Recursive partitioning is embedded into the general and well-established class of parametric models that can be fitted using M-type estimators (including maximum likelihood). An algorithm for model-based recursive partitioning is suggested for which the basic steps are: (1) fit a parametric model to a data set, (2) test for parameter instability over a set of partitioning variables, (3) if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability, (4) repeat the procedure in each of the daughter nodes. The algorithm yields a partitioned (or segmented) parametric model that can effectively be visualized and that subject-matter scientists are used to analyze and interpret. / Series: Research Report Series / Department of Statistics and Mathematics

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearily give rise to different model parameter values. We present an approach that combines generalized linear models with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's influence on a parametric model. This method conducts recursive partitioning of a the generalized linear model by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model. We will show the methods versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization. / Series: Research Report Series / Department of Statistics and Mathematics

A unified toolbox for testing, monitoring, and dating structural changes is provided for likelihood-based regression models. In particular, least-squares methods for dating breakpoints are extended to maximum likelihood estimation. The usefulness of all techniques is illustrated by assessing the stability of de facto exchange rate regimes. The toolbox is used for investigating the Chinese exchange rate regime after China gave up on a fixed exchange rate to the US dollar in 2005 and tracking the evolution of the Indian exchange rate regime since 1993. / Series: Research Report Series / Department of Statistics and Mathematics

The dissertation consists of three chapters on econometric methods related to parameter instability, forecasting and long memory. The first chapter introduces a new frequentist-based approach to forecast time series in the presence of in and out-of-sample breaks in the parameters. We model the parameters as random level shift (RLS) processes and introduce two features to make the changes in parameters forecastable. The first models the probability of shifts according to some covariates. The second incorporates a built-in mean reversion mechanism to the time path of the parameters. Our model can be cast into a non-linear non-Gaussian state-space framework. We use particle filtering and Monte Carlo expectation maximization algorithms to construct the estimates. We compare the forecasting performance with several alternative methods for different series. In all cases, our method allows substantial gains in forecasting accuracy. The second chapter extends the RLS model of Lu and Perron (2010) for the volatility of asset prices. The extensions are in two directions: a) we specify a time-varying probability of shifts as a function of large negative lagged returns; b) we incorporate a mean reverting mechanism so that the sign and magnitude of the jump component change according to the deviations of past jumps from their long run mean. We estimate the model using daily data on four major stock market indices. Compared to competing models, the modified RLS model yields the smallest mean square forecast errors overall. The third chapter proposes a method of inference about the mean or slope of a time trend that is robust to the unknown order of fractional integration of the errors. Our tests have the standard asymptotic normal distribution irrespective of the value of the long-memory parameter. Our procedure is based on using quasi-differences of the data and regressors based on a consistent estimate of the long-memory parameter obtained from the residuals of a least-squares regression. We use the exact local-Whittle estimator proposed by Shimotsu (2010). Simulation results show that our procedure delivers tests with good finite sample size and power, including cases with strong short-term correlations.

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearly give rise to different model parameter values. We present an approach that combines generalized linear models with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's in uence on a parametric model. This method conducts recursive partitioning of a generalized linear model by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model. We will show the method's versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization, and compare it to alternative approaches.

Three classes of structural change tests (or tests for parameter instability) which have been receiving much attention in both the statistics and econometrics communities but have been developed in rather loosely connected lines of research are unified by embedding them into the framework of generalized M-fluctuation tests (Zeileis and Hornik, 2003). These classes are tests based on F statistics (supF, aveF, expF tests), on OLS residuals (OLS-based CUSUM and MOSUM tests) and on maximum likelihood scores (including the Nyblom-Hansen test). We show that (represantives from) these classes are special cases of the generalized M-fluctuation tests, based on the same functional central limit theorem, but employing different functionals for capturing excessive fluctuations. After embedding these tests into the same framework and thus understanding the relationship between these procedures for testing in historical samples, it is shown how the tests can also be extended to a monitoring situation. This is achieved by establishing a general M-fluctuation monitoring procedure and then applying the different functionals corresponding to monitoring with F statistics, OLS residuals and ML scores. In particular, an extension of the supF test to a monitoring scenario is suggested and illustrated on a real-world data set. / Series: Research Report Series / Department of Statistics and Mathematics