Simple Moving Average is a method of time series smoothing and is actually a very basic forecasting technique. It does not need estimation of parameters, but rather is based on order selection. It is a part of smooth package.

In this vignette we will use data from `Mcomp`

package, so it is advised to install it.

Let’s load the necessary packages:

```
require(smooth)
require(Mcomp)
```

You may note that `Mcomp`

depends on `forecast`

package and if you load both `forecast`

and `smooth`

, then you will have a message that `forecast()`

function is masked from the environment. There is nothing to be worried about - `smooth`

uses this function for consistency purposes and has exactly the same original `forecast()`

as in the `forecast`

package. The inclusion of this function in `smooth`

was done only in order not to include `forecast`

in dependencies of the package.

By default SMA does order selection based on AICc and returns the model with the lowest value:

`sma(M3$N2457$x, h=18, silent=FALSE)`

```
## Time elapsed: 0.09 seconds
## Model estimated: SMA(13)
## Initial values were produced using backcasting.
##
## Loss function type: MSE; Loss function value: 4393167.5848
## Error standard deviation: 2114.456
## Sample size: 115
## Number of estimated parameters: 2
## Number of degrees of freedom: 113
## Information criteria:
## AIC AICc BIC BICc
## 2089.345 2089.452 2094.835 2095.089
```

It appears that SMA(13) is the optimal model for this time series, which is not obvious. Note also that the forecast trajectory of SMA(13) is not just a straight line. This is because the actual values are used in construction of point forecasts up to h=13.

If we try selecting SMA order for data without substantial trend, then we will end up with some other order. For example, let’s consider a seasonal time series N2568:

`sma(M3$N2568$x, h=18, interval=TRUE)`

```
## Time elapsed: 0.1 seconds
## Model estimated: SMA(12)
## Initial values were produced using backcasting.
##
## Loss function type: MSE; Loss function value: 3413356.6782
## Error standard deviation: 1863.663
## Sample size: 116
## Number of estimated parameters: 2
## Number of degrees of freedom: 114
## Information criteria:
## AIC AICc BIC BICc
## 2078.206 2078.312 2083.713 2083.965
##
## 95% parametric prediction interval was constructed
```

Here we end up with SMA(12). Note that the order of moving average corresponds to seasonal frequency, which is usually a first step in classical time series decomposition. We however do not have centred moving average, we deal with simple one, so decomposition should not be done based on this model.