---
title: "ces() - Complex Exponential Smoothing"
author: "Ivan Svetunkov"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{ces() - Complex Exponential Smoothing}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r global_options, include=FALSE}
knitr::opts_chunk$set(fig.width=6, fig.height=4, fig.path='Figs/', fig.show='hold',
                      warning=FALSE, message=FALSE)
```

This vignette covers `ces()` and `auto.ces()` functions, which are part of [smooth package](smooth.html).

Let's load the necessary packages:

```{r load_libraries, message=FALSE, warning=FALSE}
require(smooth)
```

`ces()` function allows constructing Complex Exponential Smoothing either with no seasonality, or with simple/partial/full one. A simple call for `ces()` results in estimation of non-seasonal model:

For the same series from M3 dataset `ces()` can be constructed using:
```{r ces_N2457}
ces(BJsales, h=12, holdout=TRUE, silent=FALSE)
```

This output is very similar to ones printed out by `adam()` function. The only difference is complex smoothing parameter values which are printed out instead of persistence vector in `adam()`.

If we want automatic model selection, then we use `auto.ces()` function:
```{r auto_ces_N2457}
auto.ces(AirPassengers, h=12, holdout=TRUE, silent=FALSE)
```

By default, the function optimises the initial values, but other options ("backcasting" and "complete") are supported as well:
```{r auto_ces_N2457_optimal}
ces(BJsales, h=12, holdout=TRUE, initial="back")
```

The function also works with explanatory variables if the data frame or a matrix is provided instead of the vector of values:
```{r es_N2457_xreg_create}
BJData <- cbind(y=BJsales, x=BJsales.lead)
cesModel <- ces(BJData, h=12, holdout=TRUE, regressors="use")
```

Finally, all the main methods for the [adam](adam.html) function are supported by `ces()` as well. For example, here how we can produce prediction interval:
```{r}
forecast(cesModel, h=12, interval="pred") |> plot()
```