Financial Innovation

Table 2 ARCH(p) model detecting volatility clustering on the day/time of audit trail data

From: A theory of very short-time price change: security price drivers in times of high-frequency trading

Lags	\({\left({X}_{t-1}\right)}^{2}\)	\({\left({X}_{t-2}\right)}^{2}\)	\({\left({X}_{t-3}\right)}^{2}\)	\({\left({X}_{t-4}\right)}^{2}\)	\({\left({X}_{t-5}\right)}^{2}\)
1	18.869***	17.745***	14.511***	14.569***	14.468***
2		17.489***	14.116***	13.862***	13.082***
3			91.218***	90.914***	90.631***
4				− 1.989**	− 2.180**
5					2.503**

Results for lags = 1 to 3 display volatility clustering (at 1%, indicated as ***) whereas at higher lags ARCH yields oscillating results (sign changes) and significance only at 5% (indicated as **). Since the number of observations is 208,114, critical t-values are: 2.576 (at 1%) and 1.96 (at 5%)

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