Charts

Moving Average (MA)

Description

A moving average creates a series of averages of different subsets. Each new subset remains a constant length by adding the newest value and removing the oldest. A moving average is defined by the user over n-periods of data. This technical indicator along with several others allow the user to select which type of moving average to use in the calculation. Below lists the formula for each type.

Formula

\[Simple = MA = \frac{\sum_{i=1}^{n} Close_{i}}{n}\]

\[Exponential = EMA = (Close_{n} - EMA_{t-1}) \times k + EMA_{n-1}\]

where k = the smoothing constant, equal to \( \frac{2}{n+1}\)

and n = the number of periods in a simple moving average roughly approximated by the EMA

\[Time\;Series = TSMA = \frac{\sum_{i=1}^{n} Close_{i}}{n}\]

\[Triangular = TMA = \frac{\sum_{i=1}^{n} MA_{i}}{n} \]

where \(MA = \frac{\sum_{i=1}^{n} Close_{i}}{n} \)

\[Variable = VMA = \frac{(w_{1} \times Close_{t}) + (w_{2} \times Close_{t-1}) + ...+ \;(w_{n} \times Close_{t-n+1})}{w_{1}+w_{2}+....+w_{n}}= \frac{\sum_{t=1}^{n} w_{t}Close_{t-n+1}}{\sum_{t=1}^{n} w_{t}}\]

\[Weighted = WMA = \frac{(w_{1} \times Close_{t}) + (w_{2} \times Close_{t-1}) + ...+ \;(w_{n} \times Close_{t-n+1})}{w_{1}+w_{2}+....+w_{n}}= \frac{\sum_{t=1}^{n} w_{t}Close_{t-n+1}}{\sum_{t=1}^{n} w_{t}}\]

\[Welles\;Wilder Smoothing = WWS_{n} = WWS_{n-1} - \left ( \frac{WWS_{n-1}}{n} \right )+(Value_{n})\]

where the first calculation of WWS uses a simple moving average \( WWS_{1} = \frac{\sum_{i=1}^{n} Close_{i}}{n}\)