Standard regression techniques like Ordinary Least Squares (OLS) are powerful but rely on assumptions that are frequently violated by real-world financial data. Asset returns are rarely normally distributed and are often subject to extreme observations, or outliers, caused by market shocks or company-specific events. Recognizing these realities, Axiom Quantitative Partners employs advanced econometric techniques designed to ensure our models are robust and our parameter estimates are reliable.

Robust Regression for Outlier Mitigation

The OLS method is highly sensitive to outliers. A single extreme data point can significantly distort the estimated coefficients of a model, leading to flawed forecasts and poor risk management. To counter this, we utilize Robust Regression techniques, which are specifically designed to be less affected by these extreme observations. By employing sophisticated M-estimators, we systematically down-weight the influence of outliers. Our process incorporates weighting functions such as the Huber and Tukey bisquare functions, which assign lower weights to observations with large residuals, ensuring that our models reflect the underlying central tendency of the data rather than being skewed by anomalous events.

Diagnostics for Model Integrity

We deploy a comprehensive suite of diagnostic checks to identify and correct for common econometric problems that can undermine model integrity. This ensures that the statistical relationships we identify are genuine and not artifacts of a misspecified model. These diagnostics include:

• Multicollinearity: We test for high correlation between the explanatory factors in our model, which can make coefficient estimates unreliable. Our methods correct for this, allowing us to isolate the true impact of each individual factor.
• Heteroscedasticity: This occurs when the variance of the model’s errors is not constant, a common feature in financial time series where volatility clusters. We employ models such as GARCH or Weighted Least Squares (WLS), ensuring our model’s predictive power is not compromised during periods of high market stress.
• Autocorrelation: We test for correlation in the model’s errors over time using diagnostics like the Durbin-Watson statistic. By correcting for this, we ensure our forecasts are not biased by historical error patterns.

By integrating these robust methodologies into our research, we build models that are resilient to the unique challenges of financial data, leading to more stable and reliable signals for both alpha generation and risk management.