Estimate linear impulse response function based on a single regime of a structural STVAR model.
linear_IRF estimates linear impulse response function based on a single regime of a structural STVAR model.
linear_IRF( stvar, N = 30, regime = 1, which_cumulative = numeric(0), scale = NULL, ci = NULL, bootstrap_reps = 100, ncores = 2, robust_method = c("Nelder-Mead", "SANN", "none"), maxit_robust = 1000, seed = NULL, ... ) ## S3 method for class 'irf' plot(x, shocks_to_plot, ...) ## S3 method for class 'irf' print(x, ..., digits = 2, N_to_print, shocks_to_print)
stvar: an object of class 'stvar' defining a structural or reduced form STVAR model. For a reduced form model, the shocks are automatically identified by the lower triangular Cholesky decomposition.
N: a positive integer specifying the horizon how far ahead should the linear impulse responses be calculated.
regime: Based on which regime the linear IRF should be calculated? An integer in .
which_cumulative: a numeric vector with values in
(d=ncol(data)) specifying which the variables for which the linear impulse responses should be cumulative. Default is none.
scale: should the linear IRFs to some of the shocks be scaled so that they correspond to a specific instantaneous response of some specific variable? Provide a length three vector where the shock of interest is given in the first element (an integer in ), the variable of interest is given in the second element (an integer in ), and its instantaneous response in the third element (a non-zero real number). If the linear IRFs 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.
ci: a real number in specifying the confidence level of the confidence intervals calculated via a fixed-design wild residual bootstrap method. Available only for models that impose linear autoregressive dynamics (excluding changes in the volatility regime).
bootstrap_reps: the number of bootstrap repetitions for estimating confidence bounds.
ncores: the number of CPU cores to be used in parallel computing when bootstrapping confidence bounds.
robust_method: Should some robust estimation method be used in the estimation before switching to the gradient based variable metric algorithm? See details.
maxit_robust: the maximum number of iterations on the first phase robust estimation, if employed.
seed: a real number initializing the seed for the random generator.
...: currently not used.
x: object of class 'irf' generated by the function linear_IRF.
shocks_to_plot: IRFs of which shocks should be plotted? A numeric vector with elements in 1,...,d.
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.
shocks_to_print: the responses to which should should be printed? A numeric vector with elements in 1,...,d. The default is that responses to all the shocks are printed.
Returns a class 'irf' list with with the following elements:
$point_est:: a 3D array [variables, shock, horizon] containing the point estimates of the IRFs. Note that the first slice is for the impact responses and the slice i+1 for the period i. The response of the variable 'i1' to the shock 'i2' is subsetted as $point_est[i1, i2, ].
$conf_ints:: bootstrapped confidence intervals for the IRFs in a [variables, shock, horizon, bound]
4D array. The lower bound is obtained as `$conf_ints[, , , 1]`, and similarly the upper bound as `$conf_ints[, , , 2]`. The subsetted 3D array is then the bound in a form similar to `$point_est`.
$all_bootstrap_reps:: IRFs from all of the bootstrap replications in a [variables, shock, horizon, rep]. 4D array. The IRF from replication i1 is obtained as $all_bootstrap_reps[, , , i1], and the subsetted 3D array is then the in a form similar to $point_est.
Other elements:: contains some of the arguments the linear_IRF was called with.
If the autoregressive dynamics of the model are linear (i.e., either M == 1 or mean and AR parameters are constrained identical across the regimes), confidence bounds can be calculated based on a fixed-design wild residual bootstrap method. We employ the method described in Herwartz and Lütkepohl (2014); see also the relevant chapters in Kilian and Lütkepohl (2017).
Employs the estimation function optim from the package stats that implements the optimization algorithms. The robust optimization method Nelder-Mead is much faster than SANN but can get stuck at a local solution. See ?optim and the references therein for further details.
For model identified by non-Gaussianity, the signs and ordering of the shocks are normalized by assuming that the first non-zero element of each column of the impact matrix of Regime 1 is strictly positive and they are in a decreasing order. Use the argument scale to obtain IRFs scaled for specific impact responses.
plot(irf): plot methodprint(irf): print method## These are long running examples that take approximately 10 seconds to run. ## A small number of bootstrap replications is used below to shorten the ## running time (in practice, a larger number of replications should be used). # p=1, M=1, d=2, linear VAR model with independent Student's t shocks identified # by non-Gaussianity (arbitrary weight function applied here): theta_112it <- c(0.644, 0.065, 0.291, 0.021, -0.124, 0.884, 0.717, 0.105, 0.322, -0.25, 4.413, 3.912) mod112 <- STVAR(data=gdpdef, p=1, M=1, params=theta_112it, cond_dist="ind_Student", identification="non-Gaussianity", weight_function="threshold", weightfun_pars=c(1, 1)) mod112 <- swap_B_signs(mod112, which_to_swap=1:2) # Estimate IRFs 20 periods ahead, bootstrapped 90% confidence bounds based on # 10 bootstrap replications. Linear model so robust estimation methods are # not required. irf1 <- linear_IRF(stvar=mod112, N=20, regime=1, ci=0.90, bootstrap_reps=1, robust_method="none", seed=1, ncores=1) plot(irf1) print(irf1, digits=3) # p=1, M=2, d=2, Gaussian STVAR with relative dens weight function, # shocks identified recursively. theta_122relg <- c(0.734054, 0.225598, 0.705744, 0.187897, 0.259626, -0.000863, -0.3124, 0.505251, 0.298483, 0.030096, -0.176925, 0.838898, 0.310863, 0.007512, 0.018244, 0.949533, -0.016941, 0.121403, 0.573269) mod122 <- STVAR(data=gdpdef, p=1, M=2, params=theta_122relg, identification="recursive") # Estimate IRF based on the first regime 30 period ahead. Scale IRFs so that # the instantaneous response of the first variable to the first shock is 0.3, # and the response of the second variable to the second shock is 0.5. # response of the Confidence bounds # are not available since the autoregressive dynamics are nonlinear. irf2 <- linear_IRF(stvar=mod122, N=30, regime=1, scale=cbind(c(1, 1, 0.3), c(2, 2, 0.5))) plot(irf2) # Estimate IRF based on the second regime without scaling the IRFs: irf3 <- linear_IRF(stvar=mod122, N=30, regime=2) plot(irf3) # p=3, M=2, d=3, Students't logistic STVAR model with the first lag of the second # variable as the switching variable. Autoregressive dynamics restricted linear, # but the volatility regime varies in time, allowing the shocks to be identified # by conditional heteroskedasticity. theta_322 <- c(0.7575, 0.6675, 0.2634, 0.031, -0.007, 0.5468, 0.2508, 0.0217, -0.0356, 0.171, -0.083, 0.0111, -0.1089, 0.1987, 0.2181, -0.1685, 0.5486, 0.0774, 5.9398, 3.6945, 1.2216, 8.0716, 8.9718) mod322 <- STVAR(data=gdpdef, p=3, M=2, params=theta_322, weight_function="logistic", weightfun_pars=c(2, 1), cond_dist="Student", mean_constraints=list(1:2), AR_constraints=rbind(diag(3*2^2), diag(3*2^2)), identification="heteroskedasticity", parametrization="mean") ## Estimate IRFs 30 periods ahead, bootstrapped 90% confidence bounds based on # 10 bootstrap replications. Responses of the second variable are accumulated. irf4 <- linear_IRF(stvar=mod322, N=30, regime=1, ci=0.90, bootstrap_reps=10, which_cumulative=2, seed=1) plot(irf4)
GIRF, GFEVD, fitSTVAR, STVAR, reorder_B_columns, swap_B_signs