GFEVD: Estimate generalized forecast error variance decomposition for structural STVAR models.

Description

GFEVD estimates generalized forecast error variance decomposition for structural STVAR models.

Usage

GFEVD(
  stvar,
  shock_size = 1,
  N = 30,
  initval_type = c("data", "random", "fixed"),
  use_data_shocks = FALSE,
  R1 = 250,
  R2 = 250,
  init_regime = 1,
  init_values = NULL,
  which_cumulative = numeric(0),
  ncores = 2,
  burn_in = 1000,
  exo_weights = NULL,
  seeds = NULL,
  use_parallel = TRUE
)
# S3 method for gfevd
plot(x, ..., data_shock_pars = NULL)
# S3 method for gfevd
print(x, ..., digits = 2, N_to_print)

Value

Returns and object of class 'gfevd' containing the GFEVD for all the variables and to the transition weights. Note that the decomposition does not exist at horizon zero for transition weights because the related GIRFs are always zero at impact. If use_data_shocks=TRUE, also contains the GFEVDs for each length \(p\) history in the data as 4D array with dimensions [horizon, variable, shock, time].

Arguments

stvar

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

shock_size

What sign and size should be used for all shocks? By the normalization, the conditional covariance matrix of the structural error is an identity matrix.

N

a positive integer specifying the horizon how far ahead should the GFEVD be calculated.

initval_type

What type initial values are used for estimating the GIRFs that the GFEVD is based on?

"data":: Estimate the GIRF for all the possible length \(p\) histories in the data.

"random":

Estimate the GIRF for several random initial values generated from the a specific regime specified by the argument init_regimes. The number of initial values is set with the argument R2.

"fixed":

Estimate the GIRF for the initial values specified with the argument init_values.

use_data_shocks

TRUE for a special feature in which for every possible length \(p\) history in the data, the GFEVD is estimated for a shock that has the sign and size of the corresponding structural shock recovered from the data. See the details section.

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

the number of initial values to be drawn/used if initval_type="random" or "fixed".

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.

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 numeric vector containing the random number generator seed for estimation of each GIRF. Should have the length...

...nrow(data) - p + 1 if initval_type="data".
...R2 if initval_type="random".
...1 if initval_type="fixed.".

Set to NULL for not initializing the seed. Exists for creating reproducible results.

use_parallel

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

object of class 'gfevd' generated by the function GFEVD.

...

graphical parameters passed to the 'ts' plot method when using data_shock_pars.

data_shock_pars

if use_data_shocks, alternative plot method can be used that plots the relative contribution of a given shock to the forecast error variance of each variable at a given horizon. Should be a length two numeric vector with the number of the shock (1,..,d) in the first element and the horizon (0,1,2,...,N) in the second element.

digits

the number of decimals to print

N_to_print

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

Functions

plot(gfevd): plot method
print(gfevd): print method

Details

The GFEVD is a forecast error variance decomposition calculated with the generalized impulse response function (GIRF). See Lanne and Nyberg (2016) for details.

If use_data_shocks == TRUE, the GIRF is estimated for a shock that has the sign and size of the corresponding structural shock recovered from the fitted model. This is done for every possible length \(p\) history in the data. The GFEVD is then calculated as the average of the GFEVDs obtained from the GIRFs estimated for the data shocks. The plot and print methods can be used as usual for this GFEVD. However, this feature also obtain the contribution of each shock to the variance of the forecast errors at various horizons in specific historical points of time. This can be done by using the plot method with the argument data_shock_pars. Note that the arguments shock_size, initval_type, and init_regime are ignored if use_data_shocks == TRUE.

References

Lanne M. and Nyberg H. 2016. Generalized Forecast Error Variance Decomposition for Linear and Nonlineae Multivariate Models. Oxford Bulletin of Economics and Statistics, 78, 4, 595-603.

Examples

Run this code

 # \donttest{
 # 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 identifed 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")

 # GFEVD for one-standard-error positive structural shocks, N=30 steps ahead,
 # with fix initial values assuming all possible histories in the data.
 gfevd1 <- GFEVD(mod32logt, shock_size=1, N=30, initval_type="data", R1=10,
   seeds=1:(nrow(mod32logt$data)-2))
 print(gfevd1) # Print the results
 plot(gfevd1) # Plot the GFEVD

 # GFEVD for one-standard-error positive structural shocks, N=30 steps ahead,
 # with fix initial values that are the last p observations of the data.
 gfevd2 <- GFEVD(mod32logt, shock_size=1, N=30, initval_type="fixed", R1=100, R2=1,
  init_values=array(mod32logt$data[(nrow(mod32logt$data) - 2):nrow(mod32logt$data),],
  dim=c(3, 2, 1)), seeds=1)
 plot(gfevd2) # Plot the GFEVD

 # GFEVD for two-standard-error negative structural shocks, N=50 steps ahead
 # with the inital values drawn from the first regime. The responses of both
 # variables are accumulated.
 gfevd3 <- GFEVD(mod32logt, shock_size=-2, N=50, initval_type="random",
  R1=50, R2=50, init_regime=1)
 plot(gfevd3) # Plot the GFEVD

 # GFEVD calculated for each lenght p history in the data in such a way that
 # for each history, the structural shock recoved from the fitted model is
 # used.
 gfevd4 <- GFEVD(mod32logt, N=20, use_data_shocks=TRUE, R1=10)
 plot(gfevd4) # Usual plot method

 # Plot the contribution of the first to the variance of the forecast errors at
 # the historial points of time using the structural shocks recovered from the data:
 plot(gfevd4, data_shock_pars=c(1, 0)) # Contribution at impact
 plot(gfevd4, data_shock_pars=c(1, 2)) # Contribution after two periods
 plot(gfevd4, data_shock_pars=c(1, 4)) # Contribution after four periods
 # }

Run the code above in your browser using DataLab