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Table 7 Granger-causality test on volatility at 10–3 s

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

Lag

F-value

p-value

Adj. R2

Null hypothesis of NO Granger causation

Volatility at 1/1000 s

    

1

1.14118

0.28541

0.00166

CANNOT reject at 25%

2

1.36304

0.25589

0.00294

CANNOT reject at 25%

3

1.29382

0.27456

0.00761

CANNOT reject at 25%

4

0.97760

0.41828

0.00759

CANNOT reject at 25%

5

0.79484

0.55314

0.00837

CANNOT reject at 25%

6

1.60233

0.14189

0.00871

CANNOT reject at 25%

7

1.44409

0.18252

0.00925

CANNOT reject at 25%

8

5.88033

0.00000

0.00985

REJECT at 1%