Threshold Autoregression for Asymmetric Cointegration

Summary

Threshold autoregression (TAR) extends a standard unit-root test to allow a series to adjust differently depending on whether it is above or below a threshold. The document illustrates the idea with the gasoline crack spread, defined as unleaded gasoline price minus West Texas Intermediate crude price. It describes prior work suggesting that this spread may move asymmetrically around a long-run fair value, with larger movements on the upside. A conventional autoregressive test uses one adjustment coefficient and therefore assumes symmetric behavior; TAR instead estimates separate coefficients for positive and negative deviations.

The proposed test compares those coefficients to assess whether adjustment is symmetric, using a Wald form of the F-test and requiring that the adjustment parameters are not both zero. When the coefficients differ, the document characterizes the cointegration as nonlinear. Its example requires a demeaned, zero-mean series and shows fitting the model and inspecting fitted values and a summary. The text explains a statistical model rather than demonstrating trading profitability. The motivating spread behavior is attributed to prior research, and the page supplies no new empirical results or trading rules.

Key ideas

• TAR allows positive and negative deviations from a threshold to have different adjustment rates.
• The example defines the gasoline crack spread as gasoline price minus WTI crude price.
• A conventional unit-root test uses a single adjustment coefficient and assumes symmetric adjustment.
• A Wald-style test can compare the two TAR coefficients to test for symmetric adjustment.
• The example requires a demeaned series, and the document provides no evidence of trading profitability.

Tags

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