Deteksi Pencilan pada Model ARIMA dengan Bayesian Information Criterion (BIC) Termodifikasi

Time series data may be affected by special events or circumstances such as promotions, natural disasters, etc. These events can lead to inconsistent observations in the series called outliers. Because outliers can make invalid conclusions, it is important to carry out procedures in detecting outlier effects. In outlier detection there is one type of outlier, namely additive outlier (AO). The process of detecting additive outliers in the ARIMA model can be said as a model selection problem, where the candidate model assumes additive outliers at a certain time. In the selection of models there are criteria that must be considered in order to produce the best model. The good criteria for models selection can use the Bayesian Information Criterion (BIC) derived by Schwarz (1978). Galeano and Pena (2011) proposed a modified Bayesian Information Criterion for model selection and detect potential outliers. The modified Bayesian Information Criterion for outlier detection will be applied to the data OutStanding Loan PT.Pegadaian Cimahi year 2013-2017. So that the best model is obtained that the model with adding 2 potential outliers with the ARIMA model (1.0,0), that outliers at observations 48, and 58 because it has a minimum BICUP value of 1064.95650.

On the Performance of Garch Family Models in the Presence of Additive Outliers

It is a common practice to detect outliers in a financial time series in order to avoid the adverse effect of additive outliers. This paper investigated the performance of GARCH family models (sGARCH; gjrGARCH; iGARCH; TGARCH and NGARCH) in the presence of different sizes of outliers (small, medium and large) for different time series lengths (250, 500, 750, 1000, 1250 and 1500)  using root mean square error (RMSE) and mean absolute error (MAE) to adjudge the models. In a simulation iteration of 1000 times in R environment using rugarch package, results revealed that for small size of outliers, irrespective of the length of time series, iGARCH dominated, for medium size of outliers, it was sGARCH and gjrGARCH that dominated irrespective of time series length, while for large size of outliers, irrespective of time series length, gjrGARCH dominated. The study further leveled that in the presence of additive outliers on time series analysis, both RMSE and MAE increased as the time series length increased.

Outliers and persistence in threshold autoregressive processes

This paper uses Monte Carlo simulations to investigate the effects of outlier observations on the properties of linearity tests against threshold autoregressive (TAR) processes. By considering different specifications and levels of persistence for the data-generating processes, we find that additive outliers distort the size of the test and that the distortion increases with the level of persistence. In addition, we also find that larger additive outliers can help to improve the power of the test in the case of persistent TAR processes.