# Classification of Normal and Abnormal Regimes in Financial Markets
## 3 Methodology
### Summarising Financial Data in DC  
Simply put, traders buy and sell for profit in financial markets. And then the transaction prices are recorded, which forms the basis of financial data. Transactions also take place in irregular time, there may be many transactions in one second, but none in the next. Thus, raw transaction data is therefore difficult to clearly be able to reason from, because of its irregularity. Most researchers would summarise the data using time-series, where one data point is recorded at the end of each fixed time interval. For example, the final price on each trading day can be recorded as the \"daily closing price\". Time series analysis is commonly used to summarise financial data in this way.  
This paper adopts an alternative way to summarise financial data. It is based on the concept of DC [2]. When summarising data under DC, it is the observer who determines what constitutes to a significant change in the data. This significant percentage of change is called the \"threshold\". Whenever the price changes in the opposite direction of the current trend and reaches the threshold, the extreme price is retrospectively recorded as a data point. Thus, financial data is recorded as a series of trends, defined by the extreme points (i.e., the peak and trough). Details of DC can be found in [7]. By recording data in this way, the use of DC makes sure that the significant changes in the market are captured, whenever they occurred.  
Figure 1 shows an example of summarising financial data under DC. When prices change from A to B, if the change is greater than or equal to the threshold, then AB is called a Directional Change Event (DC Event for short). Point \"A\" is retrospectively recognised as an extreme point which ended the previous downtrend and started the current uptrend. From Point \"C\", the price drops by the specified threshold. Therefore, C ended the current uptrend and started the next downtrend. The price movement from Point \"B\" to Point \"C\" is called an \"Overshoot Event\" (OS Event for short). In other words, a trend (e.g., from \"A\" to \"C\" in Figure 1) comprised a DC Event and an OS Event. The market is thus partitioned into a series of alternating uptends and downtrends, which could be read as the bull and bear markets that traders are familiar with.  
Therefore, to help with the analysis of DC series, [PERSON] et al. [4] has proposed a number of indicators. Below, we introduce indicators used in this paper. The percentage price change in a trend measured by an indicator is called \"Total Price Movement\" (**TMV** for short). To allow us to compare DC series generated by different thresholds, we normalised the price changes by the threshold \(\theta\):\[TMV=\frac{|Ps-Pe|/Ps}{\theta} \tag{1}\]  
where \(Ps\) is the price at the start of the trend, and \(Pe\) is the price at the end of the trend.  
The time that it takes to complete a trend is measured by another indicator which is called \"Time\" (**T** for short). \"Return\" (**R** for short) takes the usual meaning, which measures price change over time:  
\[R=\frac{|TMV|\times\theta}{T} \tag{2}\]  
For example, in Figure 1, the price difference between point \"A\" to Point \"C\" is the \(TMV\) in that trend, and the time that it takes to complete this trend is \(T\).  
Overall, in a DC-based summary, the financial data is sampled first by two types of events: a DC event, and an OS event, according to the value of the threshold, and secondly, a number of indicators are used to extract the trading information from these two events.