GIRF {sstvars}

Estimate generalized impulse response function for structural STVAR models.

Description

GIRF estimates generalized impulse response function for structural STVAR models.

Usage

GIRF(
  stvar,
  which_shocks,
  shock_size = 1,
  N = 30,
  R1 = 250,
  R2 = 250,
  init_regime = 1,
  init_values = NULL,
  which_cumulative = numeric(0),
  scale = NULL,
  scale_type = c("instant", "peak"),
  scale_horizon = N,
  ci = c(0.95, 0.8),
  ncores = 2,
  burn_in = 1000,
  exo_weights = NULL,
  seeds = NULL,
  use_parallel = TRUE
)

## S3 method for class 'girf'
plot(x, margs, ...)

## S3 method for class 'girf'
print(x, ..., digits = 2, N_to_print)

Arguments

stvar

an object of class 'stvar', created by, e.g., fitSTVAR or fitSSTVAR.

which_shocks

a numeric vector of length at most d (=ncol(data)) and elements in 1,...,d specifying the structural shocks for which the GIRF should be estimated.

shock_size

a non-zero scalar value specifying the common size for all scalar components of the structural shock. Note that the conditional covariance matrix of the structural shock is normalized to an identity matrix and that the (generalized) impulse responses may not be symmetric with respect to the sign and size of the shock.

N

a positive integer specifying the horizon how far ahead should the generalized impulse responses be calculated.

R1

the number of repetitions used to estimate GIRF for each initial value.

R2

the number of initial values to use, i.e., to draw from init_regime if init_values are not specified. The confidence bounds will be sample quantiles of the GIRFs based on different initial values. Ignored if the argument init_value is specified.

init_regime

an integer in 1,...,M specifying the regime from which the initial values should be generated from. The initial values will be generated from the stationary distribution of the specific regime. Due to the lack of knowledge of the stationary distribution, models with other than Gaussian conditional distribution uses a simulation procedure with a burn-in period. See the details section.

init_values

a size [p, d, R2] array specifying the initial values in each slice for each Monte Carlo repetition, where d is the number of time series in the system and R2 is an argument of this function. In each slice, the last row will be used as initial values for the first lag, the second last row for second lag etc. If not specified, initial values will be drawn from the regime specified in init_regimes.

which_cumulative

a numeric vector with values in 1,...,d (d=ncol(data)) specifying which the variables for which the impulse responses should be cumulative. Default is none.

scale

should the GIRFs to some of the shocks be scaled so that they correspond to a specific magnitude of instantaneous or peak response of some specific variable (see the argument scale_type)? Provide a length three vector where the shock of interest is given in the first element (an integer in 1,...,d), the variable of interest is given in the second element (an integer in 1,...,d), and the magnitude of its instantaneous or peak response in the third element (a non-zero real number). If the GIRFs of multiple shocks should be scaled, provide a matrix which has one column for each of the shocks with the columns being the length three vectors described above.

scale_type

If argument scale is specified, should the GIRFs be scaled to match an instantaneous response ("instant") or peak response ("peak"). If "peak", the scale is based on the largest magnitude of peak response in absolute value. Ignored if scale is not specified.

scale_horizon

If scale_type == "peak" what the maximum horizon up to which peak response is expected? Scaling won't based on values after this.

ci

a numeric vector with elements in (0, 1) specifying the confidence levels of the confidence intervals.

ncores

the number CPU cores to be used in parallel computing. Only single core computing is supported if an initial value is specified (and the GIRF won't thus be estimated multiple times).

burn_in

Burn-in period for simulating initial values from a regime when cond_dist!="Gaussian". See the details section.

exo_weights

if weight_function="exogenous", provide a size (N+1 x M) matrix of exogenous transition weights for the regimes: [h, m] for the (after-the-impact) period h-1 and regime m weight ([1, m] is for the impact period). Ignored if weight_function!="exogenous".

seeds

a length R2 vector containing the random number generator seed for estimation of each GIRF. A single number of an initial value is specified. or NULL for not initializing the seed. Exists for creating reproducible results.

use_parallel

employ parallel computing? If FALSE, does not print anything.

x

object of class 'girf' generated by the function GIRF.

margs

numeric vector of length four that adjusts the [bottom_marginal, left_marginal, top_marginal, right_marginal] as the relative sizes of the marginals to the figures of the responses.

...

graphical parameters passed to plot method plotting the GIRFs

digits

the number of decimals to print

N_to_print

an integer specifying the horizon how far to print the estimates and confidence intervals. The default is that all the values are printed.

Details

The confidence bounds reflect uncertainty about the initial state (but not about the parameter estimates) if initial values are not specified. If initial values are specified, confidence intervals won't be estimated.

Note that if the argument scale is used, the scaled responses of the transition weights might be more than one in absolute value.

If weight_function="exogenous", exogenous transition weights used in the Monte Carlo simulations for the future sample paths of the process must the given in the argument exo_weights. The same weights are used as the transition weights across the Monte Carlo repetitions.

Value

Returns a class 'girf' list with the GIRFs in the first element ($girf_res) and the used arguments the rest. The first element containing the GIRFs is a list with the mth element containing the point estimates for the GIRF in $point_est (the first element) and confidence intervals in $conf_ints (the second element). The first row is for the GIRF at impact (n=0), the second for n=1, the third for n=2, and so on.

The element $all_girfs is a list containing results from all the individual GIRFs obtained from the MC repetitions. Each element is for one shock and results are in array of the form [horizon, variables, MC-repetitions].

Functions

• plot(girf): plot method

• print(girf): print method

See Also

GFEVD, linear_IRF, fitSSTVAR

• Kilian L., Lütkepohl H. 20017. Structural Vector Autoregressive Analysis. 1st edition. Cambridge University Press, Cambridge.

Examples

 
 # These are long-running examples that use parallel computing.
 # It takes approximately 30 seconds to run all the below examples.
 # Note that larger R1 and R2 should be used for more reliable results;
 # small R1 and R2 are used here to shorten the estimation time.

 # Recursively identified logistic Student's t STVAR(p=3, M=2) model with the first
 # lag of the second variable as the switching variable:
 params32logt <- c(0.5959, 0.0447, 2.6279, 0.2897, 0.2837, 0.0504, -0.2188, 0.4008,
  0.3128, 0.0271, -0.1194, 0.1559, -0.0972, 0.0082, -0.1118, 0.2391, 0.164, -0.0363,
  -1.073, 0.6759, 3e-04, 0.0069, 0.4271, 0.0533, -0.0498, 0.0355, -0.4686, 0.0812,
   0.3368, 0.0035, 0.0325, 1.2289, -0.047, 0.1666, 1.2067, 7.2392, 11.6091)
 mod32logt <- STVAR(gdpdef, p=3, M=2, params=params32logt, weight_function="logistic",
  weightfun_pars=c(2, 1), cond_dist="Student", identification="recursive")

 # GIRF for one-standard-error positive structural shocks, N=30 steps ahead,
 # with the inital values drawn from the first regime.
 girf1 <- GIRF(mod32logt, which_shocks=1:2, shock_size=1, N=30, R1=50, R2=50,
  init_regime=2)
 print(girf1) # Print the results
 plot(girf1) # Plot the GIRFs

 # GIRF for one-standard-error positive structural shocks, N=30 steps ahead,
 # with the inital values drawn from the second regime. The responses of the
 # GDP and GDP deflator growth rates are accumulated.
 girf2 <- GIRF(mod32logt, which_shocks=1:2, which_cumulative=1:2, shock_size=1,
  N=30, R1=50, R2=50, init_regime=2)
 plot(girf2) # Plot the GIRFs

 # GIRF for two-standard-error negative structural shock - the first shock only.
 # N=50 steps ahead with the inital values drawn from the first regime. The responses
 # are scaled to correspond an instantanous increase of 0.5 of the first variable.
 girf3 <- GIRF(mod32logt, which_shocks=1, shock_size=-2, N=50, R1=50, R2=50,
  init_regime=1, scale_type="instant", scale=c(1, 1, 0.5))
 plot(girf3) # Plot the GIRFs