Calculate latent VAR impulse response functions

Compute Generalized or Orthogonalized Impulse Response Functions (IRFs) from mvgam models with Vector Autoregressive dynamics

Usage

irf(object, ...)

# S3 method for mvgam
irf(object, h = 1, cumulative = FALSE, orthogonal = FALSE, ...)

Arguments

object: list object of class mvgam resulting from a call to mvgam() that used a Vector Autoregressive latent process model (either as VAR(cor = FALSE) or VAR(cor = TRUE))
...: ignored
h: Positive integer specifying the forecast horizon over which to calculate the IRF
cumulative: Logical flag indicating whether the IRF should be cumulative
orthogonal: Logical flag indicating whether orthogonalized IRFs should be calculated. Note that the order of the variables matters when calculating these

Value

An object of class mvgam_irf containing the posterior IRFs. This object can be used with the supplied S3 functions plot

Details

Generalized or Orthogonalized Impulse Response Functions can be computed using the posterior estimates of Vector Autoregressive parameters. This function generates a positive "shock" for a target process at time t = 0 and then calculates how each of the remaining processes in the latent VAR are expected to respond over the forecast horizon h. The function computes IRFs for all processes in the object and returns them in an array that can be plotted using the S3 plot function. To inspect community-level metrics of stability using latent VAR processes, you can use the related stability function.

References

PH Pesaran & Shin Yongcheol (1998). Generalized impulse response analysis in linear multivariate models. Economics Letters 58: 17–29.

Author

Nicholas J Clark

Examples

# \donttest{
# Simulate some time series that follow a latent VAR(1) process
simdat <- sim_mvgam(family = gaussian(),
                    n_series = 4,
                    trend_model = VAR(cor = TRUE),
                    prop_trend = 1)
plot_mvgam_series(data = simdat$data_train, series = 'all')


# Fit a model that uses a latent VAR(1)
mod <- mvgam(y ~ -1,
             trend_formula = ~ 1,
             trend_model = VAR(cor = TRUE),
             family = gaussian(),
             data = simdat$data_train,
             silent = 2)
#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
#>                  from stan/lib/stan_math/stan/math.hpp:19,
#>                  from stan/src/stan/model/model_header.hpp:4,
#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpGcPapO/model-e5b0575a6e79.hpp:2:
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
#>   194 |       if (cdf_n < 0.0)
#>       | 
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory

# Calulate Generalized IRFs for each series
irfs <- irf(mod, h = 12, cumulative = FALSE)

# Plot them
plot(irfs, series = 1)

plot(irfs, series = 2)

plot(irfs, series = 3)

# }