gas_forecast: Forecast GAS Model

In gasmodel: Generalized Autoregressive Score Models

Forecast GAS Model

Description

A function for forecasting of generalized autoregressive score (GAS) models of Creal et al. (2013) and Harvey (2013). Method "mean_path" filters time-varying parameters based on zero score and then generates mean of time series. Method "simulated_paths" repeatedly simulates time series, simultaneously filters time-varying parameters, and then estimates mean, standard deviation, and quantiles (see Blasques et al., 2016). Instead of supplying arguments about the model, the function can be applied to the gas object obtained by the gas() function.

Usage

gas_forecast(
  gas_object = NULL,
  method = "mean_path",
  t_ahead = 1L,
  x_ahead = NULL,
  rep_ahead = 1000L,
  quant = c(0.025, 0.975),
  y = NULL,
  x = NULL,
  distr = NULL,
  param = NULL,
  scaling = "unit",
  regress = "joint",
  p = 1L,
  q = 1L,
  par_static = NULL,
  par_link = NULL,
  par_init = NULL,
  coef_est = NULL
)

Arguments

gas_object	An optional GAS estimate, i.e. a list of S3 class gas returned by function gas().
method	A method used for forecasting. Supported methods are "mean_path" and "simulated_paths".
t_ahead	A number of observations to forecast.
x_ahead	Out-of-sample exogenous variables. For a single variable common for all time-varying parameters, a numeric vector. For multiple variables common for all time-varying parameters, a numeric matrix with observations in rows. For individual variables for each time-varying parameter, a list of numeric vectors or matrices in the above form. The number of observation must be equal to t_ahead.
rep_ahead	A number of simulation repetitions for method = "simulated_paths".
quant	A numeric vector of probabilities determining quantiles for method = "simulated_paths".
y, x, distr, param, scaling, regress, p, q, par_static, par_link, par_init, coef_est	When gas_object is not supplied, the estimated model can be specified using these individual arguments. See the arguments and value of the gas() function for more details.

Value

A list of S3 class gas_forecast with components:

data$y	The time series.
data$x	The exogenous variables.
data$x_ahead	The out-of-sample exogenous variables.
model$distr	The conditional distribution.
model$param	The parametrization of the conditional distribution.
model$scaling	The scaling function.
model$regress	The specification of the regression and dynamic equation.
model$t	The length of the time series.
model$t_ahead	The length of the out-of-sample time series.
model$n	The dimension of the model.
model$m	The number of exogenous variables.
model$p	The score order.
model$q	The autoregressive order.
model$par_static	The static parameters.
model$par_link	The parameters with the logarithmic/logistic links.
model$par_init	The initial values of the time-varying parameters.
model$coef_est	The estimated coefficients.
forecast$method	The method used for forecasting.
forecast$y_ahead_mean	The mean of the forecasted time series.
forecast$y_ahead_sd	The standard deviation of the forecasted time series. Only for method = "simulated_paths".
forecast$y_ahead_quant	The quantiles of the forecasted time series. Only for method = "simulated_paths".
forecast$par_tv_ahead_mean	The mean of the forecasted time-varying parameters.
forecast$par_tv_ahead_sd	The standard deviation of the forecasted time-varying parameters. Only for method = "simulated_paths".
forecast$par_tv_ahead_quant	The quantiles of the forecasted time-varying parameters. Only for method = "simulated_paths".
forecast$score_tv_ahead_mean	The mean of the forecasted scores.
forecast$score_tv_ahead_sd	The standard deviation of the forecasted scores. Only for method = "simulated_paths".
forecast$score_tv_ahead_quant	The quantiles of the forecasted scores. Only for method = "simulated_paths".

Note

Supported generic functions for S3 class gas_forecast include summary() ans plot().

References

Blasques, F., Koopman, S. J., Łasak, K., and Lucas, A. (2016). In-Sample Confidence Bands and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation-Driven Models. International Journal of Forecasting, 32(3), 875–887. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2015.11.018")}.

Creal, D., Koopman, S. J., and Lucas, A. (2013). Generalized Autoregressive Score Models with Applications. Journal of Applied Econometrics, 28(5), 777–795. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jae.1279")}.

Harvey, A. C. (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1017/cbo9781139540933")}.

See Also

gas()

Examples

# Load the Daily Toilet Paper Sales dataset
data("toilet_paper_sales")
y <- toilet_paper_sales$quantity
x <- as.matrix(toilet_paper_sales[3:9])

# Estimate GAS model based on the negative binomial distribution
est_negbin <- gas(y = y, x = x, distr = "negbin", regress = "sep")
est_negbin

# Forecast the model by the "mean_paths" method
x_ahead <- cbind(kronecker(matrix(1, 53, 1), diag(7)), 1)[3:367, -1]
fcst_negbin <- gas_forecast(est_negbin, t_ahead = 365, x_ahead = x_ahead)
fcst_negbin

# Plot the forecasted expected value
plot(fcst_negbin)

gasmodel documentation built on Aug. 19, 2025, 1:15 a.m.