Umeå Economic Studies,
Umeå University, Department of Economics

Abstract: This thesis comprises four papers concerning modelling of financial count data. Paper [1], [2]

and [3] advance the integer-valued moving average model (INMA), a special case of integer-valued

autoregressive moving average (INARMA) model class, and apply the models to the number of

stock transactions in intra-day data. Paper [4] focuses on modelling the long memory property of

time series of count data and on applying the model in a financial setting.

Paper [1] advances the INMA model to model the number of transactions in stocks in intraday

data. The conditional mean and variance properties are discussed and model extensions to

include, e.g., explanatory variables are offered. Least squares and generalized method of moment

estimators are presented. In a small Monte Carlo study a feasible least squares estimator comes out

as the best choice. Empirically we find support for the use of long-lag moving average models in a

Swedish stock series. There is evidence of asymmetric effects of news about prices on the number

of transactions.

Paper [2] introduces a bivariate integer-valued moving average (BINMA) model and applies the

BINMA model to the number of stock transactions in intra-day data. The BINMA model allows

for both positive and negative correlations between the count data series. The study shows that

the correlation between series in the BINMA model is always smaller than one in an absolute sense.

The conditional mean, variance and covariance are given. Model extensions to include explanatory

variables are suggested. Using the BINMA model for AstraZeneca and Ericsson B it is found that

there is positive correlation between the stock transactions series. Empirically, we find support for

the use of long-lag bivariate moving average models for the two series.

Paper [3] introduces a vector integer-valued moving average (VINMA) model. The VINMA

model allows for both positive and negative correlations between the counts. The conditional and

unconditional first and second order moments are obtained. The CLS and FGLS estimators are

discussed. The model is capable of capturing the covariance between and within intra-day time

series of transaction frequency data due to macroeconomic news and news related to a specific

stock. Empirically, it is found that the spillover effect from Ericsson B to AstraZeneca is larger

than that from AstraZeneca to Ericsson B.

Paper [4] develops models to account for the long memory property in a count data framework

and applies the models to high frequency stock transactions data. The unconditional and conditional

first and second order moments are given. The CLS and FGLS estimators are discussed.

In its empirical application to two stock series for AstraZeneca and Ericsson B, we find that both

series have a fractional integration property.

Keywords: Count data; Intra-day; High frequency; Time series; Estimation; Long memory; Finance

JEL-codes: C13; C22; C25; C51; G12; G14

120 pages, April 11, 2006

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