README.Rmd

---
output: github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-"
)
```


The `tVAR` package allows R users to estimate the penalized Vector AutoRegression model with *t*-distributed innovations (*t*-VAR) proposed in [Barbaglia et al. (2020)](https://www.sciencedirect.com/science/article/pii/S0140988319303500?via%3Dihub). The package allows to compute the resulting volatility spillovers and visualize them via networks.


## Installation

You can install `tVAR` from GitHub as follows:

```{r gh-installation, eval = FALSE}
install.packages("devtools")
devtools::install_github("lucabarbaglia/t-VAR")
```


## Fit a t-VAR with estimated of the degrees of freedom

Fit a penalized `t-VAR` of order P=2 on  the `RV` data set containing the log-transformed realized volatilities for J=5 stocks and N=500 observations.

```{r test tVAR}
library(tVAR)
data(RV)
DATA <- as.matrix(RV)
fit <- Large.tVAR(Data=DATA, P=2, lambda1_OPT = 5, gamma1_OPT = 0.2) 
str(fit, max.level = 1)
```

The output of the  `Large.tVAR` function is a list containing, among other ones, the following objects:

- Beta_arr: a JxJxP array containing the estimated autoregressive coefficients;

- Omega_new: a JxJ matrix containing the estimated variance-covariance matrix;

- nu_new:  estimated degrees-of-freedom of the multivaraite t-distribution of the VAR innovations.

- lambda1_opt: selected value of the regularization parameter on the autoregressive coefficients;

- gamma1_opt: selected value of the regularization parameter on the variance-covariance matrix



If you do not wish to specify the magnitude of the penalization, you select it via BIC by setting the paramaters `lambda1_min, lambda1_max, lambda1_steps`. 
If you do not wish to estimate the degrees-of-freedom of the multivariate *t* distribution of the VAR innovations, you can use the `EM_VAR` function.


## Volatilty spillover networks

Build the volatility spillovers from the *t*-VAR estimation.

```{r spills}
# Volatility Spillovers:
vs <- Spillovers(fit = fit)
vs$spill_index 		# volatility spillover index

# volatility spillover matrix
spills <- vs$spill
colnames(spills) <- rownames(spills) <- colnames(RV)
round(spills,2)
```


Plot the network of volatility spillovers.

```{r network}
# Volatility spillover network:
network.vs(spill=round(spills))

```



## References:

* Barbaglia, L., Croux, C., & Wilms, I. (2020). Volatility spillovers in commodity markets: A large t-vector autoregressive approach. Energy Economics, 85, 104555.