Forecasting and Business Analysis

Forecast Evaluation Using EXCEL This is a simple exercise where two very simple naïve models are estimated and then a series of evaluation techniques are used. The purpose of this spreadsheet is to allow you to see the various formula that can be used for these applications. - The naive forecast tab shows the two forecasting methods - The evaluation tab shows the basic evaluation methods for these two naive forecasts

Actual

Forecast1

Forecast2

The most simple naïve forecast uses the last periods data as a forecast for the next. In other words "what ever happened last period will happen the next period" This can be expressed as Ft=At-1

The second naïve model uses the last value and the DIRECTION of the last change in values. So the last value is adjusted depending on if the last change in direction was positive or negative. This change is then weighted. This can be expressed as Ft=At-1+P(At-1-At-2) At-1-At-2 is the change Pis the weight In this example a 50% weight (p=.5) is used

CALCULATING THE ERRORS

The "error" for each data point is simply the difference between the observed value and the forecast. In other words, how wrong were you!! This is either positive or negative. In most cases the positives and negatives almost even each other out so that the positive errors are approximately equal to the negative errors. So if you take the mean of these the Mean Error is almost nothing. In most cases the "absolute error" is more important this measures the value of the error but ignores the sign. So they are all positive. Another common error estimate is the percentage error. This is simply the error expressed in terms of the actual value. This often helps in the comparison of errors for time series with different relative values. Maybe a 10% error is acceptable and this then has meaning regardless of the magnitude of the actual values. The Squared error is simply the error squared. This also removes the direction of the error (all measured as positives) and also highlights large errors by making them exponentially larger.

The final forecast evaluation is based on the summary statistics of the errors. Most of these involve taking the mean of the various errors. The mean error is thus the mean of the errors, which will often be very small because of the positive and negative values. The Mean Absolute Percentage Error is a popular measure as it measures the average error (regardless of direction) in percentage terms. The root mean squared error is also popular as it highlights forecasts when there are a number of very large errors.

Forecast Evaluation

Forecast Evaluation

The final forecast evaluation is based on the summary statistics of the errors. Most of these involve taking the mean of the various errors. The mean error is thus the mean of the errors, which will often be very small because of the positive and negative values. The Mean Absolute Percentage Error is a popular measure as it measures the average error (regardless of direction) in percentage terms. The root mean squared error is also popular as it highlights forecasts when there are a number of very large errors.