This thesis concerns the asymptotic behaviour of the sequence of 1-step recursive Chow statistics and various tests derived therefrom. The 1-step statistics are produced as diagnostic output in standard econometrics software, and are expected to reflect model misspecification. Such misspecification testing is important in validating the assumptions of a model and so ensuring that subsequent inference is correct. Original contributions to the theory of misspecification testing include (i) a result on the pointwise convergence of the 1-step statistics; (ii) a result on the extreme-value convergence of the maximum of the statistics; and (iii) a result on the weak convergence of an empirical process formed by the statistics. In Chapter 2, we describe the almost sure pointwise convergence of the 1-step statistic for a broad class of time series models and processes, including unit root and explosive processes. We develop an asymptotic equivalence result, and use this to establish the asymptotic distribution of the maximum of a sequence of 1-step statistics with normal errors. This allows joint consideration of the sequence of 1-step tests via its maximum: the sup-Chow test. In Chapter 3, we use simulation to investigate the power properties of this test and compare it with benchmark tests of structural stability. We find that the sup-Chow test may have advantages when the nature of instability is unknown. In Chapter 4, we consider how the test may be adapted to situations in which the errors cannot be assumed normal. We evaluate several promising approaches, but also note a trade-off between robustness and power. In Chapter 5 we analyse an empirical process formed from the 1-step statistics, and prove a weak convergence result. Under the assumption of normal errors, the limiting distribution reduces to that of a Brownian bridge. The asymptotic approximation appears to works well even in small samples.

Advances in constraint solving and increases in processing power have enabled new approaches for automating specification-based testing. However, writing specifications and scaling techniques that utilize them remain challenging. We introduce Milao -- a novel framework for mixed imperative and declarative formulation and solving of structural constraints -- which addresses both these challenges. One, Milao introduces a mixed style for writing specifications using a combination of declarative and imperative styles, which provides flexibility in specification formulation and reduces its burden on the user. Two, it introduces a mixed technique for solving constraints using a combination of solvers in synergy. As enabling technologies, the Alloy tool-set and the Java PathFinder model checker are used. Initial experiments witness the benefits of our framework. / text

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In this thesis we investigate some of the issues involved in creating a reversible variant of the formal software development language B. We consider the effects of regarding computation as a potentially reversible process, yielding a number of new programming structures which we integrate into an implementation-level language RB0, a more expressive variant of B0, the current implementation-level language for B. Since reversibility simplifies garbage collection, in RB0 we make use of more abstract, set-based data types, normally available in B only at the specification level. Similarly, we propose extending the domain of abstract functions currently specifiable in B to allow them to become concrete functions, thereby furnishing B with a functional sub-language. We also investigate expanding the use of Lambda calculus from the abstract stage of B to the implementation. Unlike B0, RB0 will not disallow non-determinism, and can also specify what we call Prospective Value computations (which are described). The executable language implements all of these features. After introducing some preliminary concepts, we review the work leading to the rise of Reversible Computing as a possible answer to the growing problem of energy dissipation in modern processors. We describe the language RB0, and demonstrate the use of its features, introducing the companion language RB1 and its role in the process. We then introduce our execution platform, the Reversible Virtual Machine (RVM), and translate some of the examples developed earlier into RVM code. For the concrete functions, we provide a proposed syntax and translation schema to enable consistent translation to RVM, and introduce a postfix Lambda notation to link the RB0 specification to the RVM’s own postfix notation. We provide comprehensive translation schemas for those parts of RB0 which would be found in B operations; these will form the basis of an automated translation engine. In addition, we look at a denotational semantics for Bunch theory, which has proved useful in formalising the underlying concepts.

We are interested in the stochastic properties, individual and joint, of mis- specification testing when the data are generated by an autoregressive process. Good mis-specification tests are invariant to the dynamic properties of the pro- cess summarized by its characteristic roots, and to irrelevant misspecifications. Invariance in parameter space obviates inference prior to mis-specification test- ing. This is important as the latter is used to validate the former. Mutual independence of the tests allows calibration of the overall significance level. Es- tablishing such results requires work on individual tests and on their stochastic interactions. In Chapter 2, we derive the asymptotic distribution of two types of CUSUM of squares test, one implemented with standardized one-step-ahead OLS pre- diction errors and another implemented with OLS residuals. The latter is found to be valid in all but singular explosive cases, but the former only in purely non-explosive, or regular explosive cases with all roots in the explosive region of the parameter space; in Chapter 3, we show that a nuisance term arises in the mixed case. In Chapter 4, we derive numerically a finite sam- ple correction to render the tests implementable into software, and Chapter 1 contains two examples of applications. In Chapter 5, we consider inference on the parameters associated with the stationary part of the process, together with tests for a unit root, lag length, variance constancy, and normality of the regression innovations. In character- izing the joint distribution of these tests, we rely on asymptotic theory, and show independence in the limit. A simulation experiment suggests that finite sample correlations between some of the tests are statistically significant but small. Asymptotically, then, control of the overall significance level of the test procedure is feasible, and there is no reason to discount inference for the use of these mis-specification tests in model selection.

Esse trabalho mostra alguns aspectos construtivos e de sistema que devem fazer parte do projeto e da especificação de um transformador elevador, também conhecido na literatura como generator step-up transformer. O projeto do equipamento é baseado em sua especificação técnica. No entanto, algumas vezes observa-se que a especificação técnica não contempla alguns pontos de extrema importância e que poderão ser cruciais para o bom desempenho do transformador quando em serviço. Transformadores elevadores estão sujeitos a distúrbios do sistema onde operam. O efeito desses distúrbios no equipamento pode ser atenuado através de uma especificação técnica que seja a mais completa possível, no sentido de fornecer informações a respeito do sistema e conexão do transformador tanto ao gerador quanto à rede elétrica; por parte do fabricante cabe o trabalho de interpretar a especificação do equipamento, a fim de projetar um equipamento que opere de forma satisfatória face aos requisitos especificados. / This work presents some constructive and operational aspects that should be take into account on the transformer design and specification. The design of the equipment is based on its technical specification. However, sometimes, it is observed that the technical specification does not contemplate some important points which could be crucial for the good transformer performance when in service. Generator step-up transformers are subject to some system disturbance where they are connected. The effect of these disturbances on the equipment could be minimize with a technical specification as complete as possible, on the sense of provide information regarding the network and connections between generator and power transformer. On the other hand, the manufacturer has the responsibility to interpret the technical requirements in order to design an equipment that operates satisfactory.

Alloy specifications are used to define lightweight models of systems. We present Alchemy, which compiles Alloy specifications into implementations that execute against persistent databases. Alchemy translates a subset of Alloy predicates into imperative update operations, and it converts facts into database integrity constraints that it maintains automatically in the face of these imperative actions. In addition to presenting the semantics and an algorithm for this compilation, we present the tool and outline its application to a non-trivial specification. We also discuss lessons learned about the relationship between Alloy specifications and imperative implementations.

Esse trabalho mostra alguns aspectos construtivos e de sistema que devem fazer parte do projeto e da especificação de um transformador elevador, também conhecido na literatura como generator step-up transformer. O projeto do equipamento é baseado em sua especificação técnica. No entanto, algumas vezes observa-se que a especificação técnica não contempla alguns pontos de extrema importância e que poderão ser cruciais para o bom desempenho do transformador quando em serviço. Transformadores elevadores estão sujeitos a distúrbios do sistema onde operam. O efeito desses distúrbios no equipamento pode ser atenuado através de uma especificação técnica que seja a mais completa possível, no sentido de fornecer informações a respeito do sistema e conexão do transformador tanto ao gerador quanto à rede elétrica; por parte do fabricante cabe o trabalho de interpretar a especificação do equipamento, a fim de projetar um equipamento que opere de forma satisfatória face aos requisitos especificados. / This work presents some constructive and operational aspects that should be take into account on the transformer design and specification. The design of the equipment is based on its technical specification. However, sometimes, it is observed that the technical specification does not contemplate some important points which could be crucial for the good transformer performance when in service. Generator step-up transformers are subject to some system disturbance where they are connected. The effect of these disturbances on the equipment could be minimize with a technical specification as complete as possible, on the sense of provide information regarding the network and connections between generator and power transformer. On the other hand, the manufacturer has the responsibility to interpret the technical requirements in order to design an equipment that operates satisfactory.

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