Assessing weak form information efficiency in cryptocurrency market using polynomial autoregression tools

The Efficient Market Hypothesis (EMH) posits that asset prices fully reflect publicly available information, implying that strategies based solely on such data cannot systematically outperform the market. Evidence from cryptocurrency markets remains inconclusive, given their high volatility, evolving regulatory environment, and heterogeneous participant base. This study investigates weak-form informational efficiency in BTC/USD and ETH/USD by testing whether past price information can forecast returns sufficiently to support profitable trading rules. We fitted a polynomial autoregressive (PAR) model to both series and employed its one-step-ahead forecasts to design simple trading strategies. The PAR class was chosen for its computational efficiency and its ability to capture nonlinear dependence in financial time series. Strategy performance was evaluated through backtests summarized by the Calmar ratio, measuring return relative to maximum drawdown. All empirical analyses were conducted in MATLAB. Our results indicate the presence of predictive potential in cryptocurrency time series.