In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 and management science, a tracking signal 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. Forecasts can relates to sales, inventory, or anything pertaining to an organization’s future demand.

The tracking signal is a simple indicator that forecast bias is present in the forecast model. It is most often used when the validity of the forecasting model might be in doubt.

Definition

One form of tracking signal is the ratio of the cumulative sum of forecast errors (the deviations between the estimated forecasts and the actual values) to the mean absolute deviation. The formula for this tracking signal is:

Tracking signal = Σ (a_t − f_t) / MAD

where a_t is the actual value of the quantity being forecast, and f_t is the forecast. MAD is the mean absolute deviation. The formula for the MAD is:

MAD = Σ|a_t − f_t| / n

where n is the number of periods. Plugging this in, the entire formula for tracking signal is:

Tracking signal = Σ(a_t − f_t) / Σ|a_t − f_t| / n

Another proposed tracking signal was developed by Trigg (1964). In this model, e_t is the observed error in period t and |e_t| is the absolute value of the observed error. The smoothed values of the error and the absolute error are given by:

E_t = βe_t + (1 − β)E_t−1

M_t = β|e_t| + (1 − β)M_t−1

Then the tracking signal is the ratio:

T_t = |E_t / M_t|

If no significant bias is present in the forecast, then the smoothed error E_t should be small compared to the smoothed absolute error M_t. Therefore, a large tracking signal value indicates a bias in the forecast. For example, with a β of 0.1, a value of T_t greater than .51 indicates nonrandom errors. The tracking signal also can be used directly as a variable smoothing constant.

There have also been proposed methods for adjusting the smoothing constants used in forecasting methods based on some measure of prior performance of the forecasting model. One such approach is suggested by Trigg and Leach (1967), which requires the calculation of the tracking signal. The tracking signal is then used as the value of the smoothing constant for the next forecast. The idea is that when the tracking signal is large, it suggests that the time series has undergone a shift; a larger value of the smoothing constant should be more responsive to a sudden shift in the underlying signal.

See also

• Calculating demand forecast accuracy
  Calculating Demand Forecast Accuracy
  Calculating demand forecast accuracy is the process of determining the accuracy of forecasts made regarding customer demand for a product.-Importance of forecasts:...
  
  
• Demand forecasting
  Demand forecasting
  Demand forecasting is the activity of estimating the quantity of a product or service that consumers will purchase. Demand forecasting involves techniques including both informal methods, such as educated guesses, and quantitative methods, such as the use of historical sales data or current data...
  
  

External links

• Tracking signal in forecasting by Dr Muhammad Al-Salamah
• Tracking Signal:A Measure of Forecast Accuracy by Tyler Hedin, Brigham Young University (Powerpoint)