Achury, Arredondo & Sánchez Ascanio (2024) — Filtration-Indexed ARIMA + Random-Walk Trend Model

A novel predictive analytics model for forecasting short-term trends in equity assets prices. Decision Analytics Journal 14 (2025) 100534, Elsevier. CC BY 4.0. DOI: 10.1016/j.dajour.2024.100534. Received 11 Sep 2024, accepted 13 Dec 2024, online 20 Dec 2024.

Authors

Fabián Achury-Calderón (Universidad de Salamanca / Universidad Militar Nueva Granada)
John A Arredondo (corresponding, Fundación Universitaria Konrad Lorenz, Bogotá)
Leidy Catherinne Sánchez Ascanio (Fundación Universitaria Konrad Lorenz, Bogotá)

Bibliographic

Journal: Decision Analytics Journal (Elsevier, OA)
Volume / article: 14 / 100534
Pages: 13
License: CC BY 4.0
Dataset: 25 equities × 130 daily closes ending 2023-05-31 (US, Spain, Japan, Colombia)

What the paper is

A directional classifier (bullish / bearish / undecidable) for short-horizon equity prices. The mathematical novelty is a filtration (\mathbb{R}, \mathcal{F}_A \subseteq \mathcal{F}_B \subseteq \mathcal{F}, P) that combines:

a continuous ARIMA Forecast Model density on the Borel σ-algebra \mathcal{F}_B, and
a discrete binomial Random Walk Price Pathwise mass on the coarser σ-algebra \mathcal{F}_A,

into a product measure renormalised over the random-walk bins (Proposition 1). The trend call is then a simple top-2-bin test (Observation 4): see Filtered Probability Trend Hypothesis for the decision rule.

Headline result

Market	n	Successful	Wrong	Undecidable	Hit rate (decided)
US (Dow + Nasdaq top-9)	9	9	0	0	100%
Spain (IBEX-35 picks)	5	4	1	0	80%
Japan	5	2	3	0	40%
Colombia	6	2	3	1	33% (40%)
Total	25	17	7	1	62.5%

ARIMA-vs-actual 5-day price variation ranges from −11.2% to +13.5% — the model is right on direction more often than not, but does not size the move.

Why it is in this wiki

It is the only source in the wiki that frames a short-horizon equity forecast as a filtration with two σ-algebras. The construction is mathematically clean, easy to translate to code, and the sample is large enough (25 names × 4 markets) to compare across regimes. It is also a useful negative baseline — 62.5% directional hit rate with no volume, no macro, no sentiment, no ML — that frames how much value richer signals have to add.

What it is not

Not a position-sizing or signal-to-trade model. Output is categorical.
Not transaction-cost-aware. No commission, slippage, or market-impact term.
Not regime-aware. No high-vol / low-vol state.
Not robust to outliers. Uses medians (not robust estimators) of step sizes.
Not an ML baseline. The paper itself flags LSTM / GRU / RF / WNN hybrids as obvious next steps.