TIME SERIES MODELLING OF HIGH FREQUENCY STOCK TRANSACTION DATA

This thesis comprises four papers concerning modelling of financial count data. Paper [1], [2] <p> and [3] advance the integer-valued moving average model (INMA), a special case of integer-valued <p> autoregressive moving average (INARMA) model class, and apply the models to the number of <p> stock transactions in intra-day data. Paper [4] focuses on modelling the long memory property of <p> time series of count data and on applying the model in a financial setting. <p> Paper [1] advances the INMA model to model the number of transactions in stocks in intraday <p> data. The conditional mean and variance properties are discussed and model extensions to <p> include, e.g., explanatory variables are offered. Least squares and generalized method of moment <p> estimators are presented. In a small Monte Carlo study a feasible least squares estimator comes out <p> as the best choice. Empirically we find support for the use of long-lag moving average models in a <p> Swedish stock series. There is evidence of asymmetric effects of news about prices on the number <p> of transactions. <p> Paper [2] introduces a bivariate integer-valued moving average (BINMA) model and applies the <p> BINMA model to the number of stock transactions in intra-day data. The BINMA model allows <p> for both positive and negative correlations between the count data series. The study shows that <p> the correlation between series in the BINMA model is always smaller than one in an absolute sense. <p> The conditional mean, variance and covariance are given. Model extensions to include explanatory <p> variables are suggested. Using the BINMA model for AstraZeneca and Ericsson B it is found that <p> there is positive correlation between the stock transactions series. Empirically, we find support for <p> the use of long-lag bivariate moving average models for the two series. <p> Paper [3] introduces a vector integer-valued moving average (VINMA) model. The VINMA <p> model allows for both positive and negative correlations between the counts. The conditional and <p> unconditional first and second order moments are obtained. The CLS and FGLS estimators are <p> discussed. The model is capable of capturing the covariance between and within intra-day time <p> series of transaction frequency data due to macroeconomic news and news related to a specific <p> stock. Empirically, it is found that the spillover effect from Ericsson B to AstraZeneca is larger <p> than that from AstraZeneca to Ericsson B. <p> Paper [4] develops models to account for the long memory property in a count data framework <p> and applies the models to high frequency stock transactions data. The unconditional and conditional <p> first and second order moments are given. The CLS and FGLS estimators are discussed. <p> In its empirical application to two stock series for AstraZeneca and Ericsson B, we find that both <p> series have a fractional integration property.