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.
