Core Concepts

This paper introduces novel statistical tests for identifying structural breaks in predictive quantile and CoVaR regressions, offering robustness to predictor persistence levels, a crucial aspect in economic and financial forecasting.

Abstract

**Bibliographic Information:**Hoga, Y. (2024). Persistence-Robust Break Detection in Predictive Quantile and CoVaR Regressions. arXiv preprint arXiv:2410.05861v1.**Research Objective:**To develop and assess novel statistical tests for detecting structural breaks in predictive quantile and CoVaR regressions, addressing the challenge of varying predictor persistence commonly encountered in economic and financial time series.**Methodology:**The study leverages self-normalization techniques to construct test statistics that are robust to different degrees of predictor persistence, encompassing both stationary and near-stationary dynamics. The asymptotic properties of the proposed tests are rigorously derived, and their finite-sample performance is evaluated through Monte Carlo simulations.**Key Findings:**The proposed tests demonstrate good finite-sample properties, exhibiting close-to-nominal size even for relatively small sample sizes and high power in detecting deviations from the null hypothesis of parameter constancy. Notably, the tests perform well for both quantile and CoVaR regressions, even though the latter involves estimating more extreme quantiles and thus presents a greater statistical challenge.**Main Conclusions:**The paper provides practitioners with reliable and easy-to-implement tools for detecting structural breaks in predictive quantile and CoVaR regressions, irrespective of the persistence properties of the predictors. This is particularly relevant for economic and financial forecasting, where the predictive power of variables may change over time.**Significance:**The study makes a significant contribution to the field of econometrics and financial econometrics by providing persistence-robust break detection methods for quantile and CoVaR regressions, filling a gap in the existing literature.**Limitations and Future Research:**The paper primarily focuses on single-break alternatives, and extending the methodology to accommodate multiple breaks is an avenue for future research. Additionally, exploring the attribution of breaks to specific coefficients in the CoVaR regression setting is a promising direction for further investigation.

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Stats

The simulations use sample sizes of 1000, 2000, and 3000, reflecting typical dataset dimensions in practical applications.
A nominal level of 5% is used for all statistical tests, representing a standard significance level in hypothesis testing.
The study explores a range of autoregressive parameters (r) for the predictors, spanning from 0.5 to 0.01, to assess the tests' performance under varying degrees of persistence.
The break point (s*) is set at 0.5, indicating a break occurring in the middle of the sample, to evaluate the tests' power under this specific scenario.
The deviation from the null hypothesis (δ) is varied within the interval [-1/4, 1/4] to examine the tests' power as the magnitude of the break changes.

Quotes

"In this paper, we connect the structural break literature with that focusing on robustifying inference in predictive regressions with respect to different degrees of predictor persistence."
"One key feature of our change point tests is the robustness to the predictor persistence."
"Simulations show that our tests possess excellent finite-sample performance."

Key Insights Distilled From

by Yannick Hoga at **arxiv.org** 10-10-2024

Deeper Inquiries

Adapting these break detection techniques for high-frequency financial data presents several challenges due to the characteristics of such data:
1. Microstructure Noise: High-frequency data is plagued by microstructure noise arising from bid-ask bounce, transaction costs, and other market frictions. This noise can be correlated and heteroskedastic, violating the assumptions of the break detection tests.
Solution: Employ noise-robust estimation methods for the quantile and CoVaR regressions. For instance:
Pre-averaging: Reduce noise by locally averaging prices over short intervals (Jacod et al., 2009).
Realized Measures: Utilize realized volatility or other realized measures to estimate integrated quantities robust to noise (Barndorff-Nielsen and Shephard, 2002).
Subsampling: Estimate the model at a lower frequency and aggregate the results (Zhang et al., 2005).
2. Jumps: Financial markets exhibit jumps, leading to non-continuous price paths. These jumps can be mistaken for structural breaks, leading to spurious detection.
Solution: Incorporate jump-robust estimation techniques:
Truncated Realized Variation: Filter out jumps by considering only small price changes ( Mancini, 2001).
Bipower Variation: Estimate volatility using a combination of powers of price changes that are robust to jumps (Barndorff-Nielsen and Shephard, 2004).
Separating Jumps and Volatility: Use techniques that explicitly model and estimate jumps separately from the continuous component of price variation (Lee and Mykland, 2008).
3. Intraday Patterns: High-frequency data often exhibits intraday patterns, such as increased volatility at the open and close of trading. These patterns can induce spurious breaks if not appropriately accounted for.
Solution:
Time-of-Day Dummies: Include dummy variables for different times of the trading day to capture intraday seasonality.
Time Deformation: Transform the time scale to account for variations in trading activity throughout the day (Dacorogna et al., 2001).
4. Computational Burden: The high dimensionality of high-frequency data can pose computational challenges for break detection techniques.
Solution:
Dimension Reduction: Employ techniques like Principal Component Analysis (PCA) or Factor Models to reduce the dimensionality of the predictors.
Efficient Algorithms: Utilize computationally efficient algorithms for quantile regression and break detection.
By addressing these challenges, the break detection techniques can be adapted to provide valuable insights into the dynamics of high-frequency financial data.

The persistent presence of structural breaks in economic models indeed suggests inherent limitations in assuming stable relationships. This realization has fueled the exploration of alternative modeling approaches that acknowledge and accommodate evolving dynamics:
1. Time-Varying Parameter Models: These models allow parameters to change over time, capturing evolving relationships. Popular approaches include:
Rolling Window Regression: Estimate the model over a fixed window of data, rolling the window forward to update the parameters.
Kalman Filter: A recursive algorithm for estimating the state of a dynamic system from a series of noisy measurements, allowing for time-varying parameters and state variables.
State-Space Models: A general framework for modeling time series data where the system's behavior is described by unobserved states that evolve over time.
2. Regime-Switching Models: These models assume that the data generating process switches between a finite number of regimes, each characterized by different parameter values.
Markov Switching Models: The switching process is governed by an unobserved Markov chain, allowing for sudden and discrete changes in regimes.
Smooth Transition Autoregressive (STAR) Models: Transitions between regimes are smooth and gradual, governed by a transition function.
3. Agent-Based Models (ABM): These models simulate the behavior of interacting agents in a system, allowing for emergent phenomena and complex dynamics that can lead to structural breaks. ABMs relax assumptions of equilibrium and rational expectations, providing a bottom-up approach to understanding economic phenomena.
4. Machine Learning Methods: Techniques like Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks can capture complex temporal dependencies and non-linear relationships, making them suitable for modeling systems with structural breaks.
5. Acknowledging Model Uncertainty: Instead of seeking a single "true" model, focus on model averaging or Bayesian Model Averaging (BMA) to account for uncertainty in model selection and parameter estimation.
By embracing these alternative modeling approaches, economists can move beyond the limitations of assuming stable relationships and develop more realistic and insightful models of complex economic systems.

Detecting breaks is only the first step. Effectively incorporating this information into forecasting models is crucial for improving their accuracy and reliability:
1. Post-Break Data: The most straightforward approach is to use only the data after the most recent break for forecasting. This assumes the new regime persists into the future.
Pros: Simple, avoids contamination from outdated data.
Cons: Discards potentially valuable information, sensitive to break dating accuracy.
2. Weighted Estimation: Assign higher weights to observations closer to the forecasting horizon, discounting older data potentially affected by breaks.
Pros: Smoothly incorporates information, less sensitive to precise break dating.
Cons: Requires choosing a weighting scheme, may not fully adapt to abrupt changes.
3. Regime-Specific Forecasting: If using regime-switching models, forecast conditional on the current regime identified by the model.
Pros: Directly accounts for regime-dependent dynamics.
Cons: Relies on accurate regime identification and assumes the current regime persists.
4. Time-Varying Parameter Forecasting: If using models with time-varying parameters, use the estimated parameter path to generate dynamic forecasts.
Pros: Captures evolving relationships, provides continuous updates.
Cons: Relies on accurate parameter estimation, can be sensitive to model specification.
5. Ensemble Forecasts: Combine forecasts from multiple models, each estimated on different subsets of data or using different specifications that account for breaks.
Pros: Reduces reliance on a single model, can improve robustness.
Cons: Increases complexity, requires selecting and weighting individual forecasts.
6. Break Point Monitoring: Continuously monitor for new breaks and update the forecasting model accordingly.
Pros: Adapts to evolving dynamics, maintains model relevance.
Cons: Computationally demanding, prone to false positives if not carefully implemented.
The choice of method depends on the specific application, the nature of the detected breaks, and the forecasting horizon. A combination of these approaches can often lead to the most robust and accurate forecasts in the presence of structural breaks.

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