Detecting unusual observations in time series: An application of the normal-exp model
Ro Jin Pak · Korean Journal of Applied Statistics · 2023
A method to detect unusual or abnormal data in a time series or a discrete time signal is proposed.The idea of microarray background correction has been borrowed to detect abnormal data in a time series.Background correction to isolate anomalous signals or noise from the mircroarray's real signal is a very important step in tuning the data for ambient intensity surrounding each feature.The normal-exponential distribution was proposed to model background noise and signal by convoluting the exponential and the normal distribution.It is tried to model the error terms of a time series with the normal-exponential distribution.Once the residual components were well treated by the normal-exponential distribution, the observations with unexpectedly large residuals are detected as outliers or unusual observations.The marriage event data and the real estate price index data were considered for empirical studies and we were able to find several anomalous observations consistent with when the Korean economy or society actually underwent dramatic changes.