## Method of Least Squares: Linear Trend (2020)

The least-squares principle (Method of Least Squares) says that “the sum of squares of the deviations of the observed values from the corresponding expected values should be least”. Among all the trend lines, the trend line is called a least-squares fit for which the sum …

## The Method of Moving Averages (2020)

The method of moving averages is of two types: Simple Moving Averages If the observed values of a variable $Y$ are $y_1, y_2,\cdots, y_n$ corresponding to the time periods $t_1, t_2,\cdots, t_n$, respectively, the $k$-period simple moving averages are defined as \begin{align*}a_1 &= \frac{1}{k} \sum_{i=1}^{k} …

## Method of Semi Averages (2020)

The secular trends can also be measured by the method of semi averages. The steps are: Let $y’_1$ and $y’_2$ be the semi-averages placed against the times $x_1$ and $x_2$. Let the estimated straight line $y’=a+bx$ is to pass through the points ($x_1$, $y’_1$) and …

## The Method of Free Hand Curve (2020)

The secular trend is measured by the method of the free hand curve in the following steps: In this method we draw the given times series data on graph paper, then we draw a free-hand trend line through the plotted graph according to the trend …