SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.

The Impact of Outliers on Parameter Estimation Method for Bilinear Model

Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is the best method to estimate parameters for bilinear model. However, the existence of outliers will affect the estimated value of the parameter and its validity can be doubtful. This statement was proven by conducting simulation analysis for the bilinear model, especially on bilinear (1,0,1,1) model without and with the existence of additive outlier (AO), innovational outlier (IO), temporary change (TC) and level change (LC) in the data. The performance of the NLS method is measured in terms of bias. Numerical results show that, in general, the NLS method performs better in estimating the parameters without the existence of AO, IO, TC or LC in the data. Keywords: bilinear model; nonlinear least squares; Newton-Raphson; additive outlier; innovational outlier; temporary change; level change

PREDIKSI PRODUKSI KELAPA SAWIT DI PTPN XIII DENGAN ADDITIVE OUTLIER PADA MODEL SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (SARIMA)

Model SARIMA adalah model yang sesuai untuk data yang memiliki pola musiman. Dalam data biasanya terdapat outlier yang dapat mempengaruhi kesesuaian model sehingga dilakukan deteksi outlier pada model SARIMA untuk mendapatkan model peramalan yang terbaik. Salah satu jenis outlier yaitu additive outlier (AO). Data yang digunakan dalam penelitian ini merupakan data produksi kelapa sawit periode Januari 2010 sampai Desember 2017. Data produksi kelapa sawit di Kalimantan Barat memiliki pola data musiman dan diduga memiliki outlier pada data maka dilakukan pemodelan dan peramalan dengan menggunakan additive outlier pada model SARIMA. Berdasarkan analisis diperoleh bahwa nilai AIC pada model SARIMA adalah sebesar 2.070,72 dan nilai MAPE nya sebesar 25% sedangkan model SARIMA dengan deteksi outlier diperoleh nilai AIC sebesar 1.731,42 dan nilai MAPE sebesar 15,91%. Maka dapat disimpulkan bahwa model SARIMA dengan deteksi outlier adalah model terbaik untuk peramalan produksi kelapa sawit di PTPN XIII. Kata Kunci: Kelapa sawit, peramalan, SARIMA, outlier

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.

Is per capita energy use stationary? Time series evidence for the EMU countries

This study examines the stationary properties of per capita energy use in the 19 Eurozone member countries by using annual data over 1960–2013 period. We utilize the Clemente et al. unit root test that determines structural breaks. Empirical results show that most of the country series does not reject the unit root null hypothesis at the 5% significance level, both in the case of additive outlier and of innovative outlier. Therefore, our empirical findings provide significant evidence that energy use is nonstationary in almost all Eurozone countries. For the policy makers, it is necessary to pay attention to energy use series.