## NonLinear Trends and Method of Least Squares

Secular Trend — Nonlinear Trends When a straight line does not describe accurately the long-term movement of a time series, then one might detect some curvature and decide to fit a curve instead of a straight line. The most commonly used curve, to describe the …

## 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 …