An influence method for outlier detection applied to time series traffic data

The work of Chernick et al. (1982) is extended to form a quantitative outlier detection statistic for use with time series data. The statistic is formed from the squared elements of the influence function matrix, where each element of the matrix gives the influence on the theoretical autocorrelation function at lag k (pk) of a pair of obser vations at time lag k. The approximate first four moments for the statistic are derived and, by fitting Johnson curves to these theoretical moments, critical points are also produced. The statistic is also used to form the basis of an adjustment procedure to treat outliers or estimate missing values in the time series. The nuclear power data of Chernick et al. and the traffic count data of the Department of Transport are used for practical illustration.