Author: Denis Avetisyan
This review details a method for building causally valid predictive signals from financial time series, offering improved performance in specific market conditions.
The paper introduces forward-oriented causal observables and analyzes their performance in non-stationary financial markets, emphasizing the impact of regime dependence and the need for adaptive filtering techniques.
Predicting financial time series is inherently challenging due to market non-stationarity and the need for strictly causal trading strategies. This paper, ‘Forward-Oriented Causal Observables for Non-Stationary Financial Markets’, introduces a novel methodology for constructing interpretable predictive signals from micro-features, explicitly enforcing causality and online computability. Results demonstrate that these causally constructed observables can yield substantial economic benefits in specific market regimes, yet exhibit performance degradation during regime shifts. Can adaptive signal design overcome the limitations imposed by non-stationarity and unlock more robust predictive power in financial markets?
Navigating Non-Stationarity in Financial Systems
Financial time series, such as stock prices or exchange rates, pose significant analytical hurdles due to a property known as non-stationarity. Unlike stable systems where statistical properties remain constant over time, financial data exhibits shifting means, variances, and autocorrelations. This means that patterns identified in past data are unlikely to reliably predict future behavior; a model calibrated on historical data may quickly become obsolete as the underlying statistical characteristics of the series change. Consequently, traditional time series analysis techniques – designed for stationary data – often fail to accurately model or forecast financial markets, necessitating the development of specialized methods capable of accommodating these dynamic and evolving properties. Addressing non-stationarity often involves techniques like differencing – calculating the change in values rather than their absolute levels – or employing more complex models that explicitly account for time-varying parameters, striving to capture the inherent instability of financial systems.
Conventional statistical techniques, designed for static systems, frequently falter when applied to financial time series due to their intrinsic dynamism. These series aren’t simply random fluctuations; they exhibit evolving patterns, shifting volatility, and dependencies that change over time – a characteristic known as non-stationarity. Consequently, models relying on fixed parameters or assumptions about constant distributions often produce inaccurate forecasts and unreliable risk assessments. The predictive power of these traditional methods is fundamentally limited because they cannot adequately capture the inherent complexity and continual adaptation observed in financial markets, necessitating the development of more sophisticated analytical tools capable of handling these evolving dynamics. \sigma^2(t) , representing conditional variance, is rarely constant in financial data, highlighting this limitation.
Uncovering Causal Signals for Predictive Power
Causality Analysis, when applied to Financial Time Series, aims to distinguish predictive relationships from spurious correlations. Traditional statistical methods often identify correlations where one time series simply coincides with another due to a common underlying driver, or by chance. Causality Analysis techniques, such as Granger Causality tests and more advanced methods leveraging instrumental variables or structural equation modeling, attempt to determine if changes in one time series demonstrably precede and predict changes in another, establishing a temporal precedence indicative of a causal link. This is critical because correlation alone is insufficient for reliable forecasting or risk management; identifying true causal drivers allows for the construction of models that can accurately predict future behavior and respond effectively to market dynamics. The analysis often incorporates techniques to address confounding variables and ensure the identified relationships are not merely indirect effects of other factors.
Causal signal construction prioritizes the creation of predictive indicators that are fundamentally time-ordered; a signal’s value at any given time step can only depend on past and present data, precluding the use of future information. This adherence to causal constraints is essential for achieving online computability, meaning the signal can be calculated iteratively as new data arrives without requiring a complete historical dataset. This property is critical for real-time financial applications such as algorithmic trading and risk management, where decisions must be made based on currently available information. The use of strictly causal signals avoids look-ahead bias and ensures the viability of backtesting and live deployment in transactional systems.
Hawkes Processes are utilized to model event cascades and capture temporal dependencies within financial time series by defining the intensity of future events as a function of past occurrences; the intensity \lambda(t) at time t is expressed as a sum of a baseline rate and terms representing the influence of each past event t_i where t_i < t. Specifically, the intensity function takes the form \lambda(t) = \mu + \sum_{t_i < t} g(t - t_i), where μ is the base intensity and g(t) is the kernel function defining the impact of past events at time t. Common kernel functions include exponential and power-law decays, which determine the duration and strength of the influence of each event, allowing the model to capture self-excitation – where an event increases the probability of further events – and common shock dependencies between events.
Constructing a Robust Composite Signal
The Composite Signal is constructed by integrating four distinct technical indicators: the Relative Strength Index (RSI), Money Flow Index (MFI), Moving Average Convergence Divergence (MACD) Difference, and Bollinger Bands Percentage (BB%). RSI measures the magnitude of recent price changes to evaluate overbought or oversold conditions. MFI incorporates both price and volume to identify potential reversals. The MACD Difference, calculated as the difference between the MACD line and the signal line, highlights changes in momentum. Finally, BB% indicates where the price stands within the Bollinger Band range, providing a normalized measure of price volatility and potential breakout signals. Each indicator contributes a unique perspective on market conditions, and their combined analysis aims to provide a more comprehensive and robust signal than any single indicator could achieve independently.
The application of a Kalman Filter during Causal Signal Construction serves to mitigate the impact of inherent noise present in individual technical indicators. This filter operates as a recursive estimator, predicting the state of the signal based on prior estimates and incorporating new measurements while weighting them according to their uncertainty. Specifically, the Kalman Filter minimizes the mean squared error of the estimate by optimally combining predicted and measured values; the filter’s gain, calculated dynamically, determines the relative contribution of each. This process effectively smooths the composite signal, reducing false positives and enhancing the reliability of subsequent trading decisions by providing a more stable and accurate representation of underlying market trends.
The Forward Operator within the composite signal construction process introduces a time-series element, explicitly modeling the expected future behavior of each contributing indicator – RSI, MFI, MACD Difference, and BB%. This is achieved through a state-space representation that projects current indicator values onto a predicted future state. Critically, this projection is designed for online computation; the Forward Operator utilizes only immediately preceding values and a fixed set of parameters, avoiding any requirement for historical data beyond the current time step. This maintains real-time applicability while simultaneously enhancing the signal’s ability to anticipate market movements, thus improving predictive power without sacrificing computational efficiency.
Adapting to Market Dynamics with Thresholds
The core of this adaptive trading system lies in a precisely defined decision rule based on signal thresholds. Rather than relying on ambiguous indicators, the strategy generates explicit buy and sell signals when a composite signal – a culmination of various technical and fundamental factors – crosses predetermined levels. These thresholds aren’t arbitrary; they represent critical points where the potential reward justifies the associated risk, effectively transforming complex market data into actionable trading opportunities. This clear delineation of action points minimizes subjective interpretation and allows for systematic execution, fostering a disciplined approach to capitalizing on market movements. The resulting trades are not guesses, but rather calculated responses to quantifiable changes in the composite signal’s value.
The strategy’s success hinges on dynamically adjusted thresholds for generating trading signals, a key feature known as regime dependence. Rather than relying on static values, these thresholds respond to shifts in market volatility and prevailing trends; as market uncertainty increases, the thresholds widen, requiring a more substantial signal to trigger a trade and thus reducing exposure during turbulent periods. Conversely, during calmer, trending markets, the thresholds narrow, enabling the system to capitalize on even modest price movements. This adaptive mechanism allows the strategy to navigate varying market conditions with greater agility than traditional, fixed-threshold approaches, effectively modulating risk and optimizing trade frequency based on the current market ‘regime’.
Initial testing of the adaptive trading strategy, spanning from 2023 into September 2024, revealed a compelling advantage over traditional buy-and-hold investments. During this period, the dynamically adjusted thresholds effectively capitalized on market fluctuations, generating substantial returns. However, subsequent performance analysis indicated a distinct plateauing effect; while not resulting in losses, the strategy’s outperformance diminished considerably after September 2024. This suggests the conditions that initially favored the adaptive approach-likely specific volatility patterns or trend strengths-shifted, highlighting the need for ongoing recalibration and potentially the incorporation of additional indicators to maintain a consistent edge in diverse market environments.
The adaptive trading strategy, during its period of pronounced outperformance from 2023 to September 2024, maintained a remarkably high frequency of activity, executing an average of 10,3103 trades each month. This translates to a substantial volume of transactions, indicating the system’s responsiveness to shifting market dynamics and its consistent generation of trading signals. The high trade count wasn’t simply a result of volatility; it reflected the strategy’s ability to dynamically adjust its thresholds and capitalize on even subtle shifts in market regimes, allowing for frequent, yet calculated, entries and exits. While later performance stabilized, this initial period demonstrated the potential for a highly active, adaptive system to generate significant trading volume and, consequently, outperform more passive investment approaches.
The pursuit of causally valid signals in non-stationary financial markets, as detailed in the study, echoes a fundamental principle of systemic understanding. The research acknowledges the performance sensitivity to regime shifts, highlighting that a system’s behavior is inextricably linked to its structure-change the conditions, and the outcome alters. This resonates with Nietzsche’s assertion: “There are no facts, only interpretations.” The presented methodology, while robust within defined parameters, necessitates constant recalibration; its ‘facts’-the predictive signals-are contingent upon the ‘interpretation’ of the current market regime. A truly adaptive system, like a living organism, must continually refine its understanding of the underlying structure to maintain predictive validity.
Where to Next?
The pursuit of causally valid signals in financial markets inevitably confronts the inconvenient truth of non-stationarity. This work offers a compelling, if limited, advance – a method demonstrably effective within specific regimes. However, the observed sensitivity to regime shifts underscores a fundamental point: a system’s behavior is dictated by its structure, and financial markets are rarely, if ever, structurally stable. The elegance of a solution predicated on fixed causal relationships begins to fray at the edges when those relationships themselves are transient.
Future work must therefore address adaptability. The construction of signals that learn causal structures, rather than assume them, represents a natural progression. Kalman filtering provides a useful framework, but extending it to encompass genuinely dynamic causal graphs – systems that evolve their connectivity in response to market dynamics – presents a significant challenge. If a design feels clever, it’s probably fragile; simplicity in adaptation will likely prove more valuable than complexity in static modeling.
Ultimately, the field risks becoming entangled in an endless pursuit of ever-more-sophisticated regime detectors. A more fruitful path may lie in embracing the inherent uncertainty and focusing on robust, rather than precisely optimal, strategies. The goal isn’t to know the market, but to build systems capable of navigating its unpredictable evolution.
Original article: https://arxiv.org/pdf/2512.24621.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2026-01-01 08:52