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### Trend Projection:

When numerical data are available, a trend can be plotted on graph paper to show changes through time. If desired, the trend line can then be extended or “projected” into the future on the basis of the recent rate of change. Such a projection shows where the trend should be at some point in the future assuming there is no shift in the rate of change. Example: A population with a steady 2 percent rate of annual growth will double in about thirty-five years.

This method uses the underlying long-term trend of a time series of data to forecast its future values. Suppose a forecaster has data on sales of American-made automobiles in the United States for the last 25 years. The time series data on U.S. auto sales can be plotted and examined visually. Most likely, the auto sales time series would display a gradual growth in the sales volume, despite the “up” and “down” movements from year to year. The trend may be linear (approximated by a straight line) or nonlinear (approximated by a curve or a nonlinear line).

Most often, forecasters assume a linear trend, if a linear trend is assumed when, in fact, a nonlinear trend is present; this misrepresentation can lead to grossly inaccurate forecasts. Assume that the time series on American-made auto sales is actually linear and thus it can be represented by a straight line.

Mathematical techniques are used to find the straight line that most accurately represents the time series on auto sales. This line relates sales to different points over time. If we further assume that the past trend will continue in the future, future values of the time series (forecasts) can be inferred from the straight line based on the past data. One should remember that the forecasts based on this method should also be judged on the basis of a measure of forecast errors.

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