According to the Employee Relocation Council Summary Appraisal Report, the definition of forecasting is "the process of analyzing historical trends and current factors as a basis for anticipating market trends." In its simplest terms, the definition concerns itself with projecting future trends, demand and performance.

There are several ways to forecast such things. On one extreme, someone can make a wild guess, take a stand and defend it using words, arguments, tantrums and other suitable weapons against those who might be so bold as to question the forecast's figures and the implications that flow therefrom. At the other extreme, one can take the longer, more difficult route and do the hard work that allows the forecasting statistics do the heavy lifting involved with defense.

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This month, we're probing the depths of that chaos we call the Web in search of zero-cost, non-commercial, registration-free resources aimed at providing you with practical information about forecasting.

What others have said

Forecasting been around for quite some time. I suppose it started with someone actually believing they could read chicken entrails. During the years, many people have commented on the discipline. Read the examples listed in the *Famous Forecasting Quotes*, http://www.met.rdg.ac.uk/cag/forecasting/quotes.html.

The basics

As is true with most endeavors worth pursuing, you need at least some basic idea of the specialized terminology that goes with forecasting. To start, I direct your attention to the *Forecasting Dictionary *brought to you by the good folks at The Wharton School of the University of Pennsylvania. This substantial work is found at http://morris.wharton.upenn.edu/forecast/dictionary/.

Frequently asked questions

Forecasting is a mathematically intense effort that can yield good results for those inclined to tackle the subject. Start with the International Institute of Forecasters, a non-profit organization founded in 1981 to stimulate the generation, distribution and use of knowledge on forecasting. The IIF publishes *Frequently Asked Questions About Forecasing* at http://www.ms.ic.ac.uk/iif/FAQs/faqs.htm.

Margin of error

You've heard newscasters discuss some survey or another and finish by saying something similar to, "The survey of 275 households gave an expected margin of error of three percent." Did you ever wonder about the connection between the number of responses and the margin of error? It should be intuitively obvious to even the most casual observer that surveying a large sample yields more accurate results. The relationship is nonlinearthat's for sureand you can explore it using a statistical calculator provided by the Grapentine Co., Inc., Ankeny, Iowa. Go to http://www.grapentine.com/calculator.htm for the details. Plug in your own numbers. Assume there are 280 million people in this country. Figure out how many surveys you'd really need to predict something of national scope within one or two percent.

Another site owned by Surveyguy, Hatboro, Pa., offers an explanation of the concept of margin of error. Zip on over to http://www.surveyguy.com/homepage.shtml, click on "White Papers" at the left of the home page, then bounce your mouse on *What Is A Margin of Error? *to get the explanation.

Time series forecasting

The technical definition of a time series is an ordered sequence of values of a variable at equally spaced time intervals. Examples might include the number of work orders initiated every day, the total number of departmental overtime hours worked each week or the total number of ad pages in each issue of your favorite monthly trade magazine. In any case, the general idea is to start with a tabulation of relevant data going back a sufficient number of time periods and apply various numerical procedures in search of a valid mathematical model that can be manipulated to predict future outcomes.

Dr Tony Robinson at the University of Bath in the UK teaches statistics and forecasting. He's posted a series of detailed class notes at http://www.bath.ac.uk/~masar/math0118/forecasting/forecasting.html. Think of it as a densely packed Powerpoint presentation, but without the distracting special effects, which probably explains why Robinson's slides load a lot faster.

Tools

My first guess is that you'll probably use some spreadsheet program for at least part of your forecasting effort. My second guess is that the spreadsheet you'll be using is Excel. If my humble forecasts are correct, you should know about the power spreadsheeting offer from ASAP Utilities. This company has a free download that contains more than 300 utilities to fill the gaps in the tricks you can do with Excel. Just point your old mousie to http://www.asaputilities.nl/.

If you click your way to http://www.ifigure.com/, it will take you to iFigure, a Web site operated by an outfit of the same name in Metairie, La. The site bills itself as "your source for online planning, calculating and decision-making." The meat of the matter is that it offers online calculators and worksheets that apply to business, mathematics, science and engineering. I think you should evaluate this one yourself.

Free downloads

One can perform the required math using graphite and papyrus and learn a lot about the inner workings of statistics in the process. It may not make you the paragon of productivity that you'd like to become, but consider it a form of intellectual stimulation. On the other hand, if your life is anything like mine, you're probably suffering from a chronic case of time poverty and an acute need for instant gratification, which suggests using software to see into the future.

One group that uses a lot of statistics is the sociologists, and they've been prepared to conquer data sets for a long time. Their secret weapon will be exposed right on your monitor if you use your digital prowess to take yourself to *The Impoverished Social Scientist's Guide to Free Statistical Software and Resources*, which is found at http://www.hmdc.harvard.edu/micah_altman/socsci.shtml. Although the collection isn't specifically aimed at forecasting, it will point you to various statistics packages that can help the process along.

If you have access to a Unix operating system and feel comfortable using Fortran90 or S-Plus software, you might want to go instead to http://www.isds.duke.edu/~mw/tvar.html, where Raquel Prado and Mike West have posted a page, *Nonstationary Time Series Analysis and Decomposition using Time-Varying Parameter Autoregressions*. You can download the zipped file and start exploring.

Step by step: The cookbooks

The Department of Statistics of the University of Glasgow is one of the largest statistical groups in the UK. The consortium developed an initiative called STatistical Education through Problem Solving, or STEPS. These problem-based modules support the teaching of statistics in biology, business, geography and psychology. The software available on the site includes modules for each of the disciplines, and the business module features 10 typical plant-level problems that can be solved using statistics. A few of them require another commercial software packageMintabthat's not available as a free download. Simply click your way over to http://www.stats.gla.ac.uk/steps/ to see the offering from the UK.

Well, folks, it's my humble opinion that some of our hired hands in Washington have done us a good turn. The Statistical Engineering Division of the National Institute of Science and Technology has put together a comprehensive online book, the *Engineering Statistics Handbook*, that shows how to explore, measure, characterize, model, improve, monitor, compare and check reliability of the results of your statistics and forecasting efforts. Mouse over to http://www.itl.nist.gov/div898/handbook/ to access more knowledge about the subject than you'll ever use. If you're interested, you can access appropriate software by clicking on "Tools & Aids." This is your tax money at work, and it's being well spent.

But the government isn't the only entity around here with a consummate understanding of such fuzzy math. StatSoft, Inc., Tulsa, Okla., offers the *Electronic Statistics Textbook* at http://www.statsoftinc.com/. This e-book has more than 40 chapters and covers topics both common and arcane. This, too, is a great resource if you need to prove your point with numbers. If you click on the "Download" link on the home page, you'll be given the opportunity to get a copy of Statistica 6, the company's software. This limited trial version handles basic statistics, multiple regression and graphics.

Economic Forecasting: A Provisional Text

Check your work

It's one thing to go through the effort to produce a valid mathematical model, but it's entirely another to use it to make accurate forecasts that allow you to make decisions. There's no one-to-one correspondence between forecasting models and data sets. Those same input numbers can be massaged any number of ways to produce different forecasts, some of which are better than others. The R2 statistic, for example, is one of several measures of a model's fitness for use. The model accurately explains variation in the data set to the degree that the value of R2 approaches unity, the forecaster's Holy Grail. Then, perhaps, the model can best predict future outcomes.

Once you've got your time series forecast completed, take advantage of the next site. Dr. Hossein Arsham, at the University of Baltimore, Baltimore, publishes *Time Series Analysis and Forecasting Techniques* at http://ubmail.ubalt.edu/~harsham/stat-data/opre330Forecast.htm. This is a prodigious work. It's a full textbook with 35 chapters and links to other sites that are equally packed full of useful information. The key feature of Arsham's document is at the end. There you will find the code for an interactive Fortran program that computes the statistics and provides an idea about how well your forecasting method fits your original data set. If you're into time series forecasting, this site is worth bookmarking.

Although the Bureau of Meteorology Research Centre in Melbourne, Australia, is focused on weather forecasting, it still uses the same base-ten mathematics we all use, and the models it produces still need to be verified. If you want to check your work, see *Forecast VerificationIssues, Methods and FAQ* at http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/verif_web_page.html.