R: Estimate generalized forecast error variance decomposition...

GFEVD {sstvars}

R Documentation

Estimate generalized forecast error variance decomposition for structural STVAR models.

Description

GFEVD estimates generalized forecast error variance decomposition for structural STVAR models.

Usage

GFEVD(
  stvar,
  shock_size = 1,
  N = 30,
  initval_type = c("data", "random", "fixed"),
  use_data_shocks = FALSE,
  R1 = 250,
  R2 = 250,
  init_regime = 1,
  init_values = NULL,
  which_cumulative = numeric(0),
  ncores = 2,
  burn_in = 1000,
  exo_weights = NULL,
  seeds = NULL,
  use_parallel = TRUE
)

## S3 method for class 'gfevd'
plot(x, ..., data_shock_pars = NULL)

## S3 method for class 'gfevd'
print(x, ..., digits = 2, N_to_print)

Arguments

`stvar`	an object of class `'stvar'`, created by, e.g., `fitSTVAR` or `fitSSTVAR`.
`shock_size`	What sign and size should be used for all shocks? By the normalization, the conditional covariance matrix of the structural error is an identity matrix.
`N`	a positive integer specifying the horizon how far ahead should the GFEVD be calculated.
`initval_type`	What type initial values are used for estimating the GIRFs that the GFEVD is based on? `"data"`: Estimate the GIRF for all the possible length `p` histories in the data. `"random"`: Estimate the GIRF for several random initial values generated from the a specific regime specified by the argument `init_regimes`. The number of initial values is set with the argument `R2`. `"fixed"`: Estimate the GIRF for the initial values specified with the argument `init_values`.
`use_data_shocks`	`TRUE` for a special feature in which for every possible length `p` history in the data, the GFEVD is estimated for a shock that has the sign and size of the corresponding structural shock recovered from the data. See the details section.
`R1`	the number of repetitions used to estimate GIRF for each initial value.
`R2`	the number of initial values to be drawn/used if `initval_type="random"` or `"fixed"`.
`init_regime`	an integer in `1,...,M` specifying the regime from which the initial values should be generated from. The initial values will be generated from the stationary distribution of the specific regime. Due to the lack of knowledge of the stationary distribution, models with other than Gaussian conditional distribution uses a simulation procedure with a burn-in period. See the details section.
`init_values`	a size `[p, d, R2]` array specifying the initial values in each slice for each Monte Carlo repetition, where d is the number of time series in the system and `R2` is an argument of this function. In each slice, the last row will be used as initial values for the first lag, the second last row for second lag etc. If not specified, initial values will be drawn from the regime specified in `init_regimes`.
`which_cumulative`	a numeric vector with values in `1,...,d` (`d=ncol(data)`) specifying which the variables for which the impulse responses should be cumulative. Default is none.
`ncores`	the number CPU cores to be used in parallel computing. Only single core computing is supported if an initial value is specified (and the GIRF won't thus be estimated multiple times).
`burn_in`	Burn-in period for simulating initial values from a regime when `cond_dist!="Gaussian"`. See the details section.
`exo_weights`	if `weight_function="exogenous"`, provide a size `(N+1 x M)` matrix of exogenous transition weights for the regimes: `[h, m]` for the (after-the-impact) period `h-1` and regime `m` weight (`[1, m]` is for the impact period). Ignored if `weight_function!="exogenous"`.
`seeds`	a numeric vector containing the random number generator seed for estimation of each GIRF. Should have the length... ...`nrow(data) - p + 1` if `initval_type="data"`. ...`R2` if `initval_type="random"`. ...`1` if `initval_type="fixed."`. Set to `NULL` for not initializing the seed. Exists for creating reproducible results.
`use_parallel`	employ parallel computing? If `FALSE`, does not print anything.
`x`	object of class `'gfevd'` generated by the function `GFEVD`.
`...`	graphical parameters passed to the `'ts'` plot method when using `data_shock_pars`.
`data_shock_pars`	if `use_data_shocks`, alternative plot method can be used that plots the relative contribution of a given shock to the forecast error variance of each variable at a given horizon. Should be a length two numeric vector with the number of the shock (1,..,d) in the first element and the horizon (0,1,2,...,N) in the second element.
`digits`	the number of decimals to print
`N_to_print`	an integer specifying the horizon how far to print the estimates. The default is that all the values are printed.

Details

The GFEVD is a forecast error variance decomposition calculated with the generalized impulse response function (GIRF). See Lanne and Nyberg (2016) for details.

If use_data_shocks == TRUE, the GIRF is estimated for a shock that has the sign and size of the corresponding structural shock recovered from the fitted model. This is done for every possible length p history in the data. The GFEVD is then calculated as the average of the GFEVDs obtained from the GIRFs estimated for the data shocks. The plot and print methods can be used as usual for this GFEVD. However, this feature also obtain the contribution of each shock to the variance of the forecast errors at various horizons in specific historical points of time. This can be done by using the plot method with the argument data_shock_pars. Note that the arguments shock_size, initval_type, and init_regime are ignored if use_data_shocks == TRUE.

Value

Returns and object of class 'gfevd' containing the GFEVD for all the variables and to the transition weights. Note that the decomposition does not exist at horizon zero for transition weights because the related GIRFs are always zero at impact. If use_data_shocks=TRUE, also contains the GFEVDs for each length p history in the data as 4D array with dimensions [horizon, variable, shock, time].

Functions

plot(gfevd): plot method
print(gfevd): print method

References

Lanne M. and Nyberg H. 2016. Generalized Forecast Error Variance Decomposition for Linear and Nonlineae Multivariate Models. Oxford Bulletin of Economics and Statistics, 78, 4, 595-603.

Examples

 
 # These are long-running examples that use parallel computing.
 # It takes approximately 30 seconds to run all the below examples.
 # Note that larger R1 and R2 should be used for more reliable results;
 # small R1 and R2 are used here to shorten the estimation time.

 # Recursively identifed 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")

 # GFEVD for one-standard-error positive structural shocks, N=30 steps ahead,
 # with fix initial values assuming all possible histories in the data.
 gfevd1 <- GFEVD(mod32logt, shock_size=1, N=30, initval_type="data", R1=10,
   seeds=1:(nrow(mod32logt$data)-2))
 print(gfevd1) # Print the results
 plot(gfevd1) # Plot the GFEVD

 # GFEVD for one-standard-error positive structural shocks, N=30 steps ahead,
 # with fix initial values that are the last p observations of the data.
 gfevd2 <- GFEVD(mod32logt, shock_size=1, N=30, initval_type="fixed", R1=100, R2=1,
  init_values=array(mod32logt$data[(nrow(mod32logt$data) - 2):nrow(mod32logt$data),],
  dim=c(3, 2, 1)), seeds=1)
 plot(gfevd2) # Plot the GFEVD

 # GFEVD for two-standard-error negative structural shocks, N=50 steps ahead
 # with the inital values drawn from the first regime. The responses of both
 # variables are accumulated.
 gfevd3 <- GFEVD(mod32logt, shock_size=-2, N=50, initval_type="random",
  R1=50, R2=50, init_regime=1)
 plot(gfevd3) # Plot the GFEVD

 # GFEVD calculated for each lenght p history in the data in such a way that
 # for each history, the structural shock recoved from the fitted model is
 # used.
 gfevd4 <- GFEVD(mod32logt, N=20, use_data_shocks=TRUE, R1=10)
 plot(gfevd4) # Usual plot method

 # Plot the contribution of the first to the variance of the forecast errors at
 # the historial points of time using the structural shocks recovered from the data:
 plot(gfevd4, data_shock_pars=c(1, 0)) # Contribution at impact
 plot(gfevd4, data_shock_pars=c(1, 2)) # Contribution after two periods
 plot(gfevd4, data_shock_pars=c(1, 4)) # Contribution after four periods

[Package sstvars version 1.0.1 Index]