sstvars (version 1.2.0)

hist_decomp: Compute historical decompositions for structural STVAR models.

Description

hist_decomp computes historical decompositions for structural STVAR models.

Usage

hist_decomp(stvar)
# S3 method for histdecomp
plot(x, ..., plot_by_shock = FALSE, which_to_plot)
# S3 method for histdecomp
print(x, ..., digits = 3, which_vars, which_indices)

Value

Returns a class 'histdecomp' list with the following elements:

init_cond_comp

A matrix of size \((T \times d)\) containing the contributions of the initial conditions to the movements of the variables at each time point; the element t, i giving the contribution at the time t on the variable i.

steady_state_comp

A matrix of size \((T \times d)\) containing the contributions of the steady state component to the movements of the variables at each time point; the element t, i giving the contribution at the time t on the variable i.

shock_comp

A matrix of size \((T \times d)\) containing the contributions of the shocks to the movements of the variables at each time point; the element t, i giving the contribution at the time t on the variable i.

contributions_of_shocks

A 3D array of size \((T \times d \times d)\) containing the cumulative contributions of the shocks to the movements of the variables at each time point; the element t, i1, i2 giving the contribution of the shock i1 to the variable i2 at the time t.

stvar

The original STVAR model object.

Returns the input object x invisibly.

Arguments

stvar

an object of class 'stvar' defining a structural or reduced form STVAR model. For a reduced form model (that is not readily identified statiscally), the shocks are automatically identified by the lower triangular Cholesky decomposition.

x

object of class 'histdecomp' created by the function hist_decomp.

...

currently not in use.

plot_by_shock

should the historical decompositions by plotted so that there is one figure for each shock (rather than one figure for each variable)?

which_to_plot

a numeric vector with the indices of the variables or shocks (depending on the argument plot_by_shock) to be plotted. The default is to plot all of them.

digits

how many significant digits to print?

which_vars

a numeric vector specifying the variables to print. The default is that all the variables are printed.

which_indices

a numeric vector specifying the time period indices to print. The default is that all the time periods are printed.

Functions

• plot(histdecomp): plot method

• print(histdecomp): print method

Details

The historical decomposition quantifies the cumulative effects the shocks to the movements of the variables (see, e.g., Kilian and Lütkepohl, 2017, Section~4.3) The historical decompositions are computed as described in Wong (2018). Note that due to the effect of the "initial conditions" and the "steady state component", which are not attributed to the shocks, the cumulative effects of the shocks do not sum to the observed time series.

References

• Kilian L., Lütkepohl H. 2017. Structural Vector Autoregressive Analysis. 1st edition. Cambridge University Press, Cambridge.

• Wong H. 2018. Historical decomposition for nonlinear vector autoregressive models. CAMA Working Paper No. 62/2017, available as SSRN:3057759.

See Also

GIRF, GFEVD, linear_IRF, fitSSTVAR, cfact_hist, cfact_fore, cfact_girf

Examples

# 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")

# Calculate the historical decomposition:
histdec <- hist_decomp(mod32logt)

# Print historical decomposition for Variable 1 for the first ten time periods:
print(histdec, which_vars=1, which_indices=1:10)

# Plot the historical decomposition for all variables:
plot(histdec)

# Plot the contributions of Shock 1 on the movements of all the variables:
plot(histdec, plot_by_shock=TRUE, which_to_plot=1)