How to determine what thresholds to avoid in Directional Changes

Transcription

1 How to determine what thresholds to avoid in Directional Changes Shuai Ma Edward P K Tsang 1, edward@essex.ac.uk Ran Tao 1, rtao@essex.ac.uk 1 Centre for Computational Finance and Economic Agents, University of Essex, UK 2 Everbright Securities Co. Ltd, China CCFEA Working Paper WP Draft September 2018 Abstract This is part of the research in directional change. It is based on the work in Tsang et al 2017, where given a series of transaction prices over a time period, we produce a DC profile. We use the DC profile to characterise the market over the profiled period. To produce a DC profile, we need to determine what threshold to use. In this paper, we argue that if this threshold is too big or too small, the profile will not reflect the true characteristics of the market. This paper presents a method for assessing whether a threshold is appropriate or not in a DC profile. For convenience, we refer to thresholds which are too big or too small unhealthy. Keywords: directional change, thresholds, profiling

2 1 Introduction Directional Change (DC) is a new way to summarize price changes (Guillaume et al 1997) and is an alternative way to sample data. In this approach, sample points are data-driven, which means the observer lets the data determine when to have a sample of the market. The basic idea is that the observer decides a threshold which he/she considers significant in price changes. One observer may consider 0.5% a significant change, while another observer may consider 5% is significant. Observers who use different thresholds will observe different DC events and trends. In this paper, we ask the question: can the observer use any value of threshold? Could a threshold be too big or too small? Under these circumstances, threshold will directly affect the DC event and trends which will also affect the DC profile we create. The market is seen to be in alternating uptrends and downtrends. It is considered to have changed from a downtrend to an uptrend if the price data points are sampled when the market changes direction by the predefined threshold. In this case, threshold is relevant to all indicators in Directional Change theory, different thresholds will lead to different DC profile. To show the importance of the threshold, we use EUR/USD minute by minute data in We choose the threshold of 3%, then we output a picture show in Figure 1. From Figure 1, we can point that, the value of threshold that we choose, is the benchmark to calculate the DC event. Once the threshold change, Directional Change Confirmation Point, Extreme Point, Overshoot event will change immediately. It seems that all our DC statistic are based on threshold.

3 Figure 1: Directional Changes in EUR/USD (threshold = 3%) (Tsang et al 2017) In this paper, we shall introduce a method to assess the appropriateness of threshold. The remainder of the paper is organised as follows. Section 2 describes the concept of directional change. Section 3 shows that the thresholds that one chooses for summarizing data cannot be too big or too small. Then we present a method to assess the appropriateness of a threshold in Section 4. This paper is concluded in Section 5. 2 Directional changes 2.1 Directional Change (DC) events DC is an alternative way to summarize price changes (Guillaume et al 1997). The basic idea is to partition the market into alternating Uptrends and Downtrends. An uptrend terminates when a Downturn DC Event takes place. Similarly, a downtrend terminates when an Upturn DC Event takes place. A Downturn (Upturn) DC Event is an event at which price drops (rises) by a threshold (θ) from its highest (lowest) price (PEXT) in the previous trend.

4 As a Downturn DC Event defines the beginning of a new downtrend, at the end of the Downturn DC Event, price would have dropped by the specified threshold from the highest price in the last (as well as current) trend. That highest point (or the lowest point in the case of upturn directional change) is called an Extreme Point. It must be emphasized that the extreme point was only confirmed to be the extreme point in hindsight, when DC is confirmed (i.e. when price has changed by the threshold or more from the extreme point). A downtrend continues until the next upturn DC event is observed, which defines the lowest price in the current downtrend and start the next uptrend. We refer to the price change from the end of the Downturn DC Event to the lowest price in the current trend an Overshoot Event. In other words, each trend comprises a DC Event and an Overshoot Event, as shown in Figure 1. Tsang et al (2017) aims that the Theoretical Directional Change Confirmation Point (DCC*) is the minimal or maximum directional change confirmation price for an upturn or downturn directional change event. It does not really exist in the real market. The reason we use DCC* rather than DCC, it is because in real world, EXT point and DCC point can be the same point under a fixed threshold. The price of DCC* is defined in the following way: In an uptrend: PDCC * = PEXT (1+ θ) PDCC ; In a downtrend: PDCC * = PEXT (1- θ) PDCC, Here PEXT is the price of directional change extreme point (EXT). PDCC is the price of directional change confirmation point (DCC), θ is the fixed threshold. and here represents Upturn and Downturn event. Therefore PDCC * is the DCC* price of an upturn directional change event and PDCC * is the DCC* price of a downturn directional change event. TMVEXT is the indicator to measures the price distance between the extreme points that begin and end a trend, normalized by thresholds, which is the threshold used for

5 generating the directional change summary (Tsang et al 2017). TMVEXT is an indicator to measures the maximum profit for each trend. RDC is another indicator to measure the profit, which is related to TMVEXT. RDC means the profit can be earned in a period. Tsang et al 2017 define that RDC is the return in each upturn or downturn event. We define RDC as: RDC = "#$ %&' θ " Here the threshold is a percentage that the observer considers significant. One observer may consider 0.05% a significant change, while another observer may consider 5% is significant. Observers who use different thresholds will observe different DC events and trends. 3 Appropriateness of the threshold used In this section, we use examples to show the consequences of using a threshold that is too big or too small. We are going to examine what constitutes to a reasonable threshold. Because all our DC statics are based on the value of threshold. In this case, threshold determined DCC* price, if DCC >> DCC* price, then our statistics is meaningless relevant to DC. These will be examined in the following two subsections. 3.1 A threshold which is too big If the threshold is too big, one does can only observe no, or very few directional changes in a period. There is nothing wrong with that in principle. However, if our aim is to study the profile of a period, then we want to use a threshold that produces enough number of directional changes. For example, I pick up the USD to JPY foreign exchange minute by minute data from 1 st July 2016 to 10 th August 2016.When threshold is equal to 6%, I generate a DC profile by using TR1.3. From Figure 1, we can see, there is only two DCs in this

6 profile. Which is statistically meaningless for us to analysis the market information by using Directional Change. To enable us to draw statistically meaningful conclusions in a DC profile, we would like to have 50 DCs in the profiled period. We use 50 as our guideline rather than a hard and fast rule. Figure 2: Directional Changes in USD/JPYmin ( ) (threshold = 6%) 3.2 A threshold which is too small If a threshold is too small, any small change in the opposite direction will be seen as a directional change by the observer. For instance, a trader defines his trading strategy is buy at PDCC * and sell at PDCC *. In this case, every two trends he will buy and sell once. By use EUR/JPY minute by minute data from 10/08/2016,00:00:0 to 10/08/2016,00:15:0, when threshold is equal to %, from Figure 3, we can notice that nearly every single price change would lead a DC. While the threshold is extremely small, PEXT is nearly the same as PDCC*.

7 From Figure 3 and Table 1, we can easily find out once we buy at PDCC * equal to while actual PDCC is while to next PEXT price is Under the market rule, you can t buy at a lower price. Follow by the strategy, trader would like to sell at PDCC * which is while actual price is PDCC , this means you can t sell it on that price. In this case, if the threshold is too small, trader even can t trade. Threshold(Theta) Tstart 10/08/2016,00:00:0 Tfinal 10/08/2016,00:15:0 T_EXT PEXT PDCC PDCC* 10/08/2016,00:00: /08/2016,00:01: /08/2016,00:02: /08/2016,00:05: /08/2016,00:07: /08/2016,00:09: /08/2016,00:10: /08/2016,00:12: /08/2016,00:13: /08/2016,00:14: Table 1: DC Data in USD/JPYmin (10/08/2016,00:00:0-10/08/2016,00:15:0) (threshold = )

8 Figure 3: Directional Changes in EUR/JPYmin (10/08/2016,00:00:0-10/08/2016,00:15:0 threshold = ) 4 Assessing the health of a threshold In this section, we present a method for assessing the health of a threshold. 4.1 A method for assessing the health of a threshold Tsang et al (2017) create a new indicator called T, which is the time that it takes between the extreme points that begin and end a trend, i.e. the time that it takes to complete a trend. We use Median to represent the T in a DC profile. RDC is indicator in Directional Change that is related to T. As we decrease the threshold, trends should complete in less time; this means we expect median T to decrease. However, when the threshold is too small, small price changes to the opposite direction will be classified to be DCs. Median T will not be reduced as the threshold decreases. We that happens, the statistical properties of the

9 profile will not be that useful. We consider thresholds that have little impact on median T too small. To summarize:: 1. The health of a theta depends on the data that you use, every data has its own characteristic. 2. When Median T doesn't change, that means the threshold is too small for the data. This is because all DC-based analysis are data driven. If Median T doesn't change, then the other DC indicators that are related to T, such as RDC, are not that meaningful. We shall use an example to show this result in section Example In this section, we will use an example to show the method we introduced in Section 4.1. In this section, we choose minute-by-minute market data for USD/JPY, spanning from July 2016 to August Firstly, we picked the thresholds from 0.005% to 0.01%, the interval between each number is 0.001%, and 0.02% to 0.1%, the interval between each number is 0.01%. Then I generated different DC profile by use different threshold. at last, I pick up all the Median T value from each profile into a table. Table 2 is the result of Median T from minute-by-minute market data for USD/JPY by use different threshold. Threshold(Theta) Median T % % % % % % % % % % % %

10 % % % Table 2: Median T value by use different threshold from minute-by-minute market data for USD/JPY (01/07/2016,00:00:0-10/08/2016,03:58:0) From Table 2, we can easily find that with the threshold goes down, the value of Median T decrease as well. When thresholds are smaller than 0.008%, the value of Median T does not change any more, which is 120. Recommendations We recommend researchers to check the appropriateness of a threshold before using it for research. 5 Conclusion In this paper, we have presented a method for assessing the appropriateness (which we call health) of the threshold to be used in constructing DC profile. If we use a threshold which is too big, we will get too few DCs for meaningful statistical analysis (see Section 3.1). If we use a threshold which is too small, we will get statistical properties in the profile which do not reflect the true characteristics of the data (see Section 4.2). In conclusion, at first, we recommended that to enable us to draw statistically meaningful conclusions in a DC profile, we would like to have 50 DCs in the profiled period. We use 50 as our guideline rather than a hard and fast rule. All DC-based analysis are data driven. We found that once the threshold is too small, the Median T doesn't change when threshold is reduced. Under these circumstances, whenever Median T doesn't change when threshold is reduced, then the threshold is too small.

11 References 1. Edward P K Tsang, Ran Tao, Antoaneta Serguieva and Shuai Ma, Profiling High Frequency Equity Price Movements in Directional Changes, Quantitative Finance, Vol.17, Issue 2, 2017, Aloud, M., E.P.K.Tsang & R.Olsen, Modelling the FX market traders' behaviour: an agent-based approach, Chapter 15, Alexandrova-Kabadjova B., S. Martinez-Jaramillo, A. L. Garcia-Almanza & E. Tsang (ed.), Simulation in Computational Finance and Economics: Tools and Emerging Applications, IGI Global, 2012, Aloud, M. E.P.K.Tsang, R.Olsen & A. Dupuis, A Directional-Change Events Approach for Studying Financial Time Series, Economics, No , 7 September 2012, e-journal, 4. Bisig, T., Dupuis, A., Impagliazzo, V & Olsen, R.B., The scale of market quakes, Quantitative Finance Vol.12, No.4, 2012, Glattfelder, J., Dupuis, A., and Olsen, R. (2011). Patterns in high-frequency FX data: discovery of 12 empirical scaling laws. Quantitative Finance, 11(4): URL: 6. Guillaume, D.M., Dacorogna, M.M., Davé, R.R., Müller, U.A., Olsen, R.B. & Pictet, O.V., From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets, Finance and Stochastics, Vol.1, Issue 2, 1997, (available online at: 7. Kablan, A., and Ng, W. (2011). Intraday high-frequency FX trading with adaptive neuro-fuzzy inference systems. International Journal of Financial

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