Barndorff-Nielsen & Shephard jump test

Realised variance converges to integrated variance PLUS jump variation; bipower variation converges to integrated variance alone. Their difference is therefore a jump detector, and the linear statistic z = (RV - BPV) / sqrt((theta - 2) TP / N), with theta = pi^2/4 + pi - 3, is asymptotically standard normal under "no jumps". TP is realised tripower quarticity, itself jump-robust: plain realised quarticity would let the jump being tested for inflate the standard error and destroy the power. One-sided – only a positive z is evidence of jumps.

Usage

morie_bns_jump_test(r_intraday, block_index = NULL)

Arguments

r_intraday

intraday log-returns; at least 4.

block_index

optional day/block label per return; statistics never straddle a boundary, the overnight return is not diffusive.

Value

list: statistic (z), pvalue, rv, bpv, tpq, jump_component, n_returns, days, method.

References

Barndorff-Nielsen, O. E. & Shephard, N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics 4(1), 1-30. Cross-checked against BNSjumpTest in the highfrequency package.

Examples

morie_bns_jump_test(c(0.01, -0.02, 0.015, -0.005, 0.02))$statistic
#> [1] 0.2420799