---
title: "Introduction to FARS"
author: "Gian Pietro Bellocca"
output: html_document
vignette: >
  %\VignetteIndexEntry{introduction}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# Introduction

The `FARS` package provides a comprehensive framework for modeling and forecasting economic scenarios based on the Multilevel Dynamic Factor Model (MLDFM).

# Installation

```{r}

# Install FARS from CRAN
#install.packages("FARS")

# Install FARS from GitHub
#install.packages("devtools")
#devtools::install_github("GPEBellocca/FARS")

library(FARS)
```

# Input data

```{r}
library(zoo)
library(readxl)
# Input dep variable
data_input_path <- system.file("extdata", "Data_IMF.xlsx", package = "FARS")
data_input <- read_excel(data_input_path, sheet = "data")
data_ts <- ts(data_input[, -1], frequency = 4)
data_diff <- diff(log(data_ts)) * 400
dep_variable <- data_diff[, 'United States', drop = FALSE] 
dep_variable <- dep_variable[2:60]

# Input data
data_df_path <- system.file("extdata", "DataBase.xlsx", package = "FARS")
data_df <- openxlsx::read.xlsx(data_df_path, sheet = "fulldata", cols = 2:625)
data_df <- data_df[,1:519]
data <- as.matrix(data_df)
dimnames(data) <- NULL

# Generate dates
quarters <- as.yearqtr(seq(from = as.yearqtr("2005 Q2"), by = 0.25, length.out = 59))
dates <- as.Date(quarters)

# Correct outliers
outliers_result <- correct_outliers(data, 5 )
data <- outliers_result$data

```

# MLDFM Model
This section demonstrates how to use the mldfm function to fit the Multilevel Dynamic Factor Model using the input data.

```{r}
# MULTI-LEVEL DYNAMIC FACTOR MODEL
# 3 blocks
n_blocks <- 3 # 63 248 208
block_ind <- c(63,311,519)
global = 1
local = c(1,1,1)
middle_layer <- list("1-3" = 1)


mldfm_result <- mldfm(data, 
                      globa = global,
                      local = local,
                      middle_layer = middle_layer,
                      blocks = n_blocks, 
                      block_ind = block_ind , 
                      tol = 1e-6, 
                      max_iter = 1000,
                      method = 0) 

# Plot factors
# plot(mldfm_result, dates = dates) 

```
# Subsampling

```{r}
# Subsampling
n_samples <- 100
sample_size <- 0.9
mldfm_subsampling_result <- mldfm_subsampling(data, 
                                         global = global, 
                                         local = local,
                                         middle_layer = middle_layer,
                                         blocks = n_blocks, 
                                         block_ind = block_ind , 
                                         tol = 1e-6, 
                                         max_iter = 1000, 
                                         method = 0,
                                         n_samples = n_samples,
                                         sample_size = sample_size,
                                         seed = 42) 
```

# Creating stressed scenarios

```{r}
# Create stressed scenario
scenario <- create_scenario(model = mldfm_result,
                                  subsample = mldfm_subsampling_result,
                                  data = data, 
                                  block_ind = block_ind, 
                                  alpha=0.95)
                                      
```

# FARS computation

```{r}
# Compute Quantiles
fars_result <- compute_fars(dep_variable, 
                              mldfm_result$Factors, 
                              scenario = scenario, 
                              h = 1,   
                              edge = 0.05, 
                              min = TRUE) 

# Plot quantiles
#plot(fars_result,dates=dates)
```

# Density Estimation

```{r}
# Density 
density <- density(fars_result$Quantiles,  
                             levels = fars_result$Levels,  
                             est_points = 512, 
                             random_samples = 100000,
                             seed = 42)
# Plot density
#plot(density, time_index = dates)

```

# Growth-at-Risk (GaR)

```{r}
#GaR
GaR0.05 <- quantile_risk(density, QTAU = 0.05)
GaR0.50 <- quantile_risk(density, QTAU = 0.50)
GaR0.95 <- quantile_risk(density, QTAU = 0.95)
```

# Scenario Density Estimation

```{r}
# Scenario Density 
scenario_density <- density(fars_result$Scenario_Quantiles,  
                             levels = fars_result$Levels,  
                             est_points = 512, 
                             random_samples = 100000,
                             seed = 42)

```

# Growth-in-Stress (GiS)

```{r}
#GiS
GiS0.05 <- quantile_risk(scenario_density, QTAU = 0.05)
GiS0.25 <- quantile_risk(scenario_density, QTAU = 0.25)
GiS0.75 <- quantile_risk(scenario_density, QTAU = 0.75)
GiS0.95 <- quantile_risk(scenario_density, QTAU = 0.95)

```




