Wilinski 2019
“Time series modeling and forecasting based on a Markov chain with changing transition matrices” is a peer-reviewed article by Antoni Wiliński in Expert Systems with Applications (Elsevier, Vol. 133, 1 November 2019, pp. 163-172; DOI 10.1016/j.eswa.2019.04.067). Of the four discrete-Markov price-prediction papers tracked in this vault it is the only one published in a peer-reviewed journal and the only one that reports actual trading profit — which is why it warrants the closest scrutiny. The contribution is a heterogeneous (non-homogeneous) Markov chain: instead of estimating one fixed transition matrix and assuming time-homogeneity, the chain re-estimates its matrix over a sequence of fixed-length sliding time windows. This is an explicit and well-motivated response to the Non-Stationary Transition Matrix problem — an admission, in effect, that the classic fixed-matrix Markov Chain Trading Model is not viable on its own.
Wiliński states the core design dilemma precisely. The return range Ymax - Ymin must be discretised into intervals (states): too few intervals and the state almost never changes, so the chain predicts nothing useful; too many and each state has too few observations to estimate a reliable transition probability. His response is to make the discretisation itself a tunable object: a “sequence of time windows with a fixed length and a fixed division into intervals,” with the window length, the number of windows, and the number of intervals all optimised by machine learning to maximise predictive efficiency. The strategy was simulated in MATLAB on two deliberately dissimilar instruments — 60,000 one-hour EUR USD Currency Pair candles ending 28 April 2016, and 4,000 daily WIG20 Index candles ending 28 April 2017 — and tested for both first- and second-order chains.
Wilinski 2019 [proposes_model] Markov Chain Trading Model Antoni Wiliński [proposes_model] Markov Chain Trading Model Wilinski 2019 [opposes] Non-Stationary Transition Matrix Wilinski 2019 [relates] State-Count Selection
The reported result is that the strategy produced “good results of profit according to the Calmar criterion” — the Calmar Ratio, annualised return over maximum drawdown — for both chain orders, with the paper presenting a cumulative-profit curve and judging the Calmar values “excellent” against external thresholds (citing Main, 2015). The strategy is described as “universal” and “resistant to changes” in the series, working across trend-following and mean-reverting conditions. Taken at face value this is the single most explicit profitability claim for the discrete-Markov family.
Wilinski 2019 [reports_profitability] Calmar Ratio Wilinski 2019 [tests-on] EUR USD Currency Pair Wilinski 2019 [tests-on] WIG20 Index
But the claim does not survive the grading criteria, and the reason is methodological, not a question of the author’s intent. The profit is the output of an optimisation, not of a held-out test. Three hyper-parameters — window length, window count, interval count — were searched by machine learning to maximise predictive efficiency on the simulation data; the paper does not disclose a cleanly separated out-of-sample period on which the frozen, already-tuned configuration was then evaluated. A Calmar ratio reported on the same data over which the parameters were optimised is an in-sample / data-snooped figure and is structurally exposed to Overfitting in Quantitative Trading and Data-Snooping Bias: with enough free parameters, some configuration will look profitable on any finite history. Compounding this, the paper reports no transaction costs or slippage — a decisive omission for an EUR/USD strategy trading on hourly bars, where round-trip spread and commission on frequent intraday trades can dominate gross edge — no buy-and-hold or random-walk benchmark, no Sharpe ratio, no standalone drawdown figure, and no replication package. The honest reading: Wiliński 2019 is a legitimate peer-reviewed modelling contribution — the heterogeneous-matrix idea is a real advance over the fixed-matrix chain — but its profitability claim is weak evidence of a tradeable edge: ML-tuned, in-sample (or at minimum out-of-sample status undisclosed), cost-free, and benchmark-free. Grade: weak, with explicit Overfitting in Quantitative Trading exposure.
Wilinski 2019 [suffers_overfitting_risk] Overfitting in Quantitative Trading Data-Snooping Bias [contradicts] Wilinski 2019 Transaction Costs and Slippage [contradicts] Wilinski 2019
Connections
- Markov Chain Trading Model — proposes_model, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Markov Chain Trading Model — tests_strategy, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Antoni Wiliński — proposes_model, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Calmar Ratio — reports_profitability, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- EUR USD Currency Pair — trades_market, 2010-2016, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- WIG20 Index — trades_market, 2013-2017, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Non-Stationary Transition Matrix — contradicts, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- State-Count Selection — suffers_overfitting_risk, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Overfitting in Quantitative Trading — suffers_overfitting_risk, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Data-Snooping Bias — suffers_overfitting_risk, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Transaction Costs and Slippage — excludes_costs, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033
- Out-of-Sample Backtesting — lacks_live_evidence, 2019, source: https://www.sciencedirect.com/science/article/abs/pii/S0957417419303033