What forecasting methods try to do
A forecasting method takes the past values of a series and produces an estimate of future values, ideally with a measure of how uncertain the estimate is. The methods below come from general statistics and are used on everything from sales figures to weather. Applied to cryptocurrency they work with the same mathematics but face an unusually noisy target. This review describes them in general terms. It makes no forecast and is not financial advice.
The naive baseline
The simplest method is to assume the next value equals the latest one. This is called a naive forecast, and it matters because every other method should be judged against it. For series that behave close to a random walk, the naive forecast is surprisingly hard to beat. A related simple method uses a moving average, replacing the latest value with the average of the last several values to smooth out noise. Averages lag behind turning points by design, which is the same trade-off discussed in the article on moving averages.
Exponential smoothing
Exponential smoothing is a refinement of the moving average. It averages past values but gives recent ones more weight, with the weight fading gradually into the past. Extended versions add terms for a trend or a repeating seasonal pattern. The assumption is that the recent past is more informative than the distant past, and that any trend continues in a smooth way. Crypto prices rarely have regular seasons, and trends can reverse abruptly, so the trend extensions often add more error than they remove.
ARIMA and its relatives
ARIMA stands for autoregressive integrated moving average. In plain terms, it predicts the next change in a series from a weighted combination of recent changes and recent forecast errors. The “integrated” part means the model works on differences between values rather than raw levels, because raw prices wander and do not stay around a fixed average.
ARIMA works well when a series has stable, repeated structure. Price changes in liquid markets usually have little of that. When researchers fit ARIMA models to returns, the fitted weights are often close to zero, which amounts to saying that the best forecast is close to the naive one.
Volatility models
Direction is hard to forecast, but the size of price swings shows more persistence: turbulent days tend to be followed by more turbulent days. Models in the ARCH and GARCH family capture this by letting the expected size of the next move depend on recent moves. The result is a range of plausible outcomes, not a single price.
These are used in risk measurement, and they connect to the ideas in the article on realized volatility. They still have limits. Crypto markets have had sudden jumps that are larger than the models treat as typical, and the estimates can lag behind a regime change.
Regression with outside variables
Another approach regresses price changes on other variables, such as trading volume, interest rate changes, stock market moves or on-chain activity. The appeal is that it is easy to interpret. The difficulty is that relationships between crypto and other assets shift over time, as the discussion of stock correlation shows. A relationship estimated on one period can disappear in the next, and with many candidate variables, some will look significant purely by chance.
How forecast error is measured
Forecasts are only meaningful alongside their errors. Common measures include:
- Mean absolute error (MAE): the average size of the miss, ignoring direction.
- Root mean squared error (RMSE): similar, but large misses count for more.
- Mean absolute percentage error (MAPE): the average miss as a share of the actual value.
A small illustration, using made-up numbers. Suppose actual values over three days are 102, 101 and 105, and the day before the first of them was 100. A naive forecast uses the previous value each time, giving forecasts of 100, 102 and 101. The misses are 2, 1 and 4, so the MAE is (2 + 1 + 4) / 3, which is about 2.33. Now suppose a model forecast 101, 103 and 103. Its misses are 1, 2 and 2, so the MAE is 5 / 3, about 1.67. On this tiny sample the model looks better, but three observations prove very little, and a model that wins on a handful of days may lose on the next handful.
Testing without fooling yourself
The right way to test a forecasting method is to fit it on an earlier stretch of data and then score it on a later stretch that it never saw. Better still is a rolling version, where the model is repeatedly refitted and tested as time moves forward. Mixing the order, for example by randomly shuffling days into training and test sets, lets future information leak in and flatters the results. The article on model training covers the procedure in more detail.
Reported errors should also be compared against the naive baseline and should include realistic costs of acting on the forecast. A method that is slightly more accurate than naive in a statistical sense may still be unusable once fees are counted.
Why error rates stay high for crypto
Several features of cryptocurrency make errors large and unstable. Prices are volatile. A sudden announcement or a hack can create jumps that no smooth model anticipates. The markets run around the clock, and the mix of participants changes. Errors measured in calm periods tend to understate the errors in stressful ones.
For readers, the practical lesson is to treat a forecast as one possible central estimate surrounded by a wide band of uncertainty, and to distrust any method that does not show that band. Cryptocurrency prices are volatile, past performance does not predict future results, and people can lose all they invest.