Time-Deformation Modeling of Stock Returns Directed by Duration Processes

This paper proposes a new time-deformation model for stock returns sampled in transaction time and directed by a generalized duration process. Stochastic volatility in this model is driven by an observed duration process and a latent autoregressive process. Parameter estimation in the model is carried out by using a method of simulated moments (MSM) due to its analytical tractability and numerical stability for the proposed model. Simulations are conducted to validate the choice of moments used in the formulation of MSM. Both simulation and empirical results indicate that the proposed MSM works well for the model. The main empirical findings from the analysis of IBM transaction return data include: (i) the return distribution conditional on the duration process is not Gaussian, even though the duration process itself can marginally serve as a directing process; (ii) the return process is highly leveraged; (iii) longer trade duration tends to be associated with higher return volatility; and (iv) the proposed model is capable of reproducing a return process whose marginal density function is close to that of the empirical return process.