This thesis deals with the problem of detecting faults in an environment where the measurements are affected by additive noise. To do this, a residual sensitive to faults is derived and statistical methods are used to distinguish faults from noise. Standard methods for fault detection compare a batch of data with a model of the system using the generalized likelihood ratio. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. One method to handle this is the parity-space method which solves the problem by removing the influence of the initial state using a projection. In this thesis, the case where prior knowledge about the initial state is available is treated. This can be obtained for example from a Kalman filter. Combining the prior estimate with a minimum variance estimate from the data batch results in a smoothed estimate. The influence of the estimated initial state is then removed. It is also shown that removing the influence of the initial state by an estimate from the data batch will result in the parity-space method. To model slowly changing faults, an efficient parameterization using Chebyshev polynomials is given. The methods described above have been applied to an Inertial Measurement Unit, IMU. The IMU usually consists of accelerometers and gyroscopes, but has in this work been extended with a magnetometer. Traditionally, the IMU has been used to estimate position and orientation of airplanes, missiles etc. Recently, the size and cost has decreased making it possible to use IMU:s for applications such as augmented reality and body motion analysis. Since a magnetometer is very sensitive to disturbances from metal, such disturbances have to be detected. Detection of the disturbances makes compensation possible. Another topic covered is the fundamental question of observability for fault inputs. Given a fixed or linearly growing fault, conditions for observability are given. The measurements from the IMU show that the noise distribution of the sensors can be well approximated with white Gaussian noise. This gives good correspondence between practical and theoretical results when the sensor is kept at rest. The disturbances for the IMU can be approximated using smooth functions with respect to time. Low rank parameterizations can therefore be used to describe the disturbances. The results show that the use of smoothing to obtain the initial state estimate and parameterization of the disturbances improves the detection performance drastically.

Model diagnostics for normal and non-normal state space models is based on recursive residuals which are defined from the one-step ahead predictive distribution. Routine calculation of these residuals is discussed in detail. Various tools of diagnostics are suggested to check e.g. for wrong observation distributions and for autocorrelation. The paper also covers such topics as model diagnostics for discrete time series, model diagnostics for generalized linear models, and model discrimination via Bayes factors. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this study, neutral real interest rate gap and output gap are estimated jointly under two different multivariate unobserved components models with the motivation to provide empirical measures that can be used to analyze the amount of stimulus that monetary policy is passing on to the economy, and to understand historical macroeconomic developments. In the analyses, Kalman filter technique is applied to a small-scale macroeconomic model of the Turkish economy to estimate the unobserved variables for the period 1989-2005. In addition, two alternative specifications for neutral real interest rate are used in the analyses. The first model uses a random walk model for the neutral real interest rate, whereas the second one employs more structural specification, which specifically links the neutral real rate with the trend growth rate and the long-term course of the risk premium. Comparison of the models developed by using various performance criteria clearly indicates the use of more structural specification against random walk specification. Results suggest that though there is relatively high uncertainty surrounding the neutral real interest rate estimates to use them directly in the policy-making process, estimates appear to be very useful for ex-post monetary policy evaluations.

This portfolio of compositions investigates the adaptation of state-space models, frequently used in engineering control theory, to the electroacoustic composition context. These models are mathematical descriptions of physical systems that provide several variables representing the system’s behaviours. The composer adapts a set of state-space models of either abstract, mechanical or electrical systems to a music creation environment. She uses them in eight compositions: five mixed media multi-channel pieces and three mixed media pieces. In the portfolio, the composer investigates multiple ways of meaningfully mapping these system’s behaviours into music parameters. This is done either by exploring and creating timbre in synthetic sound, or by transforming existing sounds. The research also involves the process of incorporating state-space models as a real-time software tool using Max and SuperCollider. As real-time models offer several variables of continuous evolutions, the composer mapped them to different dimensions of sound simultaneously. The composer represented the model’s evolutions with either short/interrupted, long or indefinitely evolving sounds. The evolution implies changes in timbre, length and dynamic range. The composer creates gestures, textures and spaces based on the model’s behaviours. The composer explores how the model’s nature influences the musical language and the integration of these with other music sources such as recordings or musical instruments. As the models represent physical processes, the composer observes that the resulting sounds evolve in organic ways. Moreover, the composer not only sonifies the real-time models, but actually excites them to cause changes. The composer develops a compositional methodology which involves interacting with the models while observing/designing changes in sound. In that sense, the composer regards real-time state-space models as her own instruments to create music. The models are regarded as additional forces and as sound transforming agents in mixed media pieces. In fixed media pieces, the composer additionally exploits their linearity to create space through sound de-correlation.

[pt] Esta dissertação tem como objetivo principal a apresentação, discussão e implementação de um modelo de espaço de estado, derivado do modelo desenvolvido por De Jong & Zenhwirth, no cenário de estimação de reservas IBNR. O modelo visa obter uma distribuição para as reservas e seu desvio padrão, que permite obter um intervalo de confiança para a estimativa. Também são propostas extensões para o modelo. / [en] The main purpose of this master thesis is the presentation, discussion and implementation of a state space model, derived from the De Jong & Zehnwirth model, on the IBNR Reserve estimation scenario. The model tries to obtain a distribution for the reserves and its standard deviation as well, allowing the cofidence interval estimation. Extensions for the model are also discussed.

Prediction of energy load profiles is an important topic in Smart Grid technologies. Accurate forecasts can lead to reduced costs and decreased dependency on commercial power suppliers by adapting to prices on energy market, efficient utilisation of solar and wind energy and sophisticated load scheduling. This thesis compares various statistical and machine learning models and their ability to forecast load profile for an entire day divided into 48 half-hour intervals. Additionally, we examine various preprocessing methods and their influence on the accuracy of the models. We also compare a variety of imputation methods that are designed to reconstruct missing observation commonly present in energy consumption data.

Bird migration is a poorly-known yet important phenomenon, as understanding movement patterns of birds can inform conservation strategies and public health policy for animal-borne diseases. Recent advances in wildlife tracking technology, in particular the Motus system, have allowed researchers to track even small flying birds and insects with radio transmitters that weigh fractions of a gram. This system relies on a community-based distributed sensor network that detects tagged animals as they move through the detection nodes on journeys that range from small local movements to intercontinental migrations. The quantity of data generated by the Motus system is unprecedented, is on its way to surpass the size of all other centralized databases of animal detection and requires novel statistical methods. Building from the bsam package in R, I propose two new biologically informed Bayesian state-space models for animal movement in JAGS that include informed assumptions about songbird behavior. I evaluate the models using a simulation study in realistic conditions of data missingness. One of these models is generalized to a hierarchical version that fits population-level movement through joint estimation of movement parameters over multiple animal tracks. To apply the models, I then employ a localization routine on a Motus data set from migrating songbirds (Red-eyed Vireos - Vireo olivaceus) from the Eastern coast of North America. This allows me to apply the new hierarchical model and its predecessor to estimate unobserved locations and behaviors. Migratory flights were observed to occur mostly in the evenings along the coast and directed migratory flights were detected over water over e.g. the Bay of Fundy, the Long Island Sound and the New York Bight. Area-restricted searches were confined to coastal areas, in particular the Gulf of Maine, Long Island and Cape May.

This thesis deals with the use of statistical state space models of exponential smooth- ing for estimating the conditional probability distribution of future values of time series. This knowledge allows calculation of interval predictions, not only point forecasts. Meth- ods of exponential smoothing are described and set into the context of state space models. Analytical and simulation methods used in the calculation of interval predictions are presented, in particular simulations based on assumption of normality, bootstrap method or estimated parametric model. The methods are applied to simulated as well as real data and their results are compared. 1

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[pt] Nesse artigo aplicamos a técnica de estimação dos nowcasts apresentada por Giannone, Reichlin e Small (2008), para o PIB e inflação brasileiros. Extraímos informações de um elevado número de variáveis e produzimos modelos capazes de informar contemporaneamente uma medida para as variáveis em questão. Em posse dessa leitura cotidiana, produzida por esses modelos, estimamos uma regra de Taylor diária para o Banco Central do Brasil (BCB), o que permitiu melhor identificar choques monetários e alterações na função de reação do BCB ao longo do tempo. Concluímos, primeiramente, que os modelos nowcasts apresentam acurácia comparável às previsões do relatório Focus do BCB. Segundo, 2 (duas) comparações históricas realizadas mostraram indícios que nossa proxy para choques monetários diários está relacionada às decisões explícitas de política monetária. Por fim, encontramos evidências que os modelos nowcasts puderam capturar grande parte da informação relevante para a determinação da taxa de juros de curto prazo, o que deveria estimular a aplicação de tais modelos nos processos decisórios públicos e privados. / [en] In this article we apply the two-steps nowcasting method, described in Giannone, Reichlin, and Small (2008), to build nowcast models for Brazilian GDP and inflation. Throught the application of this method, we could extract information from a large data-set and build models which could be used to produce a daily measurement of GDP and inflation. Using this measurement was possible to build a daily Taylor rule for the Brazilian Central Bank (BCB). This new application of nowcast models allowed us to extract a daily measurement of monetary shocks. Our study produced three main findings. First, the nowcast model showed an accuracy close to projections presented in the Focus survey. Second, we identified by historical comparison that the monetary shocks proxy, measured by the differences between the daily Taylor rule and the movements in the short-term interest rate, are related with unanticipated monetary policies decisions. Finally, nowcasts were able to capture a great part of relevant information to determine the short-term interest rate, which should stimulate the policymakers and financial markets members to apply those models.