---
title: "Data generation"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Data generation}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  fig.width = 10,
  fig.height = 6,
  fig.align = "center"
)


```

This vignette shows how to build stochastic models, combine them with `+`,
generate data, and plot the results.

```{r}
library(gmwmx2)
set.seed(123)
```



# Available models

You can build a single stochastic process with any of the following model
constructors:

- `wn()` (white noise)
- `ar1()` (AR(1))
- `pl()` (power-law)
- `matern()` (Matérn)
- `rw()` (random walk)
- `flicker()` (flicker)

Each constructor returns a `time_series_model` object that can be plotted or
combined with others using `+`.


# Stochastic models

## White noise
```{r}
model_wn <- wn(sigma2 = 1)
series_wn <- generate(model_wn, n = 500)
plot(series_wn)
```
The generated object is a `generated_time_series` with a numeric series in
`$series`:

```{r}
head(series_wn$series)
```

## AR(1)
```{r}
model_ar1 <- ar1(phi = 0.8, sigma2 = 1)
series_ar1 <- generate(model_ar1, n = 500)
plot(series_ar1)
```

## Power-law
```{r}
model_pl <- pl(kappa = 0.3, sigma2 = 1)
series_pl <- generate(model_pl, n = 500)
plot(series_pl)
```

## Matérn
```{r}
model_matern <- matern(sigma2 = 1, lambda = 1, alpha=1)
series_matern <- generate(model_matern, n = 500)
plot(series_matern)
```

## Random walk
```{r}
model_rw <- rw(sigma2 = 0.1)
series_rw <- generate(model_rw, n = 500)
plot(series_rw)
```

## Flicker
```{r}
model_fl <- flicker(sigma2 = 1)
series_fl <- generate(model_fl, n = 500)
plot(series_fl)
```

# Reproducible generation

You can set a random seed before calling `generate()`, or pass a seed directly
to `generate()`, to make the output deterministic. Using the same seed and
model parameters produces the exact same time series.

```{r}
model_wn <- wn(sigma2 = 1)

set.seed(1234)
series_a <- generate(model_wn, n = 100)

series_b <- generate(model_wn, n = 100, seed = 1234)
series_c <- generate(model_wn, n = 100, seed = 4321)

all.equal(series_a$series, series_b$series)
all.equal(series_a$series, series_c$series)
```

# Composite models (sum of processes)

Use `+` to build a composite model from multiple stochastic processes. The
result is a `sum_model` that can be passed to `generate()`.

```{r}
model_wn_ar1 <- wn(sigma2 = 1) + ar1(phi = 0.8, sigma2 = 0.5)
class(model_wn_ar1)
series_wn_ar1 <- generate(model_wn_ar1, n = 500)
plot(series_wn_ar1)

```

The composite output is a `generated_composite_model_time_series` with:

- `series` (the total sum)
- `components` (a list of each component series)
- `n` (length of the series)
- `model` (names of each component)
- `parameters` (parameters of each component)

```{r}
names(series_wn_ar1)
```