fevd.mvgam function

Calculate latent VAR forecast error variance decompositions

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

fevd(object, ...)

## S3 method for class 'mvgam'
fevd(object, h = 10, ...)

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

Returns

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 $k$:

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 $j$.

Examples

# 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,
  chains = 2,
  silent = 2
)

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

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

# View a summary of the error variance decompositions
summary(fevds)

References

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

See Also

VAR, irf, stability

Author(s)

Nicholas J Clark