Threshold autoregressive modeling in finance: The price differences of equivalent assets

Threshold autoregressive (TAR) models condition the first moment of a time series on lagged information using a step‐function‐type nonlinear structure. TAR techniques are expected to be relevant in financial time‐series modeling in situations where deviations of prices from equilibrium values depend on discrete transaction costs and where market regulators follow intervention rules based on threshold values of control variables. an important finance application is in modeling the difference in prices of equivalent assets in the presence of transaction costs. the focus of this paper is on motivating the use of TAR models in this context and on the statistical estimation and testing procedures. the procedures are illustrated by modeling the difference between the prices of an index futures contract and the equivalent underlying cash index. It is found that the hypothesis of linearity is conclusively rejected in favor of threshold nonlinearity and that the estimated thresholds are largely consistent with arbitrage‐related transaction costs.