Real-time Traffic Flow Detection and Prediction Algorithm: Data-Driven Analyses on Spatio-Temporal Traffic Dynamics

Traffic flows over time and space. This spatio-temporal dependency of traffic flow should be considered and used to enhance the performance of real-time traffic detection and prediction capabilities. This characteristic has been widely studied and various applications have been developed and enhanced. During the last decade, great attention has been paid to the increases in the number of traffic data sources, the amount of data, and the data-driven analysis methods. There is still room to improve the traffic detection and prediction capabilities through studies on the emerging resources. To this end, this dissertation presents a series of studies on real-time traffic operation for highway facilities focusing on detection and prediction.First, a spatio-temporal traffic data imputation approach was studied to exploit multi-source data. Different types of kriging methods were evaluated to utilize the spatio-temporal characteristic of traffic data with respect to two factors, including missing patterns and use of secondary data. Second, a short-term traffic speed prediction algorithm was proposed that provides accurate prediction results and is scalable for a large road network analysis in real time. The proposed algorithm consists of a data dimension reduction module and a nonparametric multivariate time-series analysis module. Third, a real-time traffic queue detection algorithm was developed based on traffic fundamentals combined with a statistical pattern recognition procedure. This algorithm was designed to detect dynamic queueing conditions in a spatio-temporal domain rather than detect a queue and congestion directly from traffic flow variables. The algorithm was evaluated by using various real congested traffic flow data. Lastly, gray areas in a decision-making process based on quantifiable measures were addressed to cope with uncertainties in modeling outputs. For intersection control type selection, the gray areas were identified and visualized

On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters

Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult. Based on this insight, we devise an on-line algorithm for improper learning of a linear dynamical system (LDS), which considers only a few most recent observations. We use our decay results to provide the first regret bounds w.r.t. to Kalman filters within learning an LDS. That is, we compare the results of our algorithm to the best, in hindsight, Kalman filter for a given signal. Also, the algorithm is practical: its per-update run-time is linear in the regression depth

Forecasting the CATS benchmark with the Double Vector Quantization method

The Double Vector Quantization method, a long-term forecasting method based on the SOM algorithm, has been used to predict the 100 missing values of the CATS competition data set. An analysis of the proposed time series is provided to estimate the dimension of the auto-regressive part of this nonlinear auto-regressive forecasting method. Based on this analysis experimental results using the Double Vector Quantization (DVQ) method are presented and discussed. As one of the features of the DVQ method is its ability to predict scalars as well as vectors of values, the number of iterative predictions needed to reach the prediction horizon is further observed. The method stability for the long term allows obtaining reliable values for a rather long-term forecasting horizon.Comment: Accepted for publication in Neurocomputing, Elsevie

Transformed-linear models for time series extremes

2022 Summer.Includes bibliographical references.In order to capture the dependence in the upper tail of a time series, we develop nonnegative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly-varying time series through the tail pairwise dependence function (TPDF) which is a measure of pairwise extremal dependencies. We state consistency requirements among the finite-dimensional collections of the elements of a regularly-varying time series and show that the TPDF's value does not depend on the dimension being considered. So that our models take nonnegative values, we use transformed-linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDF's. Motivated by investigating conditions conducive to the spread of wildfires, we fit models to hourly windspeed data using a preliminary estimation method and find that the fitted transformed-linear models produce better estimates of upper tail quantities than traditional ARMA models or than classical linear regularly-varying models. The innovations algorithm is a classical recursive algorithm used in time series analysis. We develop an analogous transformed-linear innovations algorithm for our time series models that allows us to perform prediction which is fundamental to any time series analysis. The transformed-linear innovations algorithm also enables us to estimate parameters of the transformed-linear regularly-varying moving average models, thus providing a tool for modeling. We construct an inner product space of transformed-linear combinations of nonnegative regularly-varying random variables and prove its link to a Hilbert space which allows us to employ the projection theorem. We develop the transformed-linear innovations algorithm using the properties of the projection theorem. Turning our attention to the class of MA(∞) models, we talk about estimation and also show that this class of models is dense in the class of possible TPDFs. We also develop an extremes analogue of the classical Wold decomposition. Simulation study shows that our class of models provides adequate models for the GARCH and another model outside our class of models. The transformed-linear innovations algorithm gives us the best prediction and we also develop prediction intervals based on the geometry of regular variation. Simulation study shows that we obtain good coverage rates for prediction errors. We perform modeling and prediction for the hourly windspeed data by applying the innovations algorithm to the estimated TPDF