  This paper introduces a Threshold Asymmetric Conditional Autoregressive Range
(TACARR) formulation for modeling the daily price ranges of financial assets.
It is assumed that the process generating the conditional expected ranges at
each time point switches between two regimes, labeled as upward market and
downward market states. The disturbance term of the error process is also
allowed to switch between two distributions depending on the regime. It is
assumed that a self-adjusting threshold component that is driven by the past
values of the time series determines the current market regime. The proposed
model is able to capture aspects such as asymmetric and heteroscedastic
behavior of volatility in financial markets. The proposed model is an attempt
at addressing several potential deficits found in existing price range models
such as the Conditional Autoregressive Range (CARR), Asymmetric CARR (ACARR),
Feedback ACARR (FACARR) and Threshold Autoregressive Range (TARR) models.
Parameters of the model are estimated using the Maximum Likelihood (ML) method.
A simulation study shows that the ML method performs well in estimating the
TACARR model parameters. The empirical performance of the TACARR model was
investigated using IBM index data and results show that the proposed model is a
good alternative for in-sample prediction and out-of-sample forecasting of
volatility.
  Key Words: Volatility Modeling, Asymmetric Volatility, CARR Models, Regime
Switching.
