Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

Road network and GPS tracking with data processing and quality assessment

GPS technology has been embedded into portable, low-cost electronic devices nowadays to track the movements of mobile objects. This implication has greatly impacted the transportation field by creating a novel and rich source of traffic data on the road network. Although the promise offered by GPS devices to overcome problems like underreporting, respondent fatigue, inaccuracies and other human errors in data collection is significant; the technology is still relatively new that it raises many issues for potential users. These issues tend to revolve around the following areas: reliability, data processing and the related application. This thesis aims to study the GPS tracking form the methodological, technical and practical aspects. It first evaluates the reliability of GPS based traffic data based on data from an experiment containing three different traffic modes (car, bike and bus) traveling along the road network. It then outline the general procedure for processing GPS tracking data and discuss related issues that are uncovered by using real-world GPS tracking data of 316 cars. Thirdly, it investigates the influence of road network density in finding optimal location for enhancing travel efficiency and decreasing travel cost. The results show that the geographical positioning is reliable. Velocity is slightly underestimated, whereas altitude measurements are unreliable.Post processing techniques with auxiliary information is found necessary and important when solving the inaccuracy of GPS data. The densities of the road network influence the finding of optimal locations. The influence will stabilize at a certain level and do not deteriorate when the node density is higher.