# Classification of Normal and Abnormal Regimes in Financial Markets
## 5 Results and Discussions
### Market Regimes in the Indicator Space  
Figure 6 shows the positions of the regimes from all data sets on the T-TMV indicator space. They are grouped by their periods as shown in Table 1. To recap, the \(x\)-axis measures the normalised average value of the indicator T, and the \(y\)-axis measures the normalised average value of the indicator TMV. Each point in the indicator space shows the position of one market regime of one data set. The red points showed the positions of Regime 1, and the blue points showed the positions of Regime 2. For example, one of the red points in Figure 6a would show the average normalised TMV and T values of all trends in Regime 1 in GBP-USD summarised under the threshold 0.1%.  
In Figure 6, we shall study the market regimes found in the four market events separately: (a) market regimes from the data of Brexit; (b) market regimes from the data of Chinese stock market turbulence of 2015-2016; (c) market regimes from the (three) data sets of the financial crisis of 2007-2008; (d) market regimes from the (two) data sets of the oil crash of 2014-2016.  
As we examined three foreign exchange pairs (EUR-USD, EUR-GBP and GBP-USD) and each data set is summarised with ten thresholds, there are 30 data points for each regime in Figure 6a. As we used two Chinese indices (SSE and SZSE) and ten thresholds per data set, there are 20 data points for each regime in Figure 6b. There are 30 and 20 data points per regime for Figure 6c,d, respectively.  
Figure 5: An example of describing market regimes in an indicator space.  
Figure 6 clearly shows that, within each group, Regime 1 and Regime 2 are clearly separable in the T-TMV indicator space. For example, Figure 6a shows that, compared to Regime 1, Regime 2 takes a much shorter time than normal to complete (readers are reminded that the \(x\)-axis represents normalised T, not absolute T). Figure 6a shows that Regime 2 has a much higher (normalised) TMV to (normalised) T ratio. The same is observed in Figure 6b-d.  
Distribution of the regimes in the normalised T-TMV space is also significant: the market regimes that occurred from the data taken from the events of Brexit and that of the Chinese stock market turbulence were linearly distributed. But the market regimes from the data of the financial crisis and the oil crash formed clusters. The obvious difference between these data sets is that high frequency (minute-to-minute) data was used for the former, and low frequency (daily) data was used for the latter. Having said that, the exact reason for these differences in distributions demands further investigation; this will be left to future research.  
In general, Regime 2 suggests a market with higher TMV to (normalised) T ratio. This means, given the same T, Regime 2 tends to have a larger TMV than Regime 1. Given the same TMV, Regime 2 tends to have a smaller T than Regime 1. As pointed out by [PERSON] et al. (2016), both larger TMV and smaller T are indicators of higher volatility. Therefore, one could roughly understand Regime 2 as a regime that represents periods of higher volatility.  
Figure 7 shows the market regimes of all the datasets together in one indicator space. We can see from Figure 7 that the positions of Regime 1 and Regime 2 are largely separable, with some exceptions around (0.11, 0.16). Figure 7 suggests that, across asset types, time and thresholds, Regimes 1 and 2 occupy different areas in the normalised T-TMV indicator space.  
Figure 6: (**a**–**d**) Market regimes in the indicator space, which are organized by four market events: (**a**) market regimes from the data of Brexit, (**b**) market regimes from the data of Chinese stock market turbulence, (**c**) market regimes from the data of financial crisis, (**d**) market regimes from the data of oil crash.