Benchmark

Alexios Galanos

2024-04-23

The package includes two published benchmarks, one for the GARCH(1,1) and one for the APARCH(1,1) model. Below we present the results of the former based on the benchmark of Fiorentini, Calzolari, and Panattoni (1996). Note that this is not a saved benchmark, but rather estimated every time it is called. As can be seen from the values of the log relative error, this achieves a very high rate of accuracy, addressing the questions raised by Hill and McCullough (2019).

Code 
library(tsgarch)
#> Loading required package: tsmethods
as_flextable(benchmark_fcp())
GARCH(1,1) Benchmark (FCP)

Estimate

Std Error (H)

Std Error (OPG)

Std Error (QML)

tsgarch

FCP

tsgarch

FCP

tsgarch

FCP

tsgarch

FCP

μ\mu

-0.0062

-0.0062

0.0085

0.0085

0.0084

0.0084

0.0092

0.0092

6.1518

6.9758

6.4222

6.3652

ω\omega

0.0108

0.0108

0.0029

0.0029

0.0013

0.0013

0.0065

0.0065

5.0391

6.1340

5.4333

6.2619

α1\alpha_1

0.1531

0.1531

0.0265

0.0265

0.0140

0.0140

0.0535

0.0535

6.3803

5.9348

5.1801

7.4731

β1\beta_1

0.8060

0.8060

0.0336

0.0336

0.0166

0.0166

0.0725

0.0725

6.3809

6.5216

6.7323

6.1553

Notes to table: values in italic are the log relative errors (LRE). The FCP benchmark is from the paper by Fiorentini, G., G. Calzolari and L. Panattoni, Analytic Derivatives and the Computation of GARCH Estimates, Journal of Applied Econometrics 11 (1996), 399--417.

Fiorentini, Gabriele, Giorgio Calzolari, and Lorenzo Panattoni. 1996. “Analytic Derivatives and the Computation of GARCH Estimates.” Journal of Applied Econometrics 11 (4): 399–417.
Hill, Chelsey, and BD McCullough. 2019. “On the Accuracy of Garch Estimation in r Packages.” Econometric Research in Finance 4 (2): 133–56.