A function for obtaining filtered time-varying parameters of generalized autoregressive score (GAS) models of Creal et al. (2013) and Harvey (2013).
It captures parameter uncertainty and can also be used for forecasting.
Method "simulated_coefs" computes a path of time-varying parameters for each simulated coefficient set under assumption of asymptotic normality with given variance-covariance matrix (see Blasques et al., 2016).
Method "given_coefs" computes a path of time-varying parameters for each supplied coefficient set.
Instead of supplying arguments about the model, the function can be applied to the gas object obtained by the gas() function.
gas_filter(
gas_object = NULL,
method = "simulated_coefs",
coef_set = NULL,
rep_gen = 1000L,
t_ahead = 0L,
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_fix_value = NULL,
coef_fix_other = NULL,
coef_fix_special = NULL,
coef_bound_lower = NULL,
coef_bound_upper = NULL,
coef_est = NULL,
coef_vcov = NULL
)A list of S3 class gas_filter with components:
The time series.
The exogenous variables.
The out-of-sample exogenous variables. Only when t_ahead > 0.
The conditional distribution.
The parametrization of the conditional distribution.
The scaling function.
The specification of the regression and dynamic equation.
The length of the time series.
The length of the out-of-sample time series. Only when t_ahead > 0.
The dimension of the model.
The number of exogenous variables.
The score order.
The autoregressive order.
The static parameters.
The parameters with the logarithmic/logistic links.
The initial values of the time-varying parameters.
The values to which coefficients are fixed.
The multiples of the estimated coefficients, which are added to the fixed coefficients.
The predefined structures of coef_fix_value and coef_fix_other.
The lower bounds on coefficients.
The upper bounds on coefficients.
The coefficient sets.
The method used for parameter uncertainty.
The mean of the time-varying parameters.
The standard deviation of the time-varying parameters.
The quantiles of the time-varying parameters.
The mean of the scores.
The standard deviation of the scores.
The quantiles of the scores.
The mean of the forecasted time series. Only when t_ahead > 0.
The standard deviation of the forecasted time series. Only when t_ahead > 0.
The quantiles of the forecasted time series. Only when t_ahead > 0.
The mean of the forecasted time-varying parameters. Only when t_ahead > 0.
The standard deviation of the forecasted time-varying parameters. Only when t_ahead > 0.
The quantiles of the forecasted time-varying parameters. Only when t_ahead > 0.
The mean of the forecasted scores. Only when t_ahead > 0.
The standard deviation of the forecasted scores. Only when t_ahead > 0.
The quantiles of the forecasted scores. Only when t_ahead > 0.
An optional GAS estimate, i.e. a list of S3 class gas returned by function gas().
A method used for parameter uncertainty. Supported methods are "given_coefs" and "simulated_coefs".
A numeric matrix of coefficient sets in rows for method = "given_coefs". Can be generated for example by gas_bootstrap().
A number of generated coefficient sets for method = "simulated_coefs".
A number of observations to forecast.
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.
A number of simulation repetitions for forecasting when t_ahead > 0.
A numeric vector of probabilities determining quantiles.
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.
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. 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. 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. tools:::Rd_expr_doi("10.1017/cbo9781139540933").
gas()
# 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
# Filter the time-varying parameters by the "simulated_coefs" method
flt_negbin <- gas_filter(est_negbin, rep_gen = 100)
flt_negbin
# Plot the time-varying parameters with confidence bands
plot(flt_negbin)
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