---
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 seasonality. 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 `es()` function. The only difference is complex smoothing parameter values which are printed out instead of persistence vector in `es()`.

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

Note that prediction interval are too narrow and do not include 95% of values. This is because CES is pure additive model and it cannot take into account possible heteroscedasticity.

If for some reason we want to optimise initial values then we call:
```{r auto_ces_N2457_optimal}
auto.ces(BJsales, h=12, holdout=TRUE, initial="o", interval="sp")
```

Now let's introduce some artificial exogenous variables:
```{r es_N2457_xreg_create}
x <- cbind(rnorm(length(BJsales),50,3),rnorm(length(BJsales),100,7))
```

`ces()` allows using exogenous variables and different types of prediction interval in exactly the same manner as `es()`:
```{r auto_ces_N2457_xreg_simple}
auto.ces(BJsales, h=12, holdout=TRUE, xreg=x, regressors="select", interval="p")
```