The financial market with its thousands of different products such as stocks, bonds, commodities, market indices and currencies generate a lot of data every second, which has accumulated to high data volumes throughout these years. The main challenge in this field lies in analysing the data under different perspectives and assumptions to understand historical and current scenarios, and then monitoring the market to forecast temporal trends and to identify recurring behaviours. Visual analytics applications can help analysts, investors and researchers in obtaining insights and understanding into previous stock market developments, as well as supporting the decision-making progress by monitoring the stock market in real-time to take necessary actions for a competitive advantage.

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This interesting domain with its huge amount of complex data can also be seen as a motivation and challenge to try new methods. In order to analyse and understand the dynamic financial market, where the asset prices change every second, mathematical or statistical models are not sufficient enough to make adequate decisions. Hence, there is a need to couple these models with modern information systems that are capable of interpreting the results in a visual way. Visual analytics aims to combine automatic data analysis methods with visualisations and interaction to solve analytical problems like these with large amounts of complex data.

The traditional stock chart looks like a 2-dimensional graph, where the x-axis represents time and the y-axis the stock price. This visualisation helps in analysing the price fluctuation of a stock. However, if we are interested in analysing a large number of stocks at the same time or a huge time series which expands across several years, then this traditional methodology would fail to deliver.

There are several approaches that visualise the stock market as a whole. Few of them propose a visualisation system of current state of the stock market and others consider visualisation of stock market dynamics where temporal data is important. In this paper, we will compare and contrast the following visualisation methods – Tree maps, Ordered Tree maps, Pixel Based Visualisation, Spectral Visualisation(Growth Matrix), Spiral method, Galaxy and Tai-Chi Visualisation.

1      Exposition

2      Galaxy Visualization

The visual analytics method we will be discussing in this section is known as the galaxy visualization technique it is based upon mathematical geometry specifically Fermat’s spiral [1]. In geometry, sophisticated models are based upon some mathematical equations. Figure1 shows Fermat’s spiral [2].

Figure 1: Shows an example of what Fermat’s spiral looks like.

Fermat’s spiral (modified) is generated using the following equation [1].
r=c×n, θ=n×α, n=0,1,…n
max

Where
r 
denotes the distance between the origin of the polar coordinate system and the nth node,
c
is the spacing constant which describes the placement of nodes,
n
is the ordered number of nodes counting from the center out.
θ
is the angle between a reference direction and the position vector of the nth node in the polar co-ordinates, the origin of the polar coordinate system is at the center of the spiral pattern and
α
is the angular constant of the spiral pattern [1].

If we vary the value of
α
, we get a varying set of different spiral patterns see figure2 [1].

Figure2: shows spiral patters which have been generated by varying the
α
values. This is an intriguing property of Fermat’s spirals, which makes it an ideal candidate for creating visual signatures. By visual signatures we mean a logo or a mark that is used to distinguish or identify different dynamics of the market [1].

The reason for using such a visualization technique is that since the market index of the stock market is composed of a set of stocks with different weighted contributions, if a stock with more weight distribution is among the leading stocks or belongs to the leading sector, and that leading sector is increasing in the near term then it is very likely that the index will rise in the near term [1], thus revealing an indicator on the markets movement. In general, the markets performance relies on a few leading stocks in their relevant sectors [1]. This makes using visual signatures and ideal approach in visualizing leading market sectors. Since floral patterns naturally give an impression of positive-ness, they can be used to represent a positive market see Figure3 [1], and we can use the simple spiral patterns to represent a negative market see Figure4 [1].

Figure3 (above): This shows an example of Fermat’s spirals with floral patterns [1].

Figure 4 (above): This shows an example of Fermat’s simple spirals[1]

Figure 5 shows an example of a galaxy visualization. In which the center shows a positive performance with the three leading sectors [1]. The way in which the data points are arranged represent the capitalization sizes [1]. Different dot sizes can be used to represent small, medium and large capitalization sizes, the outer rings represent the market data in non-leading sectors. The data points on the outer ring have been arranged according to their performance [1]. This kind of visualization technique can be modeled on the Milky Way galaxy, hence the visualization name galaxy visualization. This implementation allows the user to set a viewing angle, and also gives them the ability to check the performance detail of each stock which allows the visualization to be interactive see Figure 6 [1].

Figure 5: Galaxy visualization 40˚ viewing angle

Figure 6: The galaxy visualization allowing the user to interact with the data points [1].

Figure 7: This shows an example of the galaxy visualization which shows a negative market performance.

This type of visualization is designed to reveal visual patterns through leading sectors, as it does not loose information on the stock data of non-leading sectors [1].

The galaxy visualization technique involves three steps which are listed below.

Calculate the overall sector performance with the following formula

Sector performance = sum (Pn x Vn/Vsector_total), where

n: is the stock code.

Pn: is the percentage of one-day movement for stock n.

Vn: is the trading volume for stock n.

Vsector_total: is the total trading volume of the sector. [1]

Determine the number of leading sectors according to the value range which has been specified by the user. The performance of the market indicates what type of pattern should be drawn. If it is positive then, the floral pattern should be used, if the market index is negative then we choose the
α
on the negative value definition table [1].

The final step is to draw the outer part, in order to set the outer rings on the same plane where the inner part lies, we apply a parametric function with a fixed value of
α
.

Then that’s it then we have created a galaxy visualization based upon Fermat’s spiral. We arrange the remaining data from non-leading sectors in order of percentage change of stock price. This is then placed onto the map from the outmost location back to the inner part. The outmost location number being the sum of the total number of inner points added with the total number of outer points. This value is large enough to avoid overlapping of the two spiral patterns.

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2.1           Tai-Chi Visualization

There are many different factors which have the ability to affect stock prices. The price of a healthy stock sometimes fluctuates with the market trading movement despite of its solid fundamental financial record [1]. The Hong Kong Hang Seng stock exchange allows investors to short sell [1]. Short selling provides investors a way of betting on a negative performance of the market, whereas regular stock purchasing bets on the positive side [1]. This is where the Tai-Chi visualization technique was developed in order to visualize the forces of Ying and Yang (negative & positive) [1].

Figure8: An example of Tai-Chi visualization technique.

The data points are placed along the middle curve line based on their performance. The left hand side is negative and the right hand side is positive. The middle curve line contains data that has no change in price [1]. The chart is divided into upper and lower parts from the center circle. The data points on the lower section are more recent [1]. Within each section the data points are connected with green or red lines. The data points on the positive side are connected if there are more data points on the positive side when compared to the negative side, this line has been named as the Tai-Chi line, it indicated the overall performance of a stock [1].

There are four possibilities in the colour of the Tai-Chi lines, green-green, green-red, red-green, red-red, this is how the grouping process starts by firstly classifying stock data with the colour of the Tai-Chi lines [1].

Euclidean distance is used to compare the similarities between two stocks, the following equation is used to calculate the Euclidean distance:
Ep,q= ∑i=1n(qi–pi)2
   [1]

Where n denotes the number of trading days

qi is the price of stock q on day i, and pi is the price of stock p on day i [1].

If E has been specified, within the value of E the movements of two stocks are considered to be similar [1]. Figure9 shows this result from the grouping implementation. The 3 lines of stocks have been denoted and the stocks on the same line belong to the same group.

 Figure9: Stocks have been categorized using the Tai-Chi line. [1]

The way in which the Tai-Chi visualization is constructed is by drawing one big circle and two small inner circles. The upper circle is used for drawing data point form the first half of the dates specified, and the lower inner circle is for the second half of the date period [1]. Different radius have been used in Figure10 to place the data points, the process starts by calculating daily percentage of price movement [1]. If the price change is positive then the rate change is D+ and if its negative D- [1].  The formula used to calculate the radius of the data point on day i is as follows:
ri=r+pi modD+4c if pi>0

else:

            
ri=r+pi modD–4c id pi<0 
   [1]

where r is the radius of the middle line, pi is the price change on day i, and c is a constant value for setting the interval distance [1].

[1] Lei, Su Te (2011). “Visual signatures for financial time series” in VINCI 2011 : the 4th Visual Information Communication, International Symposium : August 4-5, Hong Kong University of Science and Technology, Hong Kong, China (1-4503-0786-8, 978-1-4503-0786-4), (p. 1).New York, New York, USA: ACM.

[2] https://en.wikipedia.org/wiki/Fermat%27s_spiral