---
title: "Estimation Demo"
author: "Alexios Galanos"
date: "`r Sys.Date()`"
output: 
    rmarkdown::html_vignette:
        css: custom.css
vignette: >
  %\VignetteIndexEntry{Estimation Demo}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This provides a quick demo to illustrate how to specify and estimate a distribution.

We'll choose the Hyperbolic distribution which is a special case of the Generalized
Hyperbolic when $\lambda = 1$. This will allow us to show how parameters can
be fixed pre-estimation.

```{r}
library(tsdistributions)
# simulate data
set.seed(101)
sim <- rgh(3000, mu = 0, sigma = 1, skew = -0.8, shape = 4, lambda = 1)
spec <- distribution_modelspec(sim, distribution = "gh")
# fix lambda to value and set it to non-estimate
spec$parmatrix[parameter == "lambda", value := 1.0]
spec$parmatrix[parameter == "lambda", estimate := 0]
mod <- estimate(spec, use_hessian = FALSE)
summary(mod, vcov_type = "QMLE")
```


A variety of estimators are available for the standard error, and the package
makes use of the sandwich package for the methods. The gradients, hessian and
scores (jacobian) are calculated using autodiff making use of the framework
provided by the [TMB](https://CRAN.R-project.org/package=TMB) package.

We can also calculate the moments of the distribution using the `tsmoments` method,
or directly call the `dskewness` and `dkurtosis` functions. Note that the kurtosis
reported is in excess of the Normal (3.0).

```{r}
tsmoments(mod)
```