| Abstract: |
We propose a new transaction-level bivariate log-price model, which yields
fractional or standard cointegration. The model provides a link between market
microstructure and lower-frequency observations. The two ingredients of our
model are a Long Memory Stochastic Duration process for the waiting times
between trades, and a pair of stationary noise processes which determine the
jump sizes in the pure-jump log-price process. Our model includes feedback
between the disturbances of the two log-price series at the transaction level,
which induces standard or fractional cointegration for any fixed sampling
interval. We prove that the cointegrating parameter can be consistently
estimated by the ordinary least-squares estimator, and obtain a lower bound on
the rate of convergence. We propose transaction-level method-of-moments
estimators of the other parameters in our model and discuss the consistency of
these estimators. We then use simulations to argue that suitably-modified
versions of our model are able to capture a variety of additional properties
and stylized facts, including leverage, and portfolio return autocorrelation
due to nonsynchronous trading. The ability of the model to capture these
effects stems in most cases from the fact that the model treats the
(stochastic) intertrade durations in a fully endogenous way. |