God, grant me the serenity to accept the things I cannot change, The courage to change the things I can, And the wisdom to know the difference. (Serenity Prayer, Reinhold Niebuhr)

* Forecasting* is the process of making statements about events whose actual outcomes (typically) have not yet been observed (Wikipedia). For business purposes, demand is commonly the object of forecasting so that specific plans can be made based on anticipated future demand.

Forecasts of events closer to the current time period are more accurate than longer range forecasts. Also, composite forecasts of a group of related products (multiple brands under a product category) are usually more accurate because the forecasting error for each brand tend to cancel each other out, making the composite forecast more accurate.

- Forecasts are almost always wrong
- Forecasts for the near term tend to be more accurate
- Forecasts for groups of products or services tend to be more accurate (than specific ones)
- Forecasts are no substitute for calculated values

** Qualitative forecasting** techniques are subjective, based on the opinion and judgment of consumers and experts; they are appropriate when past data are not available. They are usually applied to intermediate- or long-range decisions (Wikipedia).

* Composite forecasts* are developed using individual forecasts and adding them together to arrive at a composite forecast. This may includes a composite of various sales regions combined for a global (or national) sales forecast. Individual products can also be forecast and then added together to obtain a forecast for a product family.

* Survey* methods are commonly used to obtain information on customer sentiment regarding products and inclination toward future purchasing. Surveys the sampling of individuals from a population with a view towards making statistical inferences about the population using the sample (Wikipedia). In business forecasting, market research methods are commonly used to construct the surveys (Wikipedia).

The * Delphi method* is a structured communication technique, originally developed as a systematic, interactive forecasting method which relies on a panel of experts (Wikipedia).In the standard version, the experts answer questionnaires in two or more rounds. After each round, a facilitator provides an anonymous summary of the experts’ forecasts from the previous round as well as the reasons they provided for their judgments. Thus, experts are encouraged to revise their earlier answers in light of the replies of other members of their panel. It is believed that during this process the range of the answers will decrease and the group will converge towards the "correct" answer. Due to the fact that this method does not bring the expert panel together, it can reduce the impact of groupthink (Wikipedia).

**Scenario analysis** is a process of analyzing possible future events by considering alternative possible outcomes (Wikipedia).

**Forecast by analogy** is a forecasting method that assumes that two different kinds of phenomena share the same model of behaviour. For example, one way to predict the sales of a new product is to choose an existing product which "looks like" the new product in terms of the expected demand pattern for sales of the product (Wikipedia).

** Executive Opinion** - Often forecasts are done by a small group (or singular) executive based on their opinion and experience. The accuracy of this method is based on the skill and knowledge of the executive and can vary substantially. Also sometimes called executive SWAG (scientific wild ass guess).

** Quantitative forecasting** models are used to forecast future data as a function of past data. They are appropriate to use when past numerical data is available and when it is reasonable to assume that some of the patterns in the data are expected to continue into the future. These methods are usually applied to short- or intermediate-range decisions (Wikipedia).

- Naive method (last period forecast)
- Moving average
- Weighted moving average
- Exponential smoothing
- Linear regression

Also known as a last period forecast, the * naive method* simply takes the actual demand for last period as the forecast for next period. This method is highly sensitive to changes because it simply follows last period's demand.

Ft+1 = Dt

A * simple moving average* (SMA) is the unweighted mean of the previous

Ft+1 = Sum [Dt, Dt-1, ... Dt-(n-1)] / n

A * weighted moving average* is any average that has multiplying factors to give different weights to data at different positions in the sample window (Wikipedia). Because the data more recent to the forecast is usually more relevant, the more recent data usually is assigned the greater weight.

Ft+1 = [(Dt*W1)+(Dt-1*W2)...] / [Sum of Weights]

* Exponential smoothing* is a technique that can be applied to time series data to make forecasts (Wikipedia). In its simple form, exponential smoothing is a simple weighted moving average of the previous observation and the previous 'smoothed statistic'.

Ft+1 = [α*Dt] + [(1-α)*Ft], where

α = smoothing factor, is a number between 0 and 1. If α is closer to 1 the last period observation is weighted more heavily. If α is closer to 0 the last forecast (or history of all of the observed data) is weighted more heavily.

Due to the fact that this formula utilizes its out output as input, it is calcuated from some starting point in the data. If not estimate of the initial forecase (F1) is given, the first actual observation (D1) or an average of the first few observations can be used as the initial forecast.

* Linear regression* is a forecasting method which attempts to find the equation of a line that best fits the time series data (Wikipedia). The most common method is the least squares method which attempts to find the line that minimizes the squared difference bewteen the equation line and the actual data.
The easiest way to calculate a linear regression line is to use the scatter chart function in Microsoft Excel, and include the 'trendline' on the chart. To do this:

- Enter your data in excel in two columns. The x-axis is the time series (1-n), which is the independent variable. Put this time series labels in the first column. The y-axis is the dependent variable being predicted which is your actual data observations. Put the observation data in the second column.
- Select the data and choose Insert-Scatter Chart.
- With the chart highlighted, click the Layout tab.
- Click the Trendline dropdown box and choose '
*More Trendline Options*' to open the trendline dialog box. - Choose linear as the trendline method, and check the '
*Display Equation on Chart*' and '*Display R-Squared Value on Chart*' options. - The best fit linear equation will now be shown on the chart. The R-squared value is the percentage of the variation in the underlying data that is explained by the displayed linear equation.

If the linear equation is of acceptable predictive accuracy, you can forecast the value of any future point in the time series by substuting the time series number for X in the linear equation.

* Causal forecasting* methods use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast (Wikipedia).

* Multiple nonlinear regression* is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables (Wikipedia).
In Microsoft Excel's Data Analysis Toolpack add-in, multiple regression is a built-in function. To perform multiple regression in Excel, put the dependent variable (Y) into the first column of the data, and then successive independent (predictor) variables in the columns to the right.

- Select all of the data (which can include the data labels at the top of each column) and choose Tools --> Data Analysis -->> Regression to open the regression dialog box.
- The Y-input range is the column with the dependent variable
- The X-input range are the columns with the independent variables
- Click the 'labels' check box if the column labels are included
- Click the area for the regression output to be presented
- Press OK

Click here for an example with descriptions of the regression output.

There are several measures and methods for evaluation of the accuracy of a forecasting method. The forecast error is the difference between the actual value and the forecast value for a corresponding model (Wikipedia).

In order to compare the overall effectiveness of a forecasting model, there are several methods that can be used to measure overall accuracy (or error) of a forecast. The most common are:

(MFE): Average (Actuals - Forecasts)**Mean forecast error**- This method will overstate the accuracy of a forecast because the negative errors counterbalance the positive errors. It is almost never used by itself.

(MAD): Avg (abs(actuals-forecasts)**Mean absolute deviation**- This method is a good indicator of overall forecast error. The absolute value of the forecast errors are averaged to determine the average magnitude of forecast errors irregardless of the direction of the error.

(MSE): Average[(Actuals-Forecasts)^2]**Mean squared error**- A second method of removiing directionality from the forecast errors is to square the errors. The average of these squared errors is the MSE. This method is a good one to use when just a few large misses is bad for the business. The larger forecast errors are amplified greatly because of squaring them.

Once the most accurate forecasting model has been selected and implemented, it must be monitored to make sure that the method is still valid. A common measure used to do this is called Tracking Signal. A * tracking signal* monitors any forecasts that have been made in comparison with actuals, and warns when there are unexpected departures of the outcomes from the forecasts. It is a simple indicator that forecast bias is present in the forecast model (Wikipedia).

TS = Sum all Forecast Errors / Mean Absolute Deviation

Tracking Signal = Sum(Ft-At) / MAD

Interpretation: a value between -4 and +4 usually indicates that the model is still operating acceptably.