Price Implications of Bitcoin UTXO Age Changes – Galaxy Digital Global Research

Bitcoin uses an accounting system called Unspent Transaction Output (“UTXO”). All UTXOs are timestamped by the transaction and block in which they are created. All bitcoin in existence exist as UTXOs and given that the full history of all Bitcoin transactions are public on the ledger, we can see when bitcoins were last used in a transaction. For our UTXO age data, we used Unchained Capital’s publicly available data. There are two daily data sets available: one shows the absolute aggregate sum of UTXOs that reside in each age band while the other shows the aggregate sum of UTXOs as a percent of the total circulating supply. [1, 2] For our market data, we use Bitcoinity’s historical daily USD price. [3]

Our analysis is split up into two main components: 1) raw signal analysis, and 2) stationarized signal analysis.

Data Cleaning & Exploratory Analysis

Since our analysis is focused on understanding price implications of UTXO age distribution changes, we removed observations where Bitcoin’s price was $0. With this adjustment, our data set begins on July 17, 2010 and runs through May 29, 2019. Plotting the data similar to the authors at Unchained Capital:

Warmer bands represent UTXOs moving recently while cooler bands represent UTXOs that haven’t moved in a while; sudden sharp spikes in the warmer bands suggest the movement of older UTXOs and are generally associated with large price changes.

Background

Constructing and analyzing lookahead returns is a powerful tool for determining the real predictive power of a potential trading signal as it helps ensure helpful statistical properties that reduce biasness and experimental error. These returns are defined by the percentage change between a series of n desired time periods:

The error bars are standard error defined by std/sqrt(count) and provide a confidence interval for our estimation of mean correlation. These results indicate that there does not appear to be any significant statistically significant correlation in this signal. Further, if this signal did have predictive power at this time and data resolution, we would intuitively expect some sort of time decay. This lack of trend also implies a lack of a meaningful relationship. The above graph can also be visualized in a heatmap:

The size of each point represents the absolute value of the correlation (i.e. how meaningful the relationship is) and the color spectrum indicates the size of the error bounds where darker shade indicates a tighter bound and higher confidence. In the above scatter plot for the <1d signals, we see very low correlations with lookahead returns.

We can also examine the seasonality by plotting how correlations (again binned temporally) change over time at a specific lookahead. The following graphs are for the same signal above for lookahead returns of 30 days:

Intuitively, this graph does appear to make sense given the volatile nature of BTC and the different market environments over the course of the past decade. Furthermore, this shows that perhaps our prior analysis would yield more interesting results if we focused upon regions where correlation does appear to be high. Zooming in on +/- three months around 1/1/2012 and repeating the varying lookahead analysis:

As expected, our error bars are much larger given we have far fewer data points so it is still difficult to come to a meaningful and impactful conclusion. However, the results do appear interesting enough that, if the dataset was regenerated with higher resolution (per block or hourly), there could be a statistically significant relationship present.

Randomized Grouped Correlations

We randomized our grouped correlations (as opposed to binning them solely based on time intervals) and saw some interesting outcomes. One interesting result from the randomized correlation approach is the longer term signals (2–3y and 3–5y) have pretty much no correlation but other signals vary a lot and we see some nice curves. In particular, we see some strength in the 1d-1w and 1w-1m signals: the 1d-1w signal has a notable negative correlation with 30-day lookahead returns while the 1w-1m signal has some predictive power with 50 to 60-day lookahead returns.

In addition, we see a small but notable positive relationship with the 1m-3m signal and 30-day lookahead returns:

The above relationships do have some economic intuition behind them: increases in the warmer bands suggest that coins that were previously held are now on the move and indicate a higher velocity of the monetary base. According to traditional economic theory, higher velocity, ceteris paribus, leads to higher prices of a monetary base. We can also consider situations where longer-term holders moving “cold” coins to sell them should correlate with lower prices. Conversely, there should be a positive relationship between changes in older age bands and price: an increase in older bands suggest that individuals are holding more Bitcoin and therefore should correlate to higher prices.

Although the results do look very interesting, it is also important to note that this randomization with longer time intervals isn’t suitable for our production trading systems. The signal values are not randomly distributed when observed naturally and thus it would probably only be appropriate to randomize the data on a smaller time interval, such as a weekly basis. Again, we are limited with this dataset’s frequency of observations.

Background

The temporal structure of time series modeling adds an order to the observations beyond standard classification or predictive regression modeling. The observations can be subject to an underlying trend, seasonality, or other time-dependent structures that must be accounted for when building prediction models such that the summary statistics over the time series remains relatively constant by “stationarizing” the data. Our first steps are to test for stationarity and, if necessary, stationarize the data. We perform three tests: autocorrelation, partial-autocorrelation, and an Augmented Dickey-Fuller test.

Autocorrelation

Autocorrelation is the correlation of a signal with a delayed copy of itself as a function of a delay. It can help identity underlying repeat patterns, such as the presence of a periodic or relationship signal that may be obscured by noise. We plot an autocorrelation plot (correlogram) to check for randomness in the data set: if the data set is random, the autocorrelations should be near zero for all time-lag separations. If the data set is non-random, then one or more of the autocorrelations will be significantly non-zero.

The correlogram above suggests that time series of Bitcoin’s price is non-random (light blue cone is a 95% confidence interval). The positive autocorrelation indicates “persistence” or the tendency of a system to remain in the same state from one observation to the next (such as a series of positive or negative returns). Since the time series exhibits correlation, the future observations probabilistically depend on past observations.

Partial Autocorrelation

A partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values; partial autocorrelation is similar to autocorrelation, except that partial autocorrelation removes the effect of any correlations due to the terms at shorter lags. Concretely, it measures the correlation between observations of a time series that are separated by k time units yt and yt–k, after adjusting for the presence of all the other terms of shorter lag yt–1, yt–2, …, yt–k–1. The partial autocorrelation provides a “cleaner” picture of serial dependencies for individual lags. The partial autocorrelation graph of Bitcoin’s price shows multiple points (0<k<75) where the PACF shows statistically significant strong positive or negative correlations between the lagged observations of the time series.

Augmented Dicky-Fuller Test

An Augmented Dickey-Fuller (ADF) test is a type of unit root test that determines how strongly a time series is defined by an underlying trend. An ADF uses an autoregressive model and optimizes the information criterion across multiple lags. The null hypothesis of an ADF test indicates the time series is not stationary and has a time-dependent structure. The output of an ADF test is below, suggesting that Bitcoin’s price is not stationary with 90, 95, and 99% confidence.

Since the price time series is not stationary, we must stationarize the data before continuing. In particular, we must de-trend and difference the time series to remove the longer-term trend and seasonal/cyclical patterns.

Stationarizing the Data

We perform two transformations to the time series to stationarize data: de-trending (removing the underlying in a time series) and differencing (removing seasonal or cyclical patterns). We de-trend the data by calculating a z-score for each observation using a 12-month lagged lookback window and remove seasonality in the data by differencing the observations with a 12-month lag (other cyclical patterns may be present across different time windows). We perform the ADF test once again on the de-trended and lag differenced and see that the time series is now stationary, ready for signal testing. We also performed these analyses and processing to the UTXO age distribution time series as well to ensure stationarity.

Testing

Ideally, a trading signal is constructed and defined such that it will be stationary, but this usually will not be the case while examining real world data such as UTXOs. There are multiple common ways to stationarize a time series such as subtracting the rolling mean from the time series data and then dividing by the rolling standard deviation or even by simply looking at the delta of the time series (i.e. percent change from prior observation).

As it turns out, the signal we chose to examine (“<1d”) is already stationary as determined by the ADF test. The unprocessed result is reproduced again below:

Compared with the stationarized pre-processing procedure using the rolling mean and standard deviation method:

Although there are small perturbations, the resultant mean correlations are all still within the same, although significantly tighter, error bounds. The effect is far more pronounced while examining the non-stationary signal “12–18m” with/without stationarizing. Below is the non-stationary time series:

And now the stationary time series, again applied with a rolling mean and standard deviation:

Now we see a change in the mean correlations and again observe a decrease in the magnitude of the error bars and thus a tightening of our confidence interval.

Delta Method

We also compared these results by stationarizing the signals by analyzing various time shifts (“deltas”) instead. To find a shift period, you can try with one period and increase it until variance grows. The results for a basic delta shift search for the <1d signal are reproduced below; the expanded heatmap shows the effect of different delta shifts (x-axis).

It looks like across both signals, even using the lowest variance level, the delta method results look worse than the rolling mean and standard deviation method. This is not really surprising as the delta method is much simpler and requires less post-processing. This makes it more robust and more realistic to implement in trading production and defends against experimental error or some sort of inadvertent injected biasedness. More complicated post-processing procedures need to be verified with production data to be truly useful while doing research for production systems.

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