## Moving averages

Moving averages provide data analysts and scientists with a basic predictive model. Despite its simplicity, the moving average method is widely used in a variety of fields, such as marketing survey, consumer behavior, or sport statistics. Traders use the moving average method to identify different levels of support and resistance for the price of a given security.

### Note

**An average reducing function**

Let's consider the time series *x _{t} = x(t)* and function

*f(x*that reduces the last

_{t-p-1},…, x_{t})*p*observations into a value or average. The estimation of the observation at

*t*is defined by the following formula:

Here, *f* is an average reducing function from the previous *p* data points.

### The simple moving average

The simple moving average is the simplest form of the moving averages algorithms [3:1]. The simple moving average of period *p* estimates the value at time *t* by computing the average value of the previous *p* observations using the following formula.

### Note

**The simple moving average**

M1: The...