Frequency analysis of cointegrated assets with the Fourier transform: how is algorithmic trading meta-morphing the market?

Ana Medina-López, M. Jiménez-Partearroyo, Álvaro Sánchez-Paniagua Ríos, Manuel Montes Olalla

Abstract

This study explores how the increasing presence of algorithmic trading (AT) has altered the underlying structure of financial markets through changes in frequency dynamics. This research shifts the focus from isolated measures such as price levels or volatility to a frequency-based perspective, aiming to assess how the digitalization of market behavior driven by algorithmic strategies, has reshaped the periodicity and synchronicity of price movements across global stock indices. The methodology integrates cointegration analysis with frequency decomposition techniques, employing the fast Fourier transform (FFT) on stationary spreads derived from pairs of global equity indices. Potential asset pairs are first identified through the Engle-Granger procedure, after which their spreads are calculated and subjected to FFT to extract dominant spectral components over the 2000–2024 period. The temporal evolution of these frequencies is then examined to uncover common patterns and assess inter-index correlations. This approach enables a characterization of interconnected market dynamics and provides a preliminary framework for linking the presence of AT to observed spectral behaviors. The analysis indicates that financial markets display patterns that are statistically consistent with the behavior of interconnected dynamic systems, in which AT may act as a relevant coordinating factor. The spectral results show that stationary spreads tend to exhibit a gradual shift toward lower-frequency regimes (<0.001 Hz), accompanied by substantial cross-correlations (approximately 60–90%) across pairs. The sigmoid-based proxy for AT diffusion explains about 48.7% of the observed variation in dominant frequency trajectories and is negatively associated with high-frequency volatility components, suggesting a potential link between algorithmic activity and the attenuation of short-term fluctuations. Although major systemic events, such as financial crises, temporarily disrupt these spectral patterns, the evidence points to a subsequent partial realignment over time. Overall, the findings are aligned with the interpretation that the expansion of AT is associated with increasing low-frequency coherence and stronger cross-market alignment. Although our proxy is useful for capturing general trends, it is a simplified approximation. While the sigmoid function is widely used in literature to describe technological adoption processes (initiation, growth, saturation), it does not fully capture AT dynamics or regional heterogeneity. The network of algorithms operating in markets likely responds to multiple nonlinear dimensions, which may explain the unexplained variance in our model. In addition, the statistically significant results reported for trending financial series should be interpreted cautiously, because low p-values are often expected in persistent, nonstationary data and do not by themselves imply substantive significance. Another limitation is that although the dynamic beta is recalculated periodically to avoid look-ahead bias, this may temporarily disrupt cointegration in local windows, introducing uncertainty in short-term spread stationarity. Nonetheless, starting from a globally cointegrated and stationary series, these deviations are interpreted as transient fluctuations inherent to dynamic systems, and do not invalidate the historical analysis of frequency evolution via FFT, which benefits from beta's adaptability and smoothing to capture intrinsic oscillatory patterns. The proposed framework opens several avenues for future research, including the incorporation of market microstructure data to enhance empirical precision, the development of early warning indicators based on frequency convergence patterns for improved systemic risk detection, and the exploration of complex-system analogies, such as Kuramoto oscillator networks, to refine theoretical understanding of financial synchronization. Extensions may also consider alternative specifications of the AT proxy, applications to other asset classes, and the impact of regulatory or technological shifts on the spectral structure of financial markets. The findings also entail several practical implications. The identification of spectral synchronization in financial markets provides a novel perspective for systemic risk monitoring, as abrupt disruptions in frequency patterns may serve as early warning indicators of financial distress. Moreover, the role of AT as a synchronizing mechanism suggests that market microstructure regulation should consider its impact on liquidity provision and its broader influence on global market coordination. Finally, the spectral framework offers potential applications in the design of investment strategies that leverage phase alignment or amplitude reinforcement across markets, thereby enhancing portfolio stability and timing precision. With respect to the social implications of this work, the study shows how AT can help maintain systemic stability and consistency in global financial markets. By better understanding technology’s role in economic resilience, we can shape smarter regulations that may improve transparency, benefiting investors, institutions and society as a whole. Moreover, the research also emphasizes the need for responsible digital innovation in shaping fair and efficient financial systems, with implications for inclusive economic development. This study bridges cointegration, spectral analysis and AT within a unified descriptive framework. It documents persistent low-frequency convergence and cross-market synchronization consistent with the expansion of the AT diffusion proxy.

Source: semanticscholar

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