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.

### The Secular Trend is used

- For 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 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 to isolate non-trend fluctuations.

**Note that**

- These trends can be positive or negative. For example, the advancement of technology offers new opportunities but also raises concerns about job displacement and privacy.
- These trends can be interrelated. For instance, urbanization might be fueled by technological advancements that allow people to work remotely.
- Identifying secular trends can be challenging, as they unfold over a long period. However, by analyzing historical data, monitoring current developments, and considering expert opinions, one can gain valuable insights into the long-term direction of change.

By understanding and utilizing secular trends, individuals, businesses, and policymakers can make informed decisions, prepare for future challenges, and capitalize on emerging opportunities in a constantly evolving world.