The classical approach to testing for structural change employs retrospective tests using a historical data set of a given length. Here we consider a wide array of fluctuation-type tests in a monitoring situation - given a history period for which a regression relationship is known to be stable, we test whether incoming data are consistent with the previously established relationship. Procedures based on estimates of the regression coefficients are extended in three directions: we introduce (a) procedures based on OLS residuals, (b) rescaled statistics and (c) alternative asymptotic boundaries. Compared to the existing tests our extensions offer better power against certain alternatives, improved size in finite samples for dynamic models and ease of computation respectively. We apply our methods to two data sets, German M1 money demand and U.S. labor productivity. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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

Queuing systems are important parts of our daily lives and to keep their operations at an efficient level they need to be monitored by using queuing Performance Metrics, such as average queue lengths and average waiting times. On the other hand queue lengths and waiting times are generally random variables and their distributions depend on different properties like arrival rates, service times, number of servers. We focused on detecting the change in service rates in this report. Therefore, we monitored queues by using Cumulative Sum(CUSUM) charts based on likelihood ratios and compared the Average Run Length values of different service rates.

財務危機預警模式的建立一直是國內外財金學者所感興趣的課題，從早期單純的財務比率判定到統計方法的使用，至近幾年來非統計式的類神經網路之偵測分類，其模式的演變無不在增加危機預警的能力。一方面能正確的分類失敗企業與健全企業的財務結構，一方面能早期偵測出失敗企業體質的徵兆。而本研究所建模型為擷取統計方法在分類能力上的表現與類神經網路優於統計方法上的預測能力，所結合而成的一種含有類神經網路架構的動態化財務危機預警模式。以台灣股票上市公司民國七十一年以後打入全額交割股的企業為失敗企業，並在相同期間之相同產業內，挑選規模相近之正常企業為配對之健全企業。為了方便網路的學習，我們將樣本區分為以民國七十四年以前打入全額交割股的配對企業為供網路訓練之前期樣本，以及民國七十五年以後打入全額交割股的配對企業為建立財務危機預警模式之後期樣本。其實證結果有幾項結論： 　　1.經由後期樣本所推估的多變量CUSUM模式(4.1)中，我們發現固定資產／總資產比率對模式的分類結果較不敏感，而每股盈餘／每股市價比率對模式的分類結果最為敏感，且敏感度將近固定資產／總資產比率的十倍。 　　2.倒傳遞類神經網路在預測各期財務比率的誤差均方根為0.051，而多變量CUSUM模式的正確分類率為71.43%，且百分之八十的失敗企業在其危機發生（打入全額交割股）時的前六季左右，動態化多變量CUSUM模式即可偵測出徵兆。 　　3.一般而言，失敗企業的固定資產／總資產比率與存貨／營業收入比率較健全企業來得高；而失敗企業的營運資本／總資產比率，營業利益／總資產比率及每股盈餘／每股市價比率則低於健全企業，尤其在危機發生時前六季左右，更是急速下降。因此，失敗企業的流動性普遍不足，存貨積壓的結果，造成營運資金週轉不靈，而走向營運困難的窘境。

<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>

<p>Scania CV AB is a large manufacturer of heavy duty trucks that, with an increasingly stricter emission legislation, have a rising demand for an effective On Board Diagnosis (OBD) system. One idea for improving the OBD system is to employ a model for the construction of an observer based diagnosis system. The proposal in this report is, because of a nonlinear model, to use a nonlinear filtering method for improving the needed state estimates. Two nonlinear filters are tested, the Particle Filter (PF) and the Extended Kalman Filter (EKF). The primary objective is to evaluate the use of the PF for Fault Detection and Isolation (FDI), and to compare the result against the use of the EKF.</p><p>With the information provided by the PF and the EKF, two residual based diagnosis systems and two likelihood based diagnosis systems are created. The results with the PF and the EKF are evaluated for both types of systems using real measurement data. It is shown that the four systems give approximately equal results for FDI with the exception that using the PF is more computational demanding than using the EKF. There are however some indications that the PF, due to the nonlinearities, could offer more if enough CPU time is available.</p>

During recent years there has been a great focus on the climate changes within the media. More or less every day more newspaper articles are presented about the global warming issue and the effect on us human race. Climate models predict higher temperatures and more rain in the northern part of Europe. It is also predicted that the weather will become more extreme e.g. it will rain a lot during longer periods than has been the norm. If these predictions are correct, the amount of water that is going to be transported away in streams and rivers will increase and so also will the subsoil water level. The latter increases the risk for landslides in areas with fine grained soils. An early warning system that is able to alert people before a landslide take place would be of great interest. The purpose of this work is to develop a complete real-time displacement monitoring system based on observations from several GPS-receivers that could be used as an early warning system. Due to the complex correlation structure of the traditionally used double differences, an alternative method based on undifferenced observations is used. Theoretically this approach shows some advantages and simplifies the correlative structure of observables compared to the double differenced method. A complete model for the undifferenced approach is presented in this thesis including its software implementation. A displacement detection system includes not only the positioning algorithms, but also methods to detect if any displacement occurs. There are many methods available to discriminate displacements, which are used in the traditional control of manufacturing processes. Several of these methods are compared in this thesis, such as the Shewhart chart, different Weighted Moving Average (WMA) charts and the CUmulative SUMmation (CUSUM). Practical tests show that it is possible to detect an abrupt shift on sub centimetre level at the same epoch as the shift occurs. Smaller shifts are also detectable with the applied approach but with a slightly longer detection time. / QC 20100624

When flying a fighter aircraft such as the JAS 39 Gripen, the pilot is exposed to high g-loads. In order to prevent the draining of blood from the brain during this stress an anti-g protection system is used. The system consists of a pair of trousers, called the anti-g trousers, with inflatable bladders. The bladders are filled with air, pressing tightly on to the legs in order to prevent the blood from leaving the upper part of the body. The purpose of this thesis is to detect if the pressure of the anti-g trousers is deviating from the desired value. This is done by developing a detection algorithm which gives two kinds of alarm. One is given during minor deviations using a CUSUM test, and one is given at grave deviations, based on different conditions including residual, derivative and time. The thresholds, in which between the pressure should lie in a faultless system, are calculated from the g-load value. The thresholds are based upon given static guidelines for the pressure tolerance area and are modified in order to adapt to the estimated dynamics of the system. The values of the input signals, pressure and g-load, were taken from real flight sessions. The validation has been performed using both faultless and faulty flight sequences, with low false alarm rate and no missed detections. All together the detection system is considered to work well.

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.

For the last several decades, sequential change point problems have been studied in both the theoretical area (sequential analysis) and the application area (industrial SPC). In the conventional application, the baseline process is assumed to be stationary, and the shift pattern is a step function that is sustained after the shift. However, in biosurveillance, the underlying assumptions of problems are more complicated. This thesis investigates several issues in biosurveillance such as non-homogeneous populations, spatiotemporal surveillance methods, and correlated structures in regional data. The first part of the thesis discusses popular surveillance methods in sequential change point problems and off-line problems based on count data. For sequential change point problems, the CUSUM and the EWMA have been used in healthcare and public health surveillance to detect increases in the rates of diseases or symptoms. On the other hand, for off-line problems, scan statistics are widely used. In this chapter, we link the method for off-line problems to those for sequential change point problems. We investigate three methods--the CUSUM, the EWMA, and scan statistics--and compare them by conditional expected delay (CED). The second part of the thesis pertains to the on-line monitoring problem of detecting a change in the mean of Poisson count data with a non-homogeneous population size. The most common detection schemes are based on generalized likelihood ratio statistics, known as an optimal method under Lodern's criteria. We propose alternative detection schemes based on the weighted likelihood ratios and the adaptive threshold method, which perform better than generalized likelihood ratio statistics in an increasing population. The properties of these three detection schemes are investigated by both a theoretical approach and numerical simulation. The third part of the thesis investigates spatiotemporal surveillance based on likelihood ratios. This chapter proposes a general framework for spatiotemporal surveillance based on likelihood ratio statistics over time windows. We show that the CUSUM and other popular likelihood ratio statistics are the special cases under such a general framework. We compare the efficiency of these surveillance methods in spatiotemporal cases for detecting clusters of incidence using both Monte Carlo simulations and a real example. The fourth part proposes multivariate surveillance methods based on likelihood ratio tests in the presence of spatial correlations. By taking advantage of spatial correlations, the proposed methods can perform better than existing surveillance methods by providing the faster and more accurate detection. We illustrate the application of these methods with a breast cancer case in New Hampshire when observations are spatially correlated.