Estimation

We use the Deutsche Mark British Pound dataset for this demonstration throughout the document.

library(tsgarch)
suppressMessages(library(data.table))
suppressMessages(library(xts))
data(dmbp)
dmbp <- xts(dmbp, as.Date(1:nrow(dmbp), origin = '1970-01-01'))
spec <- garch_modelspec(dmbp[1:1500,1], model = 'fgarch', constant = TRUE, 
                        init = 'unconditional', distribution = 'jsu')
mod <- estimate(spec)
as_flextable(summary(mod))

FGARCH Model Summary
	Estimate	Std. Error	t value	Pr(>\|t\|)
NA	-0.0154	0.0099	-1.5574	0.1194
NA	0.0050	0.0032	1.5543	0.1201
NA	0.1621	0.0373	4.3419	0.0000	***
NA	-0.3522	0.1108	-3.1776	0.0015	**
NA	0.7829	0.1594	4.9107	0.0000	***
NA	0.8727	0.0278	31.4083	0.0000	***
NA	1.4659	0.3593	4.0799	0.0000	***
NA	-0.2595	0.0835	-3.1076	0.0019	**
NA	1.4762	0.1046	14.1174	0.0000	***
NA	0.9903	0.0104	95.0454	0.0000	***
Signif. codes: 0 '*' 0.001 '' 0.01 '*' 0.05 '.' 0.1 ' ' 1
variance targeting: FALSE
initialization value: 0.2405
LogLik: -829.1715
AIC: 1678 \| BIC: 1731
Model Equation
NA
NA

Persistence (P) and Unconditional Variance Equations
NA
NA

Notice that the as_flextable method provides for a publication ready option for printing out the model summary.

We next take a look at a summary plot of the estimated model:

oldpar <- par(mfrow = c(1,1))
par(mar = c(2,2,2,2))
plot(mod)

par(oldpar)

Notice the news impact curve which is both shifted and rotated, a particularly appealing feature of the Family GARCH model.

Simulation and Prediction

The code below shows how to predict from an estimated model and how to simulate using a specification with fixed parameters.

delta <- coef(mod)["delta"]
new_spec <- spec
new_spec$parmatrix <- copy(mod$parmatrix)
sim <- simulate(new_spec, nsim = 500, h = 10000, seed = 100, burn = 1000)
mean_sim <- mean(rowMeans(sim$sigma^delta))^(2/delta)
pred <- predict(mod, h = 1000, nsim = 0)
oldpar <- par(mfrow = c(1,1))
par(mar = c(2,2,2,2))
plot(as.numeric(pred$sigma^2), type = "l", xlab = "horizon", 
     ylab = expression(sigma^2), ylim = c(0.25, 0.41), main = "Family GARCH - JSU Prediction")
abline(h = as.numeric(unconditional(mod)), col = 2)
abline(h = mean_sim, col = 3)
legend("bottomright", c("h-step prediction","unconditional variance","simulated unconditional variance"), col = c(1,2,3), lty = 1, bty = "n")

par(oldpar)

Conclusion

There are other methods available such as one for profiling the parameter distribution (tsprofile), a backtest method (tsbacktest) as well as other methods for extracting information from the estimated object such as vcov, pit (probability integral transform), confint etc.

The package does not include any tests, as most of these have been moved to the tstests package and there are ample packages which include testing methods.

Package Demo

Estimation

Simulation and Prediction

Conclusion