Analyzing Candlesticks Quantitatively

Coding Candlesticks (II)

G TECHNIQUES

Analyzing Candlesticks Quantitatively Coding Candlesticks (II)

by Viktor Likhovidov Jan

My idea of assigning a numeric value to a single candlestick is based on the principle that the relationship between opening and closing prices is the most important for interpretation of the candle. So in construction of the quantitative characteristic of a candle, I took these prices into account as the main factor. My method uses a candle's binary code (see sidebar, "How to code a candlestick"), so characteristics of opening and closing prices should be reflected in the highest bites? BYTES? DEFINE of this code. This gives them the greatest weight. The parameters of the candle's shadows are placed in lower bites of the code, giving them lower weight. Thus, the numeric representation of the code is the weight of the candle. This automatically assigns the highest influence on the candle's weight to the body. A candle's binary code also has the sense of a candle's weight because binary representation is additive: a candle's weight is equal to the sum of its body's weight, plus its upper shadow's and lower shadow's weights.

A candle's color is the main factor in evaluation of its sense from the point of possible market movement. A white candle (close > open) shows bullish market movement, so with all other circumstances being equal, it more clearly expresses bullish market sentiment than does a black candle (close < open). Considering candles individually, without taking into account the context created by nearby candles, any white candle is more bullish than any black one, independent of their sizes and shadow configurations. My method is designed for description of isolated candles, so I place "1" in the highest bite for a white candle and "0" for a black candle. Now, any white candle has a higher value than any black candle, since a white candle's code cannot be less than 1000000 = 26 = 64, while a black candle's code cannot be greater than 0111111 = 25 + 24 + 23 + 22 + 21 + 20 = 32 + 16 + 8 + 4 + 2 + 1 = 63. Coding and weighing groups of candles is another problem and it demands another approach, although aggregating individual candles' codes into an indicator is a start.
THE STUDY                                                                                                                        Back to top
The next most important factor is the size of a candle's body: the greater the difference between opening and closing prices, the clearer the market's sentiment. What is "large" and "small" for candle-body size depends on the market's volatility statistics and on the intent of your coding procedure. You can introduce as many categories as you want: extremely small, very small, small, typical, middle, and as many categories, if not more, to the upper side. Such a scheme could be constructed if necessary, but the simplest approach is best. Therefore, I introduced only three categories: small, middle, and large. A fourth category, null, seems important to me, since a doji-type candle - which has zero body size and is white if its upper shadow is longer than its lower shadow - demonstrates the market's indecision. It is also mathematically convenient to represent the four body sizes with two portions. If anybody wants to consider as doji not only null-body candles (open = close) but also candles with very small sizes (such as 5-10 pips DEFINE), then it may be done by slight modification of the classification rules. In particular, the body of a long white candle gets 111 (value 112) because it is the most bullish of all white candles, and 000 (value zero) is assigned to the body of a long black candle, the most bearish of all black candles. The greater the body's size in a white candle, the higher the code it is assigned, and vice versa; for black candles, the lowest codes are assigned to the largest bodies. The code of a doji corresponds to the range in the middle of the weights; the doji's body has code 100 (value 64) or 001 (value 16) assigned, depending on whether white or black is assigned to it.
THE SIZE OF THE BODY                                                                                                    Back to top
THE SHADOW                                                                                                                    Back to top
A candle with a long upper shadow is more bullish than a similar candle with a small upper shadow. A candle with a long lower shadow is more bearish than a candle with a small lower shadow. Consider two candles (Figure 1). Both have a medium-sized body and small upper shadows, but candle A's lower shadow is large, while candle B has none. The code of candle A and its digital representation - weight - is 1100100 = 64+32+4 = 100, and for candle B is 1100111 = 64+32+4+2+1 = 103. If the same candles are black, the undoubtedly bearish sense of the black candle A becomes even more expressed in comparison with the black B. For the black variant of candle A, we have 0010100 = 16+4 = 20 and for the black variant of B, 0010111 = 16+4+2+1 = 23. Further, there is no need for juggling in this coding. All that is required is to apply mathematical notation to what is known and used by every chartist. Some shortcomings of my approach are evident. For example, the upper and lower shadows obtain very different weights: the maximum contribution of an upper shadow into the candle's weight is 12, but for the lower shadow it is only 3. I have used another variant of the candle index, one that I call CandleWeight (see Traders' Tips elsewhere in this issue), with a positive value for the body's weight for a white candle and a negative body's weight for a black candle. Upper shadows had positive weights and lower shadows had negative weights, and absolute values of weights for shadows were equal for equal length of shadows. However, there was a small difference in the behavior of the indicators; all support and resistance levels, trends, and crossing points of moving averages almost coincided and gave the same trade signals. Because of that, I returned to the simpler scheme, which I refer to as CandleCode. For those who want to assign different coefficients - weights - to the body and shadows, altering the formula from November 1999, you get this expression: Weight = B x CandleCode-b + U x CandleCode-u + L x CandleCode-l where B, U, and L are optimizable coefficients.
Use some statistical analysis to define small, medium, and large candle bodies. I usually use histograms of the sizes of bodies and candles for this purpose. For example, four-week intervals are used for hourly candle charts. (These histograms show that the distributions of sizes are not log-normal, but exponential.) My thresholds were initially based on the equal probabilities of clusters of body sizes. For example, 33% of candles had small bodies and 33% had middle bodies, while the rest were large. These empirical thresholds were fixed and then used for code construction; later, new four-week histograms were formed. I have used this strategy since 1998 for spot currency markets (hourly charts of yen, British pound, Deutschemark, and Swiss franc), and the sizes generated have demonstrated a high degree of stability over time. Corresponding thresholds for various currencies differed by about 10-20% on different time intervals, but such deviations hardly changed the behavior of averaged indicators. This represents some evidence of statistical robustness for averaged CandleCode indicators, proving to be a useful property in financial decisions, and at the same time suggesting the universality of the scheme.
SMALL, MEDIUM, LARGE?                                                                                                  Back to top
BOLLINGER BANDS                                                                                                           Back to top
The use of the Bollinger Bands for threshold selection seems to be a good and practical solution. The computation of bands per se does not require any specific properties of the normal distribution. For exponential distributions, the parameters I use do not give equally probable clusters of body sizes, but the high statistical stability of CandleCode indicators does give satisfactory results, so I do not regard this as disabling. In addition, if a trader wants better-fitting indicators for a certain market, he may run his own estimation of threshold selection levels for his own candlestick price charts.
The quantitative measurement of market sentiment and the attempt to express its psychology in a series of digits is an immense challenge. The problem does not have a unique and universal solution, so different approaches should be tried and objectively estimated. Quantifying candlesticks is only one attempt to do so. Viktor Likhovidov, a financial analyst and consultant based in Vladivostok, Russia, performs research in the areas of pattern recognition, neural networks, and mathematical methods in currency markets analysis. He may be reached at lita@math.dvgu.ru.
SUMMARY                                                                                                                          Back to top
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Published with special permission from Victor Jan Likhovidov