In financial markets, transaction durations refer to the duration time between two consecutive trades. It is common that more frequent trades are expected to be followed by shorter durations between consecutive transactions, while less frequent trades are expected to be followed by longer durations. Autoregressive conditional duration (ACD) model was developed to model transaction durations, based on the assumption that the expected average duration is dependent on the past durations. Empirically, transaction durations possess much longer memory than expected. The autocorrelation functions of durations decay slowly and are still significant after a large number of lags. Therefore, the fractionally integrated autoregressive conditional duration (FIACD) model was proposed to model this kind of long memory behavior. The ACD model possesses short memory as the dependence of the past durations will die out exponentially. The FIACD model possesses much longer memory as the dependence of the past durations will decay hyperbolically. However, the modeling result would be misleading if the actual dependence of the past durations decays between exponential rate and hyperbolic rate. Neither of these models can truly reveal the memory properties in this case. This thesis proposes a new duration model, named as the hyperbolic autoregressive conditional duration (HYACD) model, which combines the ACD model and the FIACD model into one. It possesses both short memory and long memory properties and allows the dependence of the past durations to decay between the exponential rate and the hyperbolic rate. It also indicates whether the dependence is close to short memory or long memory. The model is applied to the transaction data of AT&T and McDonald stocks traded on NYSE and statistically positive results are obtained when it is compared to the ACD model and the FIACD model. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

This thesis evaluates the effect of electricity co-operation regarding import and export on electricity prices for OECD countries and on CO2 emissions for the world. In addition, the study investigates which kinds of renewable energies provide the best economic future for Canada and the U.S. There are three main sections to the thesis. Firstly, panel data analysis determines the electricity price functions, using 29 OECD countries’ yearly data from 1980 to 2007. Membership of the European Union, used to investigate effect of high level co-operation on price, is seen to decrease household and industry prices, but is not significant for household price. The effect of electricity trading in OECD countries is not found to deliver cheaper electricity suggesting that these countries need to co-operate more closely to increase competition and improve efficiency in electricity markets. Secondly, panel data analysis determines parameters of the CO2 emissions function, using 131 countries’ yearly data from 1971 to 2007. The world results show that electricity co-operation is highly significant in decreasing CO2 emissions per unit of generation, thus supporting the hypothesis. At the continent level, Asia shows the highest CO2 decrease from electricity import, with the lowest decrease being for Africa. Electricity export for North America, Latin America and Europe is found to be highly significant in decreasing CO2 emissions. Finally, time series analysis of yearly data for Canada and the U.S. from 1978 to 2009 is used to determine the electricity price functions. For Canada, electricity import is found to be highly significant in decreasing household electricity price, but not so for the U.S. Renewable energies such as wind and hydro are seen to be the future of electricity generation for Canada, but the results for the U.S. indicate that no type of renewable energy can reduce electricity price.

This thesis examines the statistical properties of the Poisson AR(1) model of Al-Osh and Alzaid (1987) and McKenzie (1988). The analysis includes forecasting, estimation, testing for independence and specification and the addition of regressors to the model. The Poisson AR(1) model is an infinite server queue, and as such is well suited for modeling short-term disability claimants who are waiting to recover from an injury or illness. One of the goals of the thesis is to develop statistical methods for analyzing series of monthly counts of claimants collecting short-term disability benefits from the Workers' Compensation Board (WCB) of British Columbia. We consider four types of forecasts, which are the k-step ahead conditional mean, median, mode and distribution. For low count series the k-step ahead conditional distribution is practical and much more informative than the other forecasts. We consider three estimation methods: conditional least squares (CLS), generalized least squares (GLS) and maximum likelihood (ML). In the case of CLS estimation we find an analytic expression for the information and in the GLS case we find an approximation for the information. We find neat expressions for the score function and the observed Fisher information matrix. The score expressions leads to new definitions of residuals. Special care is taken to test for independence since the test is on the boundary of the parameter space. The score test is asymptotically equivalent to testing whether the CLS estimate of the correlation coefficient is zero. Further we define a Wald and likelihood ratio test. Then we use the general specification test of McCabe and Leybourne (1996) to test whether the model is sufficient to explain the variation found in the data. Next we add regressors to the model and update our earlier forecasting, estimation and testing results. We also show the model is identifiable. We conclude with a detailed application to monthly WCB claims counts. The preliminary analysis includes plots of the series, autocorrelation function and partial autocorrelation function. Model selection is based on the preliminary analysis, t-tests for the parameters, the general specification test and residuals. We also include forecasts for the first six months of 1995.

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