Statistical Consultants Ltd


Forecasting Services

Figures can appear unpredictable over time, but often there are strong patterns that are only obvious once the data has been analysed statistically.  Statistical models can be built which take into account these patterns, and can be used to make forecasts.

Forecasting techniques can be applied to many different types of data recorded over time (time series data), including sales figures, macroeconomic data, population demographics, and finance data.

Typical Input / Output of a Forecasting Project

A typical forecasting project would involve the client providing us with data, and then us providing the client with forecasts and a report.  The data the client provides could be in Excel or some other format.  We are fine with most data formats. 

The following is a simple example of a sales data set that a client might provide.  There would be at least one column explaining the time period.  In this set it is the week number.  Other sets might be yearly, quarterly, monthly or some other unit of time.  If the data set is quarterly or monthly, it may have separate columns for the year and the quarter or month.  There would also be at least one column containing figures the client wishes to forecast.  In this set there is a single column with sales revenue figures in dollars.

time series data set

Once the patterns have been identified, a statistical model can be fitted to the data that takes into account these patterns:

Time series graph and model

The model is then diagnosed to make sure it is a good one, and modified if necessary:

Time series model diagnostics

After the model has passed the various diagnostic tests, it can then be used to make forecasts: 

sales forecast

We would typically provide the client with an Excel file with the actual figures and the forecasts, clearly marked to prevent confusion.  In the above spreadsheet, the actual figures are coloured red and have the word 'ACTUAL' in a column off to the side.  The forecasts are in blue and green.  The blue figures in the sales column are the future values most expected.  The green figures are prediction intervals. 

The prediction intervals in this Excel file have the following interpretation: 
There is 95% confidence that the true sales figure for that period will be somewhere between that interval.

The further you forecast into the future, the wider the prediction interval will be.

If there are many variables to forecast, a client may find that the prediction intervals would add too much clutter; in which case they may choose to receive a file that contains only the point estimates like the ones coloured blue.


We can also provide the client with graphs displaying the forecasts, the prediction interval and the actual figures:


We also provide the client with a final report.  The report could be as brief as containing solely technical notes that only someone with technical knowledge would understand; or the report could be more complex, and also include written descriptions of what is happening with the data, and explanations of the forecasting process that a layperson could understand.  The level of detail is up to the client.

Sales Forecasting

An important application of forecasting techniques is sales projections.  Sales figures can be in terms of revenue or quantity sold.

Reasons to Forecast Sales:

Inventory Management - Stock shortages are bad, not just in the short term due to a lost profit opportunity, it can also detract customers in the long term.  Over stocking a product can also be bad, if it means less room available for products that are in higher demand.  Sales forecasts in terms of quantity can allow for more effective inventory management, where shortages and large surpluses are far less likely.

Marketing and Sales PlanningSales forecasts in terms of revenue or quantity could help marketing and sales planners decide on which products to promote and how to promote them.  If the sales figures are segmented by variables such as location or consumer type, and forecasts are made for each segment, then the marketing planners might be able to take measures to maximise the return from each segment, rather than take a once size fits all approach.

Financial Planning - If a business spends too much on expansionary efforts such as advertising and capital expenditure, it may become difficult for the business to satisfy their financial obligations.  Having this in mind, a business manager might behave too conservatively, stifling business growth.  Sales forecasts can help make business expansion safer, by giving financial planners estimates on how much money they are likely to have at their disposal in the near future.  The forecasts allow decision makers to take calculated risks rather than blind leaps of faith. 

Investor ConfidenceInvestors don’t just base their decisions on average rates of return.  They also take into account risk.  If sales are shown to be predicted accurately, then it is a good sign of a stable business.  The sales figures could be changing a lot over time and at first glance may appear unstable, but upon a time series analysis, trends and patterns may be revealed that show the sales figures to be easily predicted.  If investors can be convinced that a business is stable, it is more likely they can be convinced to invest in expansions to that business.


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