This is a repository copy of Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model..

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1 This is a repository copy of Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model.. White Rose Research Online URL for this paper: Monograph: Redfern, E.J., Watson, S.M., Clark, S.D. et al. (2 more authors) (1993) Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model. Working Paper. Institute of Transport Studies, University of Leeds, Leeds, UK. Working Paper 395 Reuse See Attached Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by ing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. eprints@whiterose.ac.uk

2 White Rose Research Online Institute of Transport Studies University of Leeds This is an ITS Working Paper produced and published by the University of Leeds. ITS Working Papers are intended to provide information and encourage discussion on a topic in advance of formal publication. They represent only the views of the authors, and do not necessarily reflect the views or approval of the sponsors. White Rose Repository URL for this paper: Published paper Redfern, E.J., Watson, S.M., Clark, S.D., Tight, M.R., Payne, G.A. (1993) Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model. Institute of Transport Studies, University of Leeds. Working Paper 395 White Rose Consortium eprints Repository eprints@whiterose.ac.uk

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4 Modelling Outliers and Wising values in trafac count data using the ARIMA model Redfern E.J., Watson S.M., Clark S.D., Tight M.R. and Payne G.A. Department of Statistics and Institute for Transport Studies University of Leeds Leeds LS2 9JT, England Abstract. This paper considers the application of the methodology to traffic count time series in which both missing values and outliers are present. Intervention analysis and detection using large residuals are shown to he reasonably effective but possible problems that result from nonstationarity in the data are identified. It is shown that despite considerable variabilty in the types of series the model selected from the ARIMA family is surpri~ingly homogeneous. Watson et al (1991) review the methods used for estimating missing values and identifying outliers in time series. These methods include techniques based on the estimate of the underlying autocorrelation structure and the use of a parametric model. Subsequent papers (Watson et a1 1992a and 1992b) consider in more detail the use of methods based on the estimated autowrrelation function and their application to traffic count time series. In this paper we consider the suitability of the Autoregressive Integrated Moving-Average (ARIMA) model and the use of the Box-Jenkins methodology (Box and Jenkins 1976) as a method for modelling traffic count series in the presence of missing values and outliers. This family of models has been used to model a variety of transport times series with varying degrees of success. The applications include rail and air passanger flows, journey times, public transport demand and the analysis of freeway traffic flow. (See Watson et al 1991 for a more detailed discussion.) The family of models is represented by the equation where q5 and 0 are polynomials in B of order p and and O are polynomials in B' of order P and Q respectively, B is the backward shift operator such that BXt = X(t-I), A = (1 - B) and A, = (1 - Ba), where s is the length of the seasonal period. et is a noise process and is assumed to have a Gaussian distribution with zero mean and variance u2. To model the outliers and missing values the model is extended by adding intervention series of the form 1 ift=k 0 elsewhere

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