{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T16:34:16Z","timestamp":1792946056151,"version":"4.5.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Using a return distribution predicted by deep learning for portfolio construction requires both an accurate probabilistic forecast and a validated way of translating the forecast into portfolio decisions. This paper proposes a deep learning distribution-to-strategy (D2S) framework with four stages, namely distributional modeling, portfolio signal and strategy construction, model and strategy selection, and model and strategy evaluation. Within this framework, the proposed Spatial-Temporal Multivariate Mixture Density Network (STMMDN) combines a long short-term memory (LSTM) encoder, a dynamic graph neural network (GNN) built on rolling covariance matrices, and a constrained two-component multivariate Student-$t$ mixture output layer that forecasts the joint return density. Two constraints on the mixture, fixed mixture weights and bounded degrees of freedom for the second component, give the components stable roles, the first describing ordinary market conditions over the forecast horizon and the second expressing the forecast&amp;apos;s departure from them. The predicted parameters and a volatility signal read from the predicted distribution serve as the two kinds of signal for portfolio strategy construction, and the volatility signal and the covariance input are validated and justified on the validation period before the volatility-aware strategy uses them. Two temporal-only and two spatial-temporal architectures are compared across three asset universes (TPXC30 constituents, currencies and precious metals, and DJIA constituents) and three temporal setups, net of transaction costs. A graph-based architecture attains the highest median validation likelihood in all nine universe-setup configurations, and most of the validation-period selections that the volatility-aware strategy changes attain a higher out-of-sample Sharpe score than without it.<\/jats:p>","DOI":"10.2139\/ssrn.7669859","type":"posted-content","created":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T15:43:46Z","timestamp":1792943026000},"source":"Crossref","is-referenced-by-count":0,"title":["Spatial-Temporal Multivariate Mixture Density Networks: From Distributional Forecasting to Portfolio Strategy Construction"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0756-8356","authenticated-orcid":true,"given":"Fong","family":"Lam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3167-6586","authenticated-orcid":true,"given":"Jennifer","family":"Chan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. T. Boris","family":"Choy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9803-0256","authenticated-orcid":true,"given":"Junbin","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"ref1","doi-asserted-by":"crossref","DOI":"10.1016\/j.jeconom.2024.105919","article-title":"Modelling large dimensional datasets with markov switching factor models","volume":"247","author":"M Barigozzi","year":"2025","journal-title":"Journal of Econometrics"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1002\/jae.842","article-title":"Multivariate garch models: a survey","volume":"21","author":"L Bauwens","year":"2006","journal-title":"Journal of Applied Econometrics"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.ijforecast.2013.11.007","article-title":"Selecting volatility 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