Preserving Market Regimes in Synthetic Multivariate Returns
Summary
The question seeks a way to simulate multiple asset return series that share market-wide regimes over common time intervals. It contrasts this goal with a simple univariate setup in which bullish and bearish states have different Gaussian return distributions, such as differing means and volatilities. The central modeling requirement is a shared regime state that influences assets together, rather than independently assigning each series its own regime.
The answer points to an ensemble approach from statistical mechanics that aims to preserve selected statistical properties of observed time series on average. Such an approach might capture properties associated with market regimes, but the response does not explain how to define regimes, impose synchronized transitions, or estimate parameters. It offers a research lead rather than a worked simulation method, and provides no empirical validation or comparison with explicit multivariate regime-switching models. The suggested reference’s relevance to the particular shared-regime objective therefore remains uncertain.
Key ideas
- The modeling goal is to synchronize regime changes across multiple asset return series.
- A shared latent market state can represent common bullish or bearish conditions.
- Different regime-specific return distributions can encode changes in mean and volatility.
- An ensemble method may preserve selected time-series properties on average.
- The answer does not demonstrate that its suggested approach generates synchronized regimes.
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Full text
# How to simulate asset prices/returns that display market regimes? # How to simulate asset prices/returns that display market regimes? Are there any techniques that can make a multivariate random number generating process for stock prices/returns, like geometric Brownian motion via Cholesky, also include the simulation of a finite number of market regimes (say 2 or 3) so that systematic (market-induced) movement in prices are experienced across all assets for the same span of time intervals? (e.g. observations/prices 1-250 are market regime 1 for all assets, prices 251-400 are regime 2, etc) For the univariate case, I understand that simulated returns can be generated from separate Gaussian distributions, each of which represents a "bullish" or "bearish" market regime, with: - the returns for the bullish regime drawn from a Guassian distribution with positive mean and low variance, - while returns for the bearish regime draw from a Gaussian distribution with slight negative mean but higher variance, but my question pertains to generating multivariate artificial returns instead of one-by-one univariate. ## Answer by babelproofreader (score 2) https://quant.stackexchange.com/a/55630 Maybe a "statistical mechanics" approach - paper at https://arxiv.org/pdf/1907.04925.pdf and code at https://uk.mathworks.com/matlabcentral/fileexchange/72000-canonical-ensemble-for-time-series From the paper abstract: "This consists of a statistical mechanical approach - analogous to the configuration model for networked systems - for ensembles of time series designed to preserve, on average, some of the statistical properties observed on an empirical set of time series" (highlights mine) Some of these properties may very well be bull or bearish regimes. EDIT - in response to develarist's comment
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