Do Carmo 2017
“Modeling Stock Markets Through the Reconstruction of Market Processes” is a Master’s dissertation in Economics by João Pedro Rodrigues do Carmo, submitted at ISEG (Lisbon School of Economics and Management) / University of Lisbon under supervisor Tanya Vianna de Araújo, and posted to arXiv in 2018 as preprint 1803.06653. Like Aronsson Folkesson 2023 it is a student dissertation rather than a peer-reviewed article, and this should temper how its results are weighted. The work asks whether the seemingly stochastic behaviour of equity markets can be captured by a discrete-state Markov chain, and frames the question against the Efficient Market Hypothesis versus a “stylised facts” view of markets (volatility memory, power-law tails, non-linear return dependence).
The model is a discrete N-symbol, K-length Markov chain. Returns are discretised into symbols defined relative to one standard deviation: in the minimal 3-symbol scheme a return is “flat” if it stays within ±1σ and “up”/“down” otherwise, generalised to any N >= 3 buckets. The chain is generalised in memory length as well: instead of conditioning only on day n-1 (a 1-length chain), the model conditions on the whole sequence of the previous K days, with transition frequencies stored in a transition tensor T estimated by counting empirical K-length sequences. The fitted chain is then used generatively: it regenerates a synthetic return path which is compared, via a reconstruction-error metric, against both the real series and a purely random sequence. The MATLAB code is released on GitHub, so the work is reproducible — the one genuine methodological strength relative to the rest of this cluster.
Do Carmo 2017 [proposes_model] Markov Chain Trading Model Do Carmo 2017 [defines] First-Order Memory Assumption Do Carmo 2017 [compares_benchmark] Random Walk Benchmark
The single quantitative claim is an error comparison, not a profitability result. Over 500 Monte Carlo runs, a 3-symbol 1-length Markov chain achieved a mean reconstruction error of roughly 0.351 against roughly 0.67 for a purely random sequence — so the chain reconstructs the process “at the very least, always better than a completely random model such as a Random Walk.” But the paper is honest about the limits: financial markets look “apparently random” (the author notes the visual similarity between a real index and a simulated random walk), and the error stops improving and rises again for chain length K >= 5 because each longer sequence has too few observations to estimate — the Curse of Dimensionality / data-sparsity wall that defeats higher-order chains. The interpretation offered is descriptive: the transition matrix is read as a proxy for “market sentiment,” not as a trading signal.
First-Order Memory Assumption [causes] Curse of Dimensionality Do Carmo 2017 [supports] Curse of Dimensionality
For grading this is the weakest profitability evidence in the cluster — and the most honest about it. There is no trading strategy, no backtest, no positions, no P&L, no costs, no Sharpe, no drawdown. The benchmark beaten is a reconstruction-error metric against a synthetic random sequence — a statement about how well the chain mimics the data-generating process, which says nothing about whether trading on its forecasts would make money after Transaction Costs and Slippage. There is also no out-of-sample design: the chain is fitted and the reconstruction assessed on the same data, with Monte Carlo runs giving robustness over simulation noise but not over genuine out-of-sample periods. The correct grade is inconclusive: the paper shows a Markov chain has some descriptive purchase on equity return structure beyond pure randomness, which is useful for Regime Classification, but it provides zero evidence of a tradeable edge and never claims to. Treat any citation of “do Carmo shows Markov chains beat the random walk” as referring to an error metric, never to profit.
Transaction Costs and Slippage [contradicts] Do Carmo 2017 Do Carmo 2017 [relates] Regime Classification
Connections
- Markov Chain Trading Model — proposes_model, 2017, source: https://arxiv.org/abs/1803.06653
- Random Walk Benchmark — compares_benchmark, 2017, source: https://arxiv.org/abs/1803.06653
- First-Order Memory Assumption — proposes_model, 2017, source: https://arxiv.org/abs/1803.06653
- Curse of Dimensionality — suffers_overfitting_risk, 2017, source: https://arxiv.org/abs/1803.06653
- Transaction Costs and Slippage — excludes_costs, 2017, source: https://arxiv.org/abs/1803.06653
- Out-of-Sample Backtesting — lacks_live_evidence, 2017, source: https://arxiv.org/abs/1803.06653
- Regime Classification — detects_regime, 2017, source: https://arxiv.org/abs/1803.06653
- US Equity Market — trades_market, 2017, source: https://arxiv.org/abs/1803.06653