# 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 $k=(m-1)/2$

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

##### See Also

##### Examples

```
plot(wineind)
sm <- ma(wineind,order=12)
lines(sm,col="red")
```

*Documentation reproduced from package forecast, version 7.3, License: GPL (>= 2)*

### 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 ```