This thesis discusses various issues in the estimation of models for count data. In the first part of the thesis, we derive an analytic expression for the bias of the maximum likelihood estimator (MLE) of the parameter in a doubly-truncated Poisson distribution, which proves highly effective as a means of bias correction. We explore the circumstances under which bias is likely to be problematic, and provide some indication of the statistical significance of the bias. Over a range of sample sizes, our method outperforms the alternative of bias correction via the parametric bootstrap. We show that MLEs obtained from sample sizes which elicit appreciable bias also have sampling distributions which are unsuited to be approximated by large-sample asymptotics, and bootstrapping confidence intervals around our bias-adjusted estimator is preferred, as two tiers of bootstrapping may incur a heavy computational burden. Modelling count data where the counts are strictly positive is often accomplished using a positive Poisson distribution. Inspection of the data sometimes reveals an excess of ones, analogous to zero-inflation in a regular Poisson model. The latter situation has well developed methods for modelling and testing, such as the zero-inflated Poisson (ZIP) model, and a score test for zero-inflation in a ZIP model. The issue of count inflation in a positive Poisson distribution does not seem to have been considered in a similar way. In the second part of the thesis, we propose a one-inflated positive Poisson (OIPP) model, and develop a score test to determine whether there are “too many” ones for a positive Poisson model to fit well. We explore the performance of our score test, and compare it to a likelihood ratio test, via Monte Carlo simulation. We find that the score test performs well, and that the OIPP model may be useful in many cases. The third part of the thesis considers the possibility of one-inflation in zero-truncated data, when overdispersion is present. We propose a new model to deal with such a phenomenon, the one-inflated zero-truncated negative binomial (OIZTNB) model. The finite sample properties of the maximum likelihood estimators for the parameters of such a model are discussed. This Chapter considers likelihood ratio tests which assist in specifying the OIZTNB model, and investigates the finite sample properties of such tests. The OIZTNB model is illustrated using the medpar data set, which describes the hospital length of stay for a set of patients in Arizona. This is a data set that is widely used to highlight the merits of the zero-truncated negative binomial (ZTNB) model. We find that our OIZTNB model fits the data better than does the ZTNB model, and this leads us to conclude that the data are generated by a one-inflated process. / Graduate

No description available.

No description available.

In economic time series modelling, dynamic relationships frequently have to be modelled where the explanatory variables influence the dependent variable over more than one period. Such dynamic relationships are found in business cycle forecasting with leading indicators, in marketing models describing the relationship between advertising and sales, and in many traditional econometric models. In this dissertation the transfer function model proposed by Box and Jenkins is used to describe the dynamic structure. There are several approaches that could be used to specify the model. A two-step regression approach is proposed by the author and tested by three simulation studies. Finally, the regression approach and two other approaches are used to identify transfer function models for the Swedish Index of Industrial Production using financial variables as leading indicators. / Diss. Stockholm : Handelshögsk. S. 1-22: sammanfattning, s. 23-162: 4 uppsatser

During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced. / Diss. Stockholm : Handelshögsk., 2004

The general theme of this thesis is theoretical properties and evaluation of volatility models. The thesis consists of four papers. In the first chapter the moment structure of the EGARCH model is derived. The second chapter contains new results on the A-PARCH model. The third chapter is about certain stylized facts of financial time series and the idea is to investigate how well the GARCH, EGARCH and ARSV models are able to reproduce these characteristics. The fourth chapter is about evaluating the EGARCH model. A more detailed overview of the chapters follows next.  In Chapter 1 we derive the condition for the existence of moments, the expression for the kurtosis and the one for the autocorrelation function of positive powers of the absolute-valued observations for the EGARCH model. The results of the paper are useful, for example, if we want to compare the EGARCH model with the GARCH model. They reveal certain differences in the moment structure between these models. While the autocorrelations of the squared observations decay exponentially in the GARCH model, the decay rate is not exponential in the EGARCH model. While for the GARCH model the conditions for parameters allowing the existence of higher-order moments become more and more stringent for each even moment this is not the case for the EGARCH model. The explicit expressions of the autocorrelation structure of the positive powers of the absolute-valued observations of the model are particularly important in the considerations of Chapter 3 of the thesis.The A-PARCH model contains a particular positive power parameter. By letting the power parameter approach zero, the A-PARCH family of models also includes a family of EGARCH models as a special case. In Chapter 2 we derive the autocorrelation function of squared and logarithmed observations for the A-PARCH family of models and show that it may be obtained as a limiting case of a general power ARCH (GPARCH) model. An interesting thing to notice is that the autocorrelation structure of this GPARCH process, if it exists, is exponential, and that this property is retained at the limit as the power parameter approaches zero, which means that the autocorrelation function of the process of logarithms of squared observations also decay exponentially. While this is true for the logarithmed squared observations of an EGARCH process it cannot simultaneously be true for the untransformed observations defined by these processes as we in Chapter 1 have demonstrated.In order to explain the role of the power parameter we present a detailed analysis of how the autocorrelation functions of the squared observations differ across members of the GPARCH models. In an empirical example we also show that the estimated power parameter considerably improves the correspondence between the estimated autocorrelations on the one hand and the autocorrelation estimates from the model on the other. Financial time series seem to share a number of characteristic features, sometimes called stylized facts. Given a set of stylized facts, one may ask the following question: "Have popular volatility models been parameterized in such a way that they can accommodate and explain the most common stylized facts visible in the data?" Models for which the answer is positive may be viewed as suitable for practical use. In Chapter 3, possible answers to this question for the three popular models of volatility, GARCH, EGARCH and ARSV models are investigated. Model evaluation is an important part of modelling not only for the conditional mean models but for the conditional variance specifications as well. In Chapter 4 we consider misspecification tests for an EGARCH model. We derive two new misspecification tests for an EGARCH model. Because the tests of an EGARCH model against a higher-order EGARCH model and testing parameter constancy are parametric, the alternative may be estimated if the null hypothesis is rejected. This is useful for a model builder who wants to find out possible weakness of estimated specification. Furthermore, we investigate various ways of testing the EGARCH model against GARCH ones as another check of model adequacy. An empirical example shows that there is substantial evidence for parameter nonconstancy in daily return series of the Stockholm Stock Exchange. / Diss. Stockholm : Handelshögsk., 2004

Thesis (M.S.)--Michigan State University. Dept. of Agricultural Economics, 2006. / Title from PDF t.p. (viewed on Nov. 20, 2008) Includes bibliographical references (p. 80-84). Also issued in print.

Thesis (M.S.F.)--University of Nevada, Reno, 2007. / "December, 2007." Includes bibliographical references (leaves 55-60). Online version available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [p. 72]-79).

Thesis (Ph. D.)--University of Chicago, Dept. of Economics, June 1999. / Includes bibliographical references. Also available on the Internet.