Bootstrap Confidence Intervals for Dynamic Multipliers

This function computes bootstrap confidence intervals (CI) for dynamic multipliers of a specified variable in a model estimated using the kardl package. The bootstrap method generates resampled datasets to estimate the variability of the dynamic multipliers, providing upper and lower bounds for the confidence interval.

Usage

bootstrap(kmodel, horizon = 80, replications = 100, level = 95, minProb = 0)

Arguments

kmodel: The model produced by the kardl function. This is the model object from which the dynamic multipliers are calculated.
horizon: An integer specifying the horizon over which dynamic multipliers will be computed. The horizon defines the time frame for the analysis (e.g., 40 periods).
replications: An integer indicating the number of bootstrap replications to perform. Higher values increase accuracy but also computational time. Default is 100.
level: A numeric value specifying the confidence level for the intervals (e.g., 95 for 95 Default is 90.
minProb: A numeric value specifying the minimum p-value threshold for including coefficients in the bootstrap. Coefficients with p-values above this threshold will be set to zero in the bootstrap samples. Default is 0 (no threshold). This parameter allows users to control the inclusion of coefficients in the bootstrap process based on their statistical significance. Setting a threshold can help focus the analysis on more relevant variables, but it may also exclude potentially important effects if set too stringently.

Value

A list containing the following elements:

mpsi: A data frame containing the dynamic multiplier estimates along with their upper and lower confidence intervals for each variable and time horizon.
level: The confidence level used for the intervals (e.g 95).
horizon: The horizon over which the multipliers were computed (e.g., 40).
vars: A list of variable information extracted from the model, including dependent variable, independent variables, asymmetric variables, and deterministic terms.
replications: The number of bootstrap replications performed.
type: A character string indicating the type of analysis, in this case "bootstrap".

Details

The mpsi component of the output contains the dynamic multiplier estimates along with their upper and lower confidence intervals. These values are provided for each variable and at each time horizon.

Examples


  # Example usage of the bootstrap function


 # Fit a model using kardl
 kardl_model <- kardl(imf_example_data,
                      CPI ~ ER + PPI + asy(ER) +
                       det(covid) + trend,
                      mode = c(1, 2, 3, 0))

 # Perform bootstrap with specific variables for plotting
 boot <-
   bootstrap(kardl_model,   replications=5)
 # The boot object will include all plots for the specified variables
 # Displaying the boot object provides an overview of its components
 names(boot)
#> [1] "mpsi"         "level"        "horizon"      "vars"         "replications"
#> [6] "type"        


 # Inspect the first few rows of the dynamic multiplier estimates
  head(boot$mpsi)
#>   h    ER_POS       ER_NEG     ER_dif    PPI_POS     PPI_NEG PPI_dif
#> 1 0 0.1079048 -0.005754563 0.10215020 0.01650164 -0.01650164       0
#> 2 1 0.2441508 -0.068170052 0.17598074 0.06089675 -0.06089675       0
#> 3 2 0.3105905 -0.148501449 0.16208908 0.11412494 -0.11412494       0
#> 4 3 0.3407525 -0.227554838 0.11319771 0.16957406 -0.16957406       0
#> 5 4 0.3581333 -0.281735367 0.07639793 0.22496277 -0.22496277       0
#> 6 5 0.3709116 -0.326659918 0.04425171 0.27951609 -0.27951609       0
#>   ER_CI_upper ER_CI_lower
#> 1   0.1834999  0.03199611
#> 2   0.2382231  0.09423749
#> 3   0.2886517  0.08374155
#> 4   0.2398815  0.03265227
#> 5   0.1953934 -0.01221202
#> 6   0.1533647 -0.04662558


  summary(boot)
#> Summary of Dynamic Multipliers
#> Horizon: 80 
#> 
#>        h          ER_POS           ER_NEG              ER_dif       
#>  Min.   : 0   Min.   :0.1079   Min.   :-1.766204   Min.   :-1.0230  
#>  1st Qu.:20   1st Qu.:0.5034   1st Qu.:-1.582999   1st Qu.:-0.8871  
#>  Median :40   Median :0.6212   Median :-1.293834   Median :-0.6726  
#>  Mean   :40   Mean   :0.5868   Mean   :-1.173031   Mean   :-0.5863  
#>  3rd Qu.:60   3rd Qu.:0.6959   3rd Qu.:-0.837426   3rd Qu.:-0.3340  
#>  Max.   :80   Max.   :0.7432   Max.   :-0.005755   Max.   : 0.1760  
#>     PPI_POS          PPI_NEG           PPI_dif   ER_CI_upper     
#>  Min.   :0.0165   Min.   :-2.2241   Min.   :0   Min.   :-0.4794  
#>  1st Qu.:0.9673   1st Qu.:-1.9762   1st Qu.:0   1st Qu.:-0.4269  
#>  Median :1.5849   Median :-1.5849   Median :0   Median :-0.3310  
#>  Mean   :1.4268   Mean   :-1.4268   Mean   :0   Mean   :-0.2650  
#>  3rd Qu.:1.9762   3rd Qu.:-0.9673   3rd Qu.:0   3rd Qu.:-0.1561  
#>  Max.   :2.2241   Max.   :-0.0165   Max.   :0   Max.   : 0.2887  
#>   ER_CI_lower      
#>  Min.   :-1.23049  
#>  1st Qu.:-1.02721  
#>  Median :-0.73238  
#>  Mean   :-0.69237  
#>  3rd Qu.:-0.41318  
#>  Max.   : 0.09424  

 # Retrieve plots generated during the bootstrap process
 # Accessing all plots
  plot(boot)



 # Accessing the plot for a specific variable by its name
  plot(boot, variable = "PPI")

 plot(boot, variable = "ER")




library(magrittr)

   imf_example_data %>% kardl( CPI ~ PPI + asym(ER) +trend, maxlag=2) %>%
   bootstrap(replications=5) %>% plot(variable = "ER")