Firstly rather accurate approximations to the p value functions of the common Standard CUSUM test and the OLS-based CUSUM test for structural change are derived. Secondly alternative boundaries for both tests are suggested and their properties are examined by simulation of expected p values. It turns out that the power of the OLS-based CUSUM test for early and late structural changes can be improved, whereas this weakness of the Standard CUSUM test cannot be repaired by the new boundaries. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

"As a part of an effective SETAR (self-exciting threshold autoregressive) mod- eling methodology, it is important to identify processes exhibiting SETAR-type non- linearity. A number of tests of nonlinearity have been developed in the literature, including those of Keenan (1985), Petruccelli and Davies (1986), Tsay (1986, 1989), Luukkonen (1988), and Chan and Tong (1990). However, it has recently been shown that all these tests perform poorly for SETAR-type nonlinearity detection in the presence of outliers. In this project we develop an improved test for SETAR-type nonlinearity in time series. The test is an outlier-robust variant of the Petruccelli and Davies (1986) test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits (which we call CUSUM-GM). The properties of the proposed CUSUM-GM test are illustrated by means of Monte Carlo simulations. The merits, in terms of size and power, of the proposed test are evaluated relative to the test based on ordered residuals from the ordinary least squares fit (which we call CUSUM-LS) and also to that of other tests for nonlinearity developed in literature. The simulations are run for uncontaminated data and for data contaminated with additive and innovational outliers. The simulation study strongly supports the validity of the proposed robust CUSUM-GM test, particularly in situations in which outliers might be a problem."

Abstract Under the great impact and known to all, the structural changes may be obviously clear that can be observed out, when being not so obvious, should observe whether there are structural changes to appear, it is very difficult to get a clear result clearly to turn into. This paper tries to use such models as Chow test, CUSUM test, CUSUMSQ test, STAR in unknown cases, whether going to assay the data separately has structural changes, various kinds of examination ways of result received are each different to some extent, clear conclusion not unanimous and unified. The dominance the Chow test is the most obvious; Consider heteroscedasticity and autocorrelation restriction in because CUSUM test and CUSUMSQ test model, it is not apt to demonstrate the dominance instead; The STAR depends on state of the materials.

The goal of this thesis is to examine relationship between money demand, interest rates and real GDP in the Czech Republic, United Kingdom and Eurozone in time period 2005-2013. Apart from OLS regression the work will also focus on stability of the demand form money and exogeneity of money. In the thesis is among general tools as OLS and its variants used cointegration analysis for determination of exogeneity and other methods connected with it. For analysis were used quarterly data obtained from central banks of given countries and OECD statistical database.

Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test

<p>A lane departure warning system relying exclusively on a camera has several shortcomings and tends to be sensitive to, e.g., bad weather and abrupt manoeuvres. To handle these situations, the system proposed in this thesis uses a dynamic model of the vehicle and integration of relative motion sensors to estimate the vehicle’s position on the road. The relative motion is measured using vision, inertial, and vehicle sensors. All these sensors types are affected by errors such as offset, drift and quantization. However the different sensors are sensitive to different types of errors, e.g., the camera system is rather poor at detecting rapid lateral movements, a type of situation which an inertial sensor practically never fails to detect. These kinds of complementary properties make sensor fusion interesting. The approach of this Master’s thesis is to use an already existing lane departure warning system as vision sensor in combination with an inertial measurement unit to produce a system that is robust and can achieve good warnings if an unintentional lane departure is about to occur. For the combination of sensor data, different sensor fusion models have been proposed and evaluated on experimental data. The models are based on a nonlinear model that is linearized so that a Kalman filter can be applied. Experiments show that the proposed solutions succeed at handling situations where a system relying solely on a camera would have problems. The results from the testing show that the original lane departure warning system, which is a single camera system, is outperformed by the suggested system.</p>

A lane departure warning system relying exclusively on a camera has several shortcomings and tends to be sensitive to, e.g., bad weather and abrupt manoeuvres. To handle these situations, the system proposed in this thesis uses a dynamic model of the vehicle and integration of relative motion sensors to estimate the vehicle’s position on the road. The relative motion is measured using vision, inertial, and vehicle sensors. All these sensors types are affected by errors such as offset, drift and quantization. However the different sensors are sensitive to different types of errors, e.g., the camera system is rather poor at detecting rapid lateral movements, a type of situation which an inertial sensor practically never fails to detect. These kinds of complementary properties make sensor fusion interesting. The approach of this Master’s thesis is to use an already existing lane departure warning system as vision sensor in combination with an inertial measurement unit to produce a system that is robust and can achieve good warnings if an unintentional lane departure is about to occur. For the combination of sensor data, different sensor fusion models have been proposed and evaluated on experimental data. The models are based on a nonlinear model that is linearized so that a Kalman filter can be applied. Experiments show that the proposed solutions succeed at handling situations where a system relying solely on a camera would have problems. The results from the testing show that the original lane departure warning system, which is a single camera system, is outperformed by the suggested system.

Στην παρούσα εργασία παρουσιάζονται οι έλεγχοι για διαρθρωτικές μεταβολές στις αποδόσεις χρηματοοικονομικών χρονοσειρών που διερευνώνται στην διεθνή βιβλιογραφία. Έλεγχοι τύπου σωρευτικών αθροισμάτων (CUSUM) όπως των Kokoszka και Leipus, ο LM και ο LR έλεγχος του Andrews και των Bai και Perron αντίστοιχα και ο έλεγχος τύπου ελαχίστων τετραγώνων των Lavielle και Moullines. Τέλος εφαρμόζουμε τον έλεγχο των Kokoszka και Leipus για την εύρεση διαρθρωτικών μεταβολών στους δείκτες NASDAQ και S&P500. / --

This study aims at analysing how African oil benchmarks within the OPEC Reference Basket relative to the WTI and Brent benchmarks which are considered as global pricing benchmarks for the period starting from 1997-2008. The Nigerian Bonny Light and Algerian Saharan blend were the two benchmarks used for this study. A time series analysis was applied to the weekly price data series set and with the aid of a breakpoint unit root test and Cusum of Squared test to determine if there was a change in the persistence of the spread of each African benchmark relative to the global benchmarks. The results for from the unit root test indicated the presence of a structural break in the price spread in 2004 for the Bonny Light benchmark and in 2005 for the Saharan blend relative to both global benchmarks. The Cusum Squared test for the four benchmark pairings indicated a change in persistence of the price spreads. The null hypothesis was rejected for the alternative hypothesis of the price spread process having a relatively high persistence value after a while. The Cusum Test results showed a change in persistence for both African benchmarks relative to the WTI benchmark and no change in persistence relative to the Brent benchmark. The results of from the Time series analysis indicated the competitive nature of African benchmarks relative to global benchmarks and this could benefit exporting countries by virtue of setting up derivative markets. The derivative markets would allow for the trade of benchmark spreads, futures contracts, options and other financial instruments for African oil producers.

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