# ma

##### Moving-average smoothing

`ma`

computes a simple moving average smoother of a given time series.

- Keywords
- ts

##### Usage

`ma(x, order, centre = TRUE)`

##### Arguments

- x
Univariate time series

- order
Order of moving average smoother

- centre
If TRUE, then the moving average is centred for even orders.

##### Details

The moving average smoother averages the nearest `order`

periods of
each observation. As neighbouring observations of a time series are likely
to be similar in value, averaging eliminates some of the randomness in the
data, leaving a smooth trend-cycle component. $$\hat{T}_{t} =
\frac{1}{m} \sum_{j=-k}^k
y_{t+j}$$ where
\(k=\frac{m-1}{2}\)

When an even `order`

is specified, the observations averaged will
include one more observation from the future than the past (k is rounded
up). If centre is TRUE, the value from two moving averages (where k is
rounded up and down respectively) are averaged, centering the moving
average.

##### Value

Numerical time series object containing the simple moving average smoothed values.

##### See Also

##### Examples

```
# NOT RUN {
plot(wineind)
sm <- ma(wineind,order=12)
lines(sm,col="red")
# }
```

*Documentation reproduced from package forecast, version 8.3, License: GPL-3*

### Community examples

**twigt.arie@gmail.com**at Sep 23, 2018 forecast v8.4

## Example to get an understanding how values are calculated by applying the `ma()` function. ```{r} # create a numerical vector which is easy to understand numbers <- c(3, 5, 3, 6, 4, 5, 3, 4, 4, 6, 3, 5, 4, 6, 3, 5, 4, 4, 6, 3, 5) # apply the 'ma' function ma(numbers, order = 5) ``` Calculate the average for the first 5 numbers by hand. ```{r} (sum(3, 5, 3, 6, 4))/5 ```