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:

Least Squares Method (secular 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.

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

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