Threshold Autoregression for Asymmetric Spread Adjustment

Summary

The document implements a threshold autoregressive model for testing whether a spread adjusts differently after positive and negative deviations. It first differences the input series to form changes, lags the spread by one period, and assigns each lagged value to a nonnegative or negative regime. Separate regressors then represent the lagged spread in each regime, and ordinary least squares estimates their adjustment coefficients.

The summary procedure reports each coefficient and Wald tests for whether each regime coefficient is zero and whether the two coefficients are equal. This provides a way to examine stationarity and asymmetric mean reversion in a spread series. The code assumes the input represents an appropriate spread, uses a zero threshold, and does not show data preparation, lag selection, model diagnostics, or empirical results. Those choices matter for inference, so the implementation alone does not establish a profitable trading signal or validate its statistical assumptions.

Key ideas

• The model separates spread adjustment into regimes based on whether the lagged spread is nonnegative or negative.
• It regresses spread changes on the regime-specific lagged spread terms.
• Wald tests assess whether each adjustment coefficient is zero and whether the coefficients differ.
• The implementation uses a zero threshold and provides no diagnostics or trading performance evidence.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.