously and its parameters estimated
appropriately, the model is to be used to make forecasts, and the users of the
forecasts will be evaluating the pros and cons of the model as time
progresses.
• A forecasting assignment is not complete when the model has been fitted to
the known data. The performance of the model can only be properly
evaluated after the data for the forecast period have become available.
Exercise
• You are asked to provide sales forecasts of several products for a large biscuit
manufacturing company. Define the five steps of forecasting in the context of
this project.
Exercise: Step 1: Problem definition
• This would involve understanding the nature of the individual product lines to
be forecast. For example, are they high-demand products or specialty biscuits
produced for individual clients?
Exercise: Step 1: Problem definition
• It is also important to learn who requires the forecasts and how they will be
used.
• Are the forecasts to be used in scheduling production, or in inventory management, or for
budgetary planning?
• Will the forecasts be studied by senior management, or by the production manager, or
someone else?
• Have there been stock shortages so that demand has gone unsatisfied in the recent past?
If so, would it be better to try to forecast demand rather than sales so that we can try to
prevent this happening again in the future?
Exercise: Step 1: Problem definition
• The forecaster will also need to learn whether the company requires one-off
forecasts or whether the company is planning on introducing a new
forecasting system.
• If the latter, are they intending it to be managed by their own employees and, if
so, what software facilities do they have available and what forecasting
expertise do they have in-house?
Exercise: Step 2: Gathering information
• It will be necessary to collect historical data on each of the product lines we
wish to forecast. The company may be interested in forecasting each of the
product lines for individual selling points.
• If so, it is important to check that there are sufficient data to allow reasonable forecasts to
be obtained.
• For each variable the company wishes to forecast, at least a few years of data will be
needed.
Exercise: Step 2: Gathering information
• There may be other variables which impact the biscuit sales, such as
economic fluctuations, advertising campaigns, introduction of new product
lines by a competitor, advertising campaigns of competitors, production
difficulties.
• This information is best obtained by key personnel within the company. It will be necessary
to conduct a range of discussions with relevant people to try to build an understanding of
the market forces.
• If there are any relevant explanatory variables, these will need to be collected.
Exercise: Step 3: Preliminary (exploratory) analysis
• Each series of interest should be graphed and its features studied. Try to
identify consistent patterns such as trend and seasonality.
• Check for outliers. Can they be explained? Do any of the explanatory
variables appear to be strongly related to biscuit sales?
Exercise: Step 4: Choosing and fitting models
• A range of models will be fitted. These models will be chosen on the basis of
the analysis in Step 3.
Exercise: Step 5: Using and evaluating a forecasting
model
• Forecasts of each product line will be made using the best forecasting model
identified in Step 4. These forecasts will be compared with expert in-house
opinion and monitored over the period for which forecasts have been made.
• There will be work to be done in explaining how the forecasting models work
to company personnel. There may even be substantial resistance to the
introduction of a mathematical approach to forecasting. Some people may
feel threatened. A period of education will probably be necessary.
• A review of the forecasting models should be planned.
The statistical forecasting perspective
• The thing we are trying to forecast is unknown (or we wouldn’t be forecasting
it), and so we can think of it as a random variable.
• In most forecasting situations, the variation associated with the thing we are
forecasting will shrink as the event approaches. In other words, the further
ahead we forecast, the more uncertain we are.
The statistical forecasting perspective
• When we obtain a forecast, we are estimating the middle of the range of
possible values the random variable could take.
• Very often, a forecast is accompanied by a prediction interval giving a range of values the
random variable could take with relatively high probability.
• For example, a 95% prediction interval contains a range of values which should include the
actual future value with probability 95%.
Statistical perspective (cont.)
• A forecast is always based on some observations. Suppose we denote all the
information we have observed as ℐ and we want to forecast yi. We then write
yi |ℐ meaning “the random variable yi given what we know in ℐ”.
• The set of values that this random variable could take, along with their relative
probabilities, is known as the “probability distribution” of yi |ℐ. In forecasting,
we call this the “forecast distribution”.
Statistical perspective (cont.)
• When we talk about the “forecast”, we usually mean the average value of the
forecast distribution, and we put a “hat” over y to show this.
• Thus, we write the forecast of yi as ŷi, meaning the average of the possible
values that yi could take given everything we know.
• Occasionally, we will use ŷi to refer to the median (or middle value) of the forecast
distribution instead.
Statistical Perspective (cont.)

With time series forecasting, it is often useful to specify exactly what information we have
use in calculating the forecast. Then we will write, for example, yˆ t t 1 to mean the forecast
of yt taking account of all previous observations (y1,…,yt-1). Similarly, yˆT  h T means the
forecast of yT+h taking account of (y1,…,yT) (i.e., an h-step forecast taking account of all
observations up to time T).