Calculate latent VAR forecast error variance decompositions

Compute forecast error variance decompositions from mvgam models with Vector Autoregressive dynamics

Usage

fevd(object, ...)

# S3 method for mvgam
fevd(object, h = 1, ...)

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

Value

An object of class mvgam_fevd containing the posterior forecast error variance decompositions. This object can be used with the supplied S3 functions plot

Details

A forecast error variance decomposition is useful for quantifying the amount of information each series that in a Vector Autoregression contributes to the forecast distributions of the other series in the autoregression. This function calculates the forecast error variance decomposition using the orthogonalised impulse response coefficient matrices $\Psi_h$, which can be used to quantify the contribution of series $j$ to the h-step forecast error variance of series $k$: $$ \sigma_k^2(h) = \sum_{j=1}^K(\psi_{kj, 0}^2 + \ldots + \psi_{kj, h-1}^2) \quad $$ If the orthogonalised impulse reponses $(\psi_{kj, 0}^2 + \ldots + \psi_{kj, h-1}^2)$ are divided by the variance of the forecast error $\sigma_k^2(h)$, this yields an interpretable percentage representing how much of the forecast error variance for $k$ can be explained by an exogenous shock to $j$.

References

Lütkepohl, H (2006). New Introduction to Multiple Time Series Analysis. Springer, New York.

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-e5b066e7c36.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 forecast error variance decompositions for each series
fevds <- fevd(mod, h = 12)

# Plot median contributions to forecast error variance
plot(fevds)

# }