Overview

ARIMA (AutoRegressive Integrated Moving Average) models the conditional mean of a price or return series. Within the eXpeed Research Lab framework, ARIMA is used specifically to model direction, in combination with GARCH, which separately models the conditional variance. Treating these as two distinct problems, direction versus volatility, is a recurring theme across the mathematical models discussed on this site.

Mathematical Formulation

An ARIMA(p, d, q) model differences the series d times to induce stationarity, then models the differenced series as a combination of p autoregressive lags and q moving-average lag terms of the forecast error. The order (p, d, q) is typically selected via information criteria (AIC/BIC) and diagnostic checks on the residual autocorrelation structure.

Empirical Notes

In internal testing on BTCUSD, a 4-hour-ahead ARIMA direction forecast produced roughly 50% directional accuracy, with a Theil’s U statistic close to 1.0, indicating performance close to a naive (persistence) forecast. This is not treated as a failure of implementation; it is broadly consistent with near-efficient-market behavior at that horizon. Reporting this honestly, rather than presenting only favorable subsets of results, is treated as more informative than a headline accuracy figure.

Where the Edge (If Any) Comes From

Because directional accuracy near 50% is close to the theoretical floor for a symmetric binary outcome, incremental improvement is more likely to come from additional features external to the ARIMA framework itself, such as order book imbalance, funding rates, on-chain flow, and volume, than from switching to a different class of mean model. ARIMA’s role in this framework is to provide an honest, well-understood baseline for the directional component, against which more elaborate approaches can be measured.

Limitations

Directional accuracy figures must not be conflated with profitability; a model can have accuracy at or near 50% and still be assessed for a trading system, or conversely have accuracy above 50% and still be unprofitable after costs. ARIMA assumes a linear dependence structure and does not by itself capture volatility clustering, which is the domain of GARCH.

Related

Math Models · GARCH · Kalman Filter · Wavelet Transform · Methodology