Representation Learning for Regime detection in Block Hierarchical Financial Markets

TL;DR

It is shown that using a singular performance metric is misleading in financial market investment use cases where deep learning models overfit in learning spatio-temporal correlation dynamics.

Abstract

We consider financial market regime detection from the perspective of deep representation learning of the causal information geometry underpinning traded asset systems using a hierarchical correlation structure to characterise market evolution. We assess the robustness of three toy models: SPDNet, SPD-NetBN and U-SPDNet whose architectures respect the underlying Riemannian manifold of input block hierarchical SPD correlation matrices. Market phase detection for each model is carried out using three data configurations: randomised JSE Top 60 data, synthetically-generated block hierarchical SPD matrices and block-resampled chronology-preserving JSE Top 60 data. We show that using a singular performance metric is misleading in our financial market investment use cases where deep learning models overfit in learning spatio-temporal correlation dynamics.

Figures (11)

• Figure 1: Average correlation matrices for each regime identified from the JSE Top 60 data. Distance metric: $\sqrt{2(1 - C})$, where $C$ is the sample correlation matrix. Matrices are classified into three regimes according to the ex ante Sharpe ratio ($SR$). Stressed: $SR < -0.5$; normal: $SR \in [-0.5,2.0]$; rally: $SR > 2.0$. In the stressed class we can see a large cluster in the lower left, as many assets have synchronised movements, as compared to the normal market condition where the block diagonal structure suggests improved diversification. Average rally regimes exhibit this same hierarchical structure with lower inter- and intra-block correlation strength.
• Figure 2: JSE Top 60 correlation coefficient density per class. The stressed, normal and rally regimes have mean correlations of 0.24, 0.205 and 0.17, respectively. Average correlation and standard deviation vary per regime, supporting the findings of miori2022returnsdriven in the South African market of traded stocks, where varying underlying distributions characterise different macroeconomic regimes. Interrelatedness of assets is greater in times of market stress with greater volatility, while normal and rally regimes are characterised by lower average correlation and volatility. The regime correlation asymmetries identified by AngAndrew2004HRAA prevail in the JSE top 60 data. The average correlation matrices for each market regime are shown in Figure \ref{['fig:corrmats']}.
• Figure 3: We show representative (simulated) block hierarchical SPD correlation matrices per regime. The synthetic construction uses techniques for nested factor timeseries generation as proposed by yelibi2021ALC to create 5 clusters with 3 hierarchies each, sampled from Student's t-distribution with $v = 3$ d.o.f. The SPD correlation matrices computed on these datasets are permuted to introduce realistic noise with seed = 27. The simulated correlation matrices can be visually compared with the empirical average correlation matrices for each market regime as shown in Figure \ref{['fig:corrmats']}.
• Figure 4: Synthetic block hierarchical SPD matrix correlation coefficient density per regime. By construction, the stressed, normal and rally regimes have average correlations of 0.24, 0.18 and 0.10 respectively, with descending standard deviation values. The separability of underlying distributions per regime class is preserved to emulate Figure \ref{['fig:corrcoeffdensity']}.
• Figure 5: U-SPDNet matrix evolutions. Here, the 60x60 input space (left), 20x20 latent space (center) and the reconstructed 60x60 layer (right) matrices of U-SPDNet trained and validated on both synthetic nested block hierarchical correlation matrices (lower row) and their JSE Top 60 data counterpart (upper row). Representational example drawn from the 600th epoch.