The Effects of Additive Outliers on Time Series Components and Robust Estimation: A Case Study on the Oymapinar Dam, Turkey

Abstract

In this paper, the behaviour of the body of the Oymapinar Dam (Antalya, Turkey) resulting from reservoir water level changes was investigated by time series analysis. First, the possible best fitting methods for determining the existing additive outliers in series were investigated. For this purpose, a time series with known parameters consisting of trend, periodical and stochastic components was obtained. Then, a new time series with additive outlier(s) was created by adding outlier(s) to series with known parameters. The parameters of the components were determined by the least squares method and it was seen that outlier(s) affect the components of the series. It was found that the correct data were contaminated by an outlier to a similar degree as the autoregressive model. The outliers affecting the components were determined by Andrews, Bisquare, Cauchy, Huber and Welsch estimators in trend analysis. The results show that the parameters of the trend were not affected by outliers and the results produced by the estimators are numerically close to each other. Thus, series of the outlier(s) of the Oymapinar Dam were determined by Bisquare estimator in a trend analysis. As a result of series analysis it was determined that the linear trend resulted from a long-term periodical of changes and the dam body responded periodically depending on the water level changes.