High Frequency Econometrics Package in R

Saef, Danial 11/05/2022

This library serves as a companion to the publication “Understanding Jumps in High Frequency Digital Asset Markets”. However it can also be used independently for clustering high dimensional datasets and fitting an implied stochastic volatility model.

1 Methodology

This library contains implementations of a few recent publications in the field of High Frequency Econometrics:

• Lee & Mykland Jump Test (Lee and Mykland 2012)
• Ait-Sahalia & Jacod Jump Test & Test for Jump Activity + variation estimation (Aït-Sahalia and Jacod 2012)
• Ait-Sahalia, Jacod & Li Jump Test (Ait-Sahalia, Jacod, and Li 2012)
• Pre-averaging approach ( Jacod et al. (2009), Jacod, Podolskij, and Vetter (2010) )

The methods can be used in a stand-alone fashion or when obtained from the Blockchain Research Center with additional functionalities.

2 Usage

2.1 Installing

The usage is pretty simple. First, install the package with devtools. Note that this library is still experimental, s.t. no proper unit testing or object classes have been implemented yet. In case of bugs please report them and I will work on fixing them.

library(devtools)
install_github("YalDan/hf.econometrics")
library(hf.econometrics)

2.2 Running the model

Now we can just load a suitable dataset and run the test statistics we desire. A sample dataset is provided to illustrate the necessary file structure.

# load the data
# currently, for this to work the data needs to be stored in "./data/raw/csv_dump/"
DT_list <- make_data("./data/raw/csv_dump/DT_sample.csv")
DT_split_list <-  list("impute" = split_by_id(DT_list),
                                "no_impute" =  split_by_id(DT_list))

Once the data is loaded we can calculate the jump test statistic:

## get LM result ##
DT_LM_result_id <- jump_test(DT_split_list$no_impute, which_test = "LM_JumpTest")

## get AJL result ##
DT_AJL_result_id <- jump_test(DT_split_list$impute, which_test = "AJL_JumpTest")

Finally, some processing can be made to denoise the jump statistic.

## Preprocess LM result ##
DT_jumps_crypto <- preprocess_jump_data(DT_LM_result_id, sign_level = 0.01)

3 References

Ait-Sahalia, Yacine, Jean Jacod, and Jia Li. 2012. “Testing for Jumps in Noisy High Frequency Data.” Journal of Econometrics 168 (2): 207–22. https://econpapers.repec.org/article/eeeeconom/v_3a168_3ay_3a2012_3ai_3a2_3ap_3a207-222.htm.

Aït-Sahalia, Yacine, and Jean Jacod. 2012. “Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data.” Journal of Economic Literature 50 (4): 1007–50. https://www.jstor.org/stable/23644910.

Jacod, Jean, Yingying Li, Per A. Mykland, Mark Podolskij, and Mathias Vetter. 2009. “Microstructure Noise in the Continuous Case: The Pre-Averaging Approach.” Stochastic Processes and Their Applications 119 (7): 2249–76. https://doi.org/10.1016/j.spa.2008.11.004.

Jacod, Jean, Mark Podolskij, and Mathias Vetter. 2010. “Limit Theorems for Moving Averages of Discretized Processes Plus Noise.” The Annals of Statistics 38 (3): 1478–1545. https://doi.org/10.1214/09-AOS756.

Lee, Suzanne S., and Per A. Mykland. 2012. “Jumps in Equilibrium Prices and Market Microstructure Noise.” {SSRN} {Scholarly} {Paper} 1693644. Rochester, NY: Social Science Research Network. https://papers.ssrn.com/abstract=1693644.