Buy-and-hold beat all four coins, and the paper still recommends it

No prop desk should touch this model yet: its live test trailed buy-and-hold on all four traded assets. Andriushchenko and co-authors state the result plainly in the abstract: "the buy-and-hold approach outperformed the proposed automated system for each of the four cryptocurrencies examined." Yet the same abstract recommends the findings "for practical application in prop trading firms as a basis for building automated trading systems with integrated risk management mechanisms and as a tool for hyperparameter optimization of trading strategies including through Bayesian optimization." The pitch rests on infrastructure and parameter tuning. Returns offer no support for it. Any framework sold on those grounds still needs its one traded instance to avoid losing money, and this one lost on all four.

Five families, one smoothing filter

The framework starts with a smoothing filter. It projects a window of prices onto an orthogonal polynomial basis, then uses the fitted curve in place of a moving average. Five families appear: Legendre, Chebyshev types I and II, Laguerre, Hermite, and a Chebyshev-Hermite hybrid constructed by the paper. Each uses a different index transformation. For Laguerre, x = period - i, placing the newest bar at x = 0 while discounting older observations. Hermite is centered through x[i] = (period - 2i - 1)/2, making the transformation symmetric around the window midpoint.

The weights are w_n = sum(P_n(i) * price(i)) / sum(P_n(i)^2). The authors then apply a discrete correction that makes the degree-1-and-above values sum to zero. At degree zero, the result is w_0 = sum(price)/N, exactly the SMA.

Four strategy variants use the filters. In the price-crossing version, a cross above the polynomial curve opens a buy and closes the open sell. Another has one polynomial crossing another, effectively replacing both legs of a dual-SMA system. The CCI version swaps the SMA in the numerator for a higher-degree polynomial, measuring mean absolute deviation from that curve. An RSI-like measure counts the observations within the window that lie above the fit. Degree is capped at 9 because higher degrees "increase rather than decrease exposure to noise," according to the authors. They add that degree 3 "will generally suffice," covering the SMA, a linear trend, and quadratic plus cubic structure. Indicator length must exceed the degree.

Live intraday trading then used a Polynomial Autoregressive model, named PAR in the abstract and POLAR in the conclusions. Bitcoin, Ethereum, Cardano and a fourth asset that is never identified made up the traded set. The horizon was six months. The paper gives no calendar dates, bar frequency, exchange or data source.

A scorecard reduced to a sentence

The paper reports its own model only in directional terms. Buy-and-hold beat it on all four coins. Relative PAR performance was strongest on Ethereum and Bitcoin, with Cardano weakest. I looked for a return, a Sharpe, a drawdown, a hit rate, a t-stat, a benchmark spread. I did not find one. Neither the text nor the captions for Figs. 6-10 provide an equity, return or drawdown value. The description of the third-order polynomial CCI as showing "fairly consistent positive progression with moderate drawdown periods" therefore cannot be verified. Nor is the PAR specification written mathematically. The paper never explains how the four indicator variants feed into the PAR model used in trading.

Only the direction of the gap is reported. Its magnitude remains unknown, leaving a near-miss with lower drawdown indistinguishable from a rout. For a prop firm operating under a daily loss limit, that distinction determines whether the system preserves capital. The paper also omits transaction costs, slippage, funding and exchange fees. Those charges matter in intraday crypto.

The authors attribute the loss to market regime. They describe the six-month window as trending rather than oscillating, causing the mean-reversion logic to exit profitable positions too early. Crypto can certainly trend. But this explanation follows a result observed in a single window, without regime classification or a second period for comparison. The authors acknowledge that the sample "might not cover all the regimes of the cryptocurrency market." Four assets and one six-month sample support no statistical claim in either direction, and the paper calculates none.

Can anyone trade the signal?

Repainting stops the analysis earlier. The authors acknowledge that the indicator "will tend to redraw every time there is new data available." Their defense is that this "should not be viewed negatively because it allows the indicator to recalculate the best possible approximation each time additional market data is received."

The signal's tradability depends on where the fitted curve is read within the window. The centered Hermite transformation, x[i] = (period - 2i - 1)/2, exposes the issue. A fitted value at the window midpoint depends on bars from both sides. Any crossover evaluated there incorporates information unavailable when the signal supposedly occurred. The paper gives no causal end-of-window evaluation rule that would make those signals realizable. As the transformations are written, the authors need to identify the exact signal location.

Historical optimizer runs produce the four indicator variants, but no data split is described. The authors observe that "most of the prop firms use simulation liquidity in the crypto market." They never identify where the six-month test took place. They also describe the objective function as non-convex and possibly non-differentiable, ruling out gradient methods and narrowing the available hyperparameter search. According to the paper, that search becomes difficult when the universe grows to 13 underlying assets and 620 unique instruments.

Why we ran no backtest

We could not backtest this. The strategy trades cryptocurrencies, and we have no price data for that universe. An equities substitution would test a different strategy. Even with suitable data, two missing pieces would prevent replication. The paper does not specify the prop-firm risk rules used for position sizing in the live test. Minute bars also cannot reconstruct the exchange-level spreads, order-book depth or fills obtained by the authors. Degree, lookback and band width would need strictly walk-forward selection; otherwise, any result we produced would overstate itself.

Keep the w_0 identity

That one identity deserves attention. Fitting a polynomial basis to a price window decomposes the result into a moving average and a set of nearly-uncorrelated higher-order corrections. Each correction has an inspectable weight. For linear price filters, this is cleaner than stacking raw powers. At fixed degree and fixed sample, replacing raw powers with an orthogonal basis is an invertible reparameterization. The fitted values and forecasts remain the same object. The improvement is numerical, with predictive content unchanged. The paper goes too far when it claims orthogonality makes the method "less prone to overfitting" than machine learning methods.

The framework is still a sensible way to express a family of filters.

I would examine the Laguerre variant first. It gives the newest bar the greatest weight and is one-sided by construction, so it is causal. Its evidence consists of being tested once, over six months on four coins, and losing on every one. A per-coin table comparing PAR with buy-and-hold, net of realistic taker fees, would change my mind. The signal should be read at the end of the window, and the execution venue should be named. Once those figures existed, the negative result would carry information even if it remained negative.