Exchange Rate Determination and Forecasting: Can the Microstructure Approach Rescue Us from the Exchange Rate Disparity?

Table 3

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

Horizon, ℎ	Level 𝜏𝜇	1st difference 𝜏𝜇	Level 𝜏𝜏	1st difference 𝜏𝜏
5-minute
𝑥𝑡	−20.60183	−13.58463 (9)	−20.65302	−13.57312 (9)
𝑥Ratio𝑡	−21.05210	−15.15247 (7)	−21.15086	−15.13972 (7)
30-minute
𝑥𝑡	−10.55059	−12.63489 (1)	−10.68869	−12.56727 (1)
𝑥Ratio𝑡	−10.69478	−10.59656 (2)	−11.26808	−10.53929 (2)

The symbols 𝑥_𝑡 and 𝑥Ratio_𝑡 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. 𝜏_𝜇 is the test statistic allowing for only constant in mean and 𝜏_𝜏 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).