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Limit Laws in Transaction-Level Asset Price Models

Authors: Aue, Alexander
Horvath, Lajos
Hurvich, Clifford
Issue Date: 26-May-2009
Series/Report no.: CeDER-09-02
Abstract: We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such e®ects as intraday seasonal patterns in volatility, and non-trading periods that may be di®erent for the two assets. Most assumptions are stated directly on the point process, though we provide su±cient conditions on the corresponding inter-trade durations for these assumptions to hold. We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrat- ing parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. Finally, we obtain the limiting distribution of the ordinary least-squares estimator of the autoregressive parameter in a simpli¯ed transaction-level univariate model with a unit root.
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