Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

Stochastic Modelling of Train Delay Time Series in Skåne, Sweden

Vestin, Filip LU and Zulj, Valentin LU (2018) STAH11 20172
Department of Statistics
Abstract
The purpose of this paper is to provide a foundation for modelling train delays as multivariate time series. A pertinent issue with this kind of analysis is that the individual time series do not follow the Gaussian normal distribution. Since the normal distribution constitutes an assumption of classical time series methods, these cannot be applied blindly to the data. The solution explored by the paper is to identify the distributions of the time series and subsequently transforming the data into normal distributions.

To this end, a dataset from the Swedish Transport Administration was used containing delays for every train that either departed from the region Skåne as a first departure, or arrived in Skåne as a final destination. The... (More)
The purpose of this paper is to provide a foundation for modelling train delays as multivariate time series. A pertinent issue with this kind of analysis is that the individual time series do not follow the Gaussian normal distribution. Since the normal distribution constitutes an assumption of classical time series methods, these cannot be applied blindly to the data. The solution explored by the paper is to identify the distributions of the time series and subsequently transforming the data into normal distributions.

To this end, a dataset from the Swedish Transport Administration was used containing delays for every train that either departed from the region Skåne as a first departure, or arrived in Skåne as a final destination. The dataset spans from January 1st, 2014 to December 31st, 2016. Time series were constructed for every station with a significant amount of data points by computing the mean daily delays for these stations. Using software for distribution fitting it was found that the asymmetric Laplace distribution best described the distribution of the train delays. The data was successfully transformed into a normal distribution using the empirical cumulative distribution function of the asymmetric Laplace distribution. Comparing the cross-correlation functions before and after the transformations showed mild increases in the time dependence between stations. (Less)
Please use this url to cite or link to this publication:
author
Vestin, Filip LU and Zulj, Valentin LU
supervisor
organization
course
STAH11 20172
year
type
M2 - Bachelor Degree
subject
keywords
Stochastic models, train delays, time series
language
English
id
8932612
date added to LUP
2018-02-02 13:41:57
date last changed
2018-02-02 13:41:57
@misc{8932612,
  abstract     = {{The purpose of this paper is to provide a foundation for modelling train delays as multivariate time series. A pertinent issue with this kind of analysis is that the individual time series do not follow the Gaussian normal distribution. Since the normal distribution constitutes an assumption of classical time series methods, these cannot be applied blindly to the data. The solution explored by the paper is to identify the distributions of the time series and subsequently transforming the data into normal distributions. 

To this end, a dataset from the Swedish Transport Administration was used containing delays for every train that either departed from the region Skåne as a first departure, or arrived in Skåne as a final destination. The dataset spans from January 1st, 2014 to December 31st, 2016. Time series were constructed for every station with a significant amount of data points by computing the mean daily delays for these stations. Using software for distribution fitting it was found that the asymmetric Laplace distribution best described the distribution of the train delays. The data was successfully transformed into a normal distribution using the empirical cumulative distribution function of the asymmetric Laplace distribution. Comparing the cross-correlation functions before and after the transformations showed mild increases in the time dependence between stations.}},
  author       = {{Vestin, Filip and Zulj, Valentin}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Stochastic Modelling of Train Delay Time Series in Skåne, Sweden}},
  year         = {{2018}},
}