Table 3: Tests for a unit root in the data (order flow and order flow ratio).

Horizon, Level 1st difference Level 1st difference

5-minute
−20.60183−13.58463 (9)−20.65302−13.57312 (9)
−21.05210−15.15247 (7)−21.15086−15.13972 (7)
30-minute
−10.55059−12.63489 (1)−10.68869−12.56727 (1)
−10.69478−10.59656 (2)−11.26808−10.53929 (2)

The symbols and denote, respectively, order flow and order flow ratio (see the text for data source and exact definitions). The reported numbers in the columns are the Dickey-Fuller statistics for the null hypothesis that the sum of the coefficients in the autoregressive representation of the variables sum to unity. is the test statistic allowing for only constant in mean and is the test statistic allowing for both constant and trend in mean. The numbers in parenthesis after these statistics indicate the lag length used in the autoregression, determined by the Schwarz information criterion. For the test statistics, the null hypothesis is that the series in question is I(1).