Time Series Modelling Of High Frequency Stock Transaction Data
This thesis comprises four papers concerning modelling of financial count data. Paper ,  and  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  focuses on modelling the long memory property of time series of count data and on applying the model in a financial setting. Paper  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  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  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  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.
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- Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004.
"Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks,"
Umeå Economic Studies
637, Umeå University, Department of Economics.
- Kurt Brannas & A. M. M. Shahiduzzaman Quoreshi, 2010. "Integer-valued moving average modelling of the number of transactions in stocks," Applied Financial Economics, Taylor & Francis Journals, vol. 20(18), pages 1429-1440.
- Bhardwaj, Geetesh & Swanson, Norman R., 2006.
"An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series,"
Journal of Econometrics,
Elsevier, vol. 131(1-2), pages 539-578.
- Geetesh Bhardwaj & Norman Swanson, 2004. "An Empirical Investigation of the Usefulness of ARFIMA Models for Predicting Macroeconomic and Financial Time Series," Departmental Working Papers 200422, Rutgers University, Department of Economics.
- Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
- Francis X. Diebold, 1988. "Random walks versus fractional integration: power comparisons of scalar and joint tests of the variance-time function," Finance and Economics Discussion Series 41, Board of Governors of the Federal Reserve System (U.S.).
- Andrew W. Lo, 1989.
"Long-term Memory in Stock Market Prices,"
NBER Working Papers
2984, National Bureau of Economic Research, Inc.
- Bask, Mikael, 1998. "Essays on Exchange Rates: Deterministic Chaos and Technical Analysis," Umeå Economic Studies 465, Umeå University, Department of Economics.
- Quoreshi, Shahiduzzaman, 2005. "Bivariate Time Series Modelling of Financial Count Data," Umeå Economic Studies 655, Umeå University, Department of Economics.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
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