Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Real-Time Recognition System for Traffic Signs

The aim of this thesis project is to develop the Traffic Sign Recognition algorithm for real time. Inreal time environment, vehicles move at high speed on roads. For the vehicle intelligent system itbecomes essential to detect, process and recognize the traffic sign which is coming in front ofvehicle with high relative velocity, at the right time, so that the driver would be able to pro-actsimultaneously on instructions given in the Traffic Sign. The system assists drivers about trafficsigns they did not recognize before passing them. With the Traffic Sign Recognition system, thevehicle becomes aware of the traffic environment and reacts according to the situation.The objective of the project is to develop a system which can recognize the traffic signs in real time.The three target parameters are the system’s response time in real-time video streaming, the trafficsign recognition speed in still images and the recognition accuracy. The system consists of threeprocesses; the traffic sign detection, the traffic sign recognition and the traffic sign tracking. Thedetection process uses physical properties of traffic signs based on a priori knowledge to detect roadsigns. It generates the road sign image as the input to the recognition process. The recognitionprocess is implemented using the Pattern Matching algorithm. The system was first tested onstationary images where it showed on average 97% accuracy with the average processing time of0.15 seconds for traffic sign recognition. This procedure was then applied to the real time videostreaming. Finally the tracking of traffic signs was developed using Blob tracking which showed theaverage recognition accuracy to 95% in real time and improved the system’s average response timeto 0.04 seconds. This project has been implemented in C-language using the Open Computer VisionLibrary.

Traffic and Road Sign Recognition

This thesis presents a system to recognise and classify road and traffic signs for the purpose of developing an inventory of them which could assist the highway engineers’ tasks of updating and maintaining them. It uses images taken by a camera from a moving vehicle. The system is based on three major stages: colour segmentation, recognition, and classification. Four colour segmentation algorithms are developed and tested. They are a shadow and highlight invariant, a dynamic threshold, a modification of de la Escalera’s algorithm and a Fuzzy colour segmentation algorithm. All algorithms are tested using hundreds of images and the shadow-highlight invariant algorithm is eventually chosen as the best performer. This is because it is immune to shadows and highlights. It is also robust as it was tested in different lighting conditions, weather conditions, and times of the day. Approximately 97% successful segmentation rate was achieved using this algorithm.Recognition of traffic signs is carried out using a fuzzy shape recogniser. Based on four shape measures - the rectangularity, triangularity, ellipticity, and octagonality, fuzzy rules were developed to determine the shape of the sign. Among these shape measures octangonality has been introduced in this research. The final decision of the recogniser is based on the combination of both the colour and shape of the sign. The recogniser was tested in a variety of testing conditions giving an overall performance of approximately 88%.Classification was undertaken using a Support Vector Machine (SVM) classifier. The classification is carried out in two stages: rim’s shape classification followed by the classification of interior of the sign. The classifier was trained and tested using binary images in addition to five different types of moments which are Geometric moments, Zernike moments, Legendre moments, Orthogonal Fourier-Mellin Moments, and Binary Haar features. The performance of the SVM was tested using different features, kernels, SVM types, SVM parameters, and moment’s orders. The average classification rate achieved is about 97%. Binary images show the best testing results followed by Legendre moments. Linear kernel gives the best testing results followed by RBF. C-SVM shows very good performance, but ?-SVM gives better results in some case.

Data based Calibration System for Radar used by Vehicle Activated Signs

The accurate measurement of a vehicle’s velocity is an essential feature in adaptive vehicle activated sign systems. Since the velocities of the vehicles are acquired from a continuous wave Doppler radar, the data collection becomes challenging. Data accuracy is sensitive to the calibration of the radar on the road. However, clear methodologies for in-field calibration have not been carefully established. The signs are often installed by subjective judgment which results in measurement errors. This paper develops a calibration method based on mining the data collected and matching individual vehicles travelling between two radars. The data was cleaned and prepared in two ways: cleaning and reconstructing. The results showed that the proposed correction factor derived from the cleaned data corresponded well with the experimental factor done on site. In addition, this proposed factor showed superior performance to the one derived from the reconstructed data.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).