GIRF_Dichotomous_model: GIRF for Dichotomous models
In EWS: Early Warning System

Description Usage Arguments Value Author(s) References Examples

This function estimates the response functions of dichotomous models in a univariate framework using the method proposed by Lajaunie (2021). The response functions are based on the 4 specifications proposed by Kauppi & Saikkonen (2008).

1	GIRF_Dicho(Dicho_Y, Exp_X, Lag, Int, t_mod, horizon, shock_size, OC)

`Dicho_Y`	Vector of the binary time series.
`Exp_X`	Vector or Matrix of explanatory time series.
`Lag`	Number of lags used for the estimation.
`Int`	Boolean value: TRUE for an estimation with intercept, and FALSE otherwise.
`t_mod`	Model number: 1, 2, 3 or 4. -> 1 for the static model: P_{t-1}(Y_{t}) = F(π_{t})=F(α + β'X_{t}) -> 2 for the dynamic model with lag binary variable: P_{t-1}(Y_{t}) = F(π_{t})=F(α + β'X_{t} + γ Y_{t-l}) -> 3 for the dynamic model with lag index variable: P_{t-1}(Y_{t}) = F(π_{t})=F(α + β'X_{t} + η π_{t-l}) -> 4 for the dynamic model with both lag binary variable and lag index variable: P_{t-1}(Y_{t}) = F(π_{t})=F(α + β'X_{t} + η π_{t-l} + γ Y_{t-l})
`horizon`	Numeric variable corresponding to the horizon target for the GIRF analysis.
`shock_size`	Numeric variable equal to the size of the shock. It can be estimated with the Vector_Error function.
`OC`	Numeric variable equal to the Optimal Cut-off (threshold). This threshold can be considered arbitrarily, with a value between 0 and 1, or it can be estimated with one of the functions EWS_AM_Criterion, EWS_CSA_Criterion, or EWS_NSR_Criterion.

Matrix with 7 columns:

`column 1`	horizon
`column 2`	index
`column 3`	index with shock
`column 4`	probability associated to the index
`column 5`	probability associated to the index with shock
`column 6`	binary variable associated to the index
`column 7`	binary variable associated to the index with shock

Jean-Baptiste Hasse and Quentin Lajaunie

Kauppi, Heikki, and Pentti Saikkonen. "Predicting US recessions with dynamic binary response models." The Review of Economics and Statistics 90.4 (2008): 777-791.

Lajaunie, Quentin. Generalized Impulse Response Function for Dichotomous Models. No. 2852. Orleans Economics Laboratory/Laboratoire d'Economie d'Orleans (LEO), University of Orleans, 2021.

# NOT RUN {

# Import data
data("data_USA")

# Data process
Var_Y <- as.vector(data_USA$NBER)
Var_X <- as.vector(data_USA$Spread)

# Estimate the logit regression
Logistic_results <- Logistic_Estimation(Dicho_Y = Var_Y, Exp_X = Var_X, Intercept = TRUE,
                      Nb_Id = 1, Lag = 1, type_model = 1)

# Vector of probabilities
vector_proba <- as.vector(rep(0,length(Var_Y)-1))
vector_proba <- Logistic_results$prob

# Vector of binary variables
Lag <- 1
vector_binary <- as.vector(rep(0,length(Var_Y)-1))
vector_binary <- Var_Y[(1+Lag):length(Var_Y)]

# optimal cut-off that maximizes the AM criterion
Threshold_AM <- EWS_AM_Criterion(Var_Proba = vector_proba, Dicho_Y = vector_binary,
                      cutoff_interval = 0.0001)

# Estimate the estimation errors
Residuals <- Vector_Error(Dicho_Y = Var_Y, Exp_X = Var_X, Intercept = TRUE,
                      Nb_Id = 1, Lag = 1, type_model = 1)

# Initialize the shock
size_shock <- quantile(Residuals,0.95)

# GIRF Analysis
results <- GIRF_Dicho(Dicho_Y = Var_Y, Exp_X = Var_X, Lag = 1, Int = TRUE, t_mod = 1,
                      horizon = 3, shock_size = size_shock, OC = Threshold_AM)

# print results
results

#}