The Secular Trend

For the estimation of the secular trend of a time series, the most commonly used method is to fit a straight line $\hat{y} = a+bx$, an exponential curve $\hat{y}=ab^x$, and a second-degree parabola $\hat{y}=a +bx+ cx^2$, etc, where $y$ is the value of a time series variable, $x$ representing the time and all others are constants (the intercept $a$, and the slope $b$). The method of least squares is a widely used method to determine the values of the constants appearing in such an equation.

It is used

• For the purpose of prediction (or projection) into the future
• The detrending process (removal of trend) in a time series for studying other non-trend fluctuations.
• It is used for historical description

The secular trend can be represented either by a straight line or by some type of smooth curve. It is measured by the following methods:

• Method of the free-hand curve
• Method of semi-averages
• Method of moving averages
• Method of least squares (Linear Trend, Nonlinear Trend)

The secular trend may be used whether in determining how a time series has grown in the past or in making a forecast. The trend line is used to adjust a series to eliminate the effect of the secular trend in order to isolate non-trend fluctuations.