# A Bitcoin Volume and Price Index: Application of Quantile Regression

Abstract: This article uses quantile regression and other methods to construct a Bitcoin volume and price indicator, and briefly describes its application scenarios. A deeper understanding of the Bitcoin market can provide more references for regulators.

People analyze Bitcoin’s trading volume and price changes in order to predict its future price. Although we believe that the price of Bitcoin at the next moment is difficult to predict, through its volume-price relationship, we can still obtain some information from it and make a rough estimate of its price at a particular moment.

1. A special case of the relationship between volume and price

When analyzing the relationship between volume and price, there is a special case-the transaction volume is large, but the price does not change much. For the general volatile market, this price balance provides 3 pieces of information that may be correct:

1. There is a difference between the main force of the long and the short, and the price is considered to be the current bottom or top;

2. The amount of capital that the main players of longs and shorts are willing to invest for this price;

3. To break this balance, long or short should invest more money than this.

Second, the principle of the index

After the emergence of this special situation, the bulls and the bears completed the first round of the game. After the “ammunition” is exhausted, the next round of evaluation, trial and game may be carried out. This generally takes time, so two rounds The possibility of a period of time between is higher. This is similar to that after an earthquake occurs in a certain place, the deformed rock will quickly release the accumulated elastic potential energy through rupture. Generally, it will take a long time before the next earthquake of the same degree occurs.

Therefore, Bitcoin may briefly fluctuate around this price for a short period of time, which is the approximate price of the next moment. However, this situation only indicates that the possibility of drastic price changes in the next moment is small, but this possibility still exists. Therefore, the volume and price index established accordingly is mainly used as an auxiliary indicator, and it must be combined with other indicators in actual operation. Use together.

It should be noted that “the volume is large, but the price does not change much” This situation may be reflected on one K-pillar, or it may be reflected on several consecutive K-pillars-long and short After a long period of game, the price fluctuates sharply, but the final price change is still small (the opening price of the first one of these consecutive K-pillars is close to the closing price of the last one), when the indicator is realized Both cases should be fully considered.

Then, how much volume and how small price changes can be included in the judgment of the indicator? In a light or hot market, this standard should be different, and should be set flexibly in consideration of recent general trading volume and price changes. We use quantile regression to achieve this.

3. Introduction to Quantile Regression -

The main purpose of classical regression is to estimate the mean value of the dependent variable based on the explanatory variable. When the regression hypothesis holds, this method is effective; but when there is a non-standard situation, it will fail. Some data cannot satisfy two key assumptions-the normality assumption and the homogeneity of variance assumption. This is exactly the problem that quantile regression can handle, because it relaxes these assumptions. In addition, quantile regression provides researchers with a new perspective (which cannot be obtained from classical regression) to study the effect of explanatory variables on the position, scale, and shape of the dependent variable distribution.

The idea of ​​quantile regression originated in 1760, when Rudjer Josip Boscovich, a traveling scholar and Croatian Christian, had many titles: physicist, astronomer , Diplomat, philosopher, poet and mathematician-came to London to teach his immature median regression method.

Keenke and Basett (1978) proposed a more general model than the median regression model—quantile regression model (QRM).    Fourth, a Bitcoin volume and price indicator-using quantile regression

1. Construct “K-pillar summary data”

Summarize the K-pillar data of several mainstream spot exchanges per minute (for this article, Binance, Gemini, Huobi and OKEx are used temporarily). Among them, the opening price, closing price, highest price and lowest price of each K-pillar are the average of the corresponding values ​​of the K-pillars of these exchanges at the same time, and the trading volume of each K-pillar is the K-pillars of these exchanges at the same time. The sum of volume. In this way, K-pillar data that can initially reflect the overall situation of the market is constructed.

Only the most recent 120 K-bar data is used here.

2. Exclude K-pillars with small trading volume

The indicator value of this volume and price indicator comes from the above “K-pillar summary data”. Since we are considering the situation that “the volume is large, but the price does not change much”, when selecting indicator values, we should exclude the K-pillars with small volume and only keep the ones with large volume.

For example, the current trading volume of each K-pillar is between 20-1000 coins, so obviously most of the K-pillars with a trading volume of 20-50 coins can be excluded, and the indicator value should not be generated by it.

3. Constructing “volume-price difference” data

In order to use fractional regression, we need to construct the “volume-price difference” data in the K-pillar summary data.

The volume data of each K-pillar is calculated as described above, and the price difference data is the absolute value of the closing price of the K-pillar minus the opening price.

If the “volume is large, but the price does not change much” occurs on several consecutive K-pillars, then the “price difference” is the opening price of the first of these consecutive K-pillars and The absolute value of the difference between the closing price of the last one.

4. Use “volume-price difference” data to perform quantile regression figure 1

For the results of quantile regression, we only choose the most recent time, which may have an impact on the subsequent market.

The figure above shows the results of a certain quantile regression. For the convenience of observation, we only draw regression lines for the 0.05th quantile, the 0.25th quantile, the 0.5th quantile, and the 0.75th quantile.

Generally speaking, the greater the trading volume, the greater the possibility of price fluctuations, and more points (data) that fit this situation will appear on the upper right of the graph. The point at the bottom right of the graph (if any) has smaller price fluctuations in the overall data, and larger trading volume-quantile regression plays such a screening role.

The data with large volume under the 0.05th quantile regression line is represented by red dots as the indicator value. Its meaning is that in the latest 120 K-bars at most, there is a point (data) where the trading volume is large enough and the price movement is small enough. It is one of the data that accounts for less than 5% of the total data.

The indicator value shown in the figure above is actually formed based on 3 consecutive K-pillars from 03:59-04:01 on October 30, 2021.10.30, Beijing time. The total trading volume of these 3 K-pillars was 523.5 coins, but only caused a price fluctuation of about \$3.4. This shows the three-minute game between the bulls and the bears. The opening price of this 3 minutes is 62392.47 US dollars and the closing price is 62389.04 US dollars. Since then, the trading volume of each K-pillar has remained at a low level, and the price of Bitcoin fluctuates slightly around \$62,300-62,500. This indicator value can be visually drawn as follows: figure 2

Let us give another example. The indicator value shown in the figure below is formed based on 4 K-pillars. The total trading volume of these 4 K-pillars is 1646.6 coins, but only caused a price fluctuation of about 14.7 US dollars. Since then, the trading volume of each K-pillar has remained at a relatively low level. In the following 12 minutes, the price fluctuated slightly around US\$61,000-61200. And the farther away from the large transaction indicated by the indicator value, the greater the possibility of a large price change. image 3

Five, the use of this volume and price index Figure 4

The more volatile market shown in the above figure occurred at 2:00 Beijing time 2021.11.4 (18:00 UTC). The Bitcoin perpetual futures contract on a certain exchange experienced price fluctuations of nearly \$2,000. At that time, 4 companies traded The total spot transaction volume is about 2682.6 coins. Although this can be understood as the impact of the market on the Fed’s announcement of the November Monetary Policy Committee resolution at that point in time-the Fed will officially start the Taper process as expected by the market while maintaining the policy interest rate unchanged. Reduce the rate of bond purchases by 15 billion US dollars, but such market conditions are not uncommon when there is no relevant news. In similar market conditions, it will be difficult to execute trading instructions at the expected price, and there are huge uncontrollable risks in placing orders, opening positions, and closing positions. Therefore, for important strategies, we expect to be executed in a relatively stable market.

However, if there is an indicator value for the volume and price indicators described in this article, it means that “the volume is large, but the price does not change much”, indicating that the main force of the long and short positions may have just gone through a round of game, and the market revolves around the corresponding The price temporarily reaches the equilibrium state of supply and demand, which provides a short-term and rough price estimation stage-the subsequent decline in trading volume, small fluctuations around the corresponding price, and a greater probability of stable market conditions. However, as time goes by, the impact of market balance will gradually weaken, so the information revealed by the indicator is time-sensitive.

Bitcoin’s market is relatively stable most of the time, and if there is an indicator value for this volume and price indicator, there is a high probability that the subsequent market will be stable. There are multiple benefits in this way. For example, the operations of placing orders, opening positions, and closing positions mentioned above can avoid the risks caused by drastic changes in prices. At the same time, in a stable market, trading instructions can also be smoothly executed by the exchange, avoiding the risk of the exchange being overloaded and unable to execute instructions under extreme market conditions. In addition, the main force can also learn the volume level of the market balance from this, and can try to increase the investment for testing, so as to break the current balance and make the price develop in a certain direction.

Six, summary

This article discusses the situation that “the volume is large, but the price does not change much”, and uses methods such as quantile regression to construct a Bitcoin volume and price indicator. Of course, there are other “intelligent” solutions that can be used to construct this indicator, but quantile regression is easy to understand and quick to calculate, which has obvious advantages.

It needs to be emphasized again that although sometimes there is an indicator value for this volume and price indicator, there is still the possibility of drastic price changes in the next moment, so it should be used as an aid in actual operation and used together with other indicators.