Forecasting-4-2-Exp-Smoothing.Rmd

## `ets()` function

The `ets()` function in the **forecast** package fits  exponential smoothing models and produces forecasts from the fitted models. It also includes functions for plotting forecasts.

Load the data by loading the **FishForecast** package.

```{r load_data_exp_smoothing}
require(FishForecast)
```

Fit the model.

```{r fit.ann}
fit <- forecast::ets(anchovy87ts, model="ANN")
```
`model="ANN"` specifies the simple exponential smoothing model.

Create a forecast for 5 time steps into the future.

```{r fr.ann}
fr <- forecast::forecast(fit, h=5)
```

Plot the forecast.
```{r}
plot(fr)
```

Look at the estimates

```{r}
fit
```

### The weighting function

The first coefficient of the ets fit is the $\alpha$ parameter for the weighting function.

```{r ann.weighting, fig.cap="Weighting function for the simple exponential smoothing model for anchovy."}
alpha <- coef(fit)[1]
wts <- alpha*(1-alpha)^(0:23)
plot(1987:1964, wts/sum(wts), lwd=2, ylab="weight", xlab="", type="l")
```


### Decomposing your model fit

Sometimes you would like to see the smoothed level that the model estimated. You can see that with `plot(fit)` or `autoplot(fit)`.

```{r fig.height=4, fig.cap="Decompositon of an ets fit."}
autoplot(fit)
```