The recent advent of high frequency data provides researchers with transaction by transaction level data. Examples include scanner data from grocery stores or financial transactions data. These new data sets allow researchers to take an unprecedented look at the underlying economic structure of the markets. Often the hypothesis of interest is in the context of multivariate time series data. Analysis of multivariate high frequency data is complicated by the fact that the multiple processes are irregularly spaced in time with different arrival rates. This has lead many investigators to work with aggregated data which can blur the market structure and contaminate the analysis. In this paper we propose a new method of working with the dissaggregated data and develop an econometric model for the arrival rates of multivariate dependent point processes. We apply the model to financial transactions data and estimate models for the bivariate point process of transaction and limit order arrival times. Since limit orders dictate the structure of the limit order book they are a direct determinant of market liquidity. To our knowledge little work has examined the dynamic structure of limit order submissions. Since transactions represent a floor trader or market order demand for liquidity the bivariate model characterizes the dynamic behavior of liquidity supply and demand. The proposed model also allows for marks, or characteristics associated with the arrival times, to influence future arrival rates. For the stock market data analyzed we find strong evidence of codependence in the two processes and both liquidity demand and supply are influenced by past volume and prevailing spreads.
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