An Empirical Study of Error Evaluation in Trend and Seasonal Time Series Forecasting Based on SSA | [Pakistan Journal of Statistics and Operation Research • 2018]

Author(s):

1. Winita Sulandari: Department of Mathematics, Universitas Gadjah Mada, Indonesia; Study Program of Statistics, Universitas Sebelas Maret, Indonesia

2. Subanar: Department of Mathematics Universitas Gadjah Mada, Indonesia

3. Suhartono: Department of Statistics Institut Teknologi Sepuluh Nopember, Indonesia

4. Herni Utami: Department of Mathematics Universitas Gadjah Mada, Indonesia

5. Muhammad Hisyam Lee: Department of Mathematical Sciences Universiti Teknologi Malaysia, Malaysia

Abstract:

SSA (Singular Spectrum Analysis) starts to become a popular method in decomposing time series into some separable and interpretable series. This study provides an error evaluation in the SSA-based model for trend and multiple seasonal time series forecasting. This error evaluation is obtained by means of a numerical study on the mean square error of the estimators and mean absolute percentage error of the forecast values. Four distinct types of data generating processes (DGP) with varying sample sizes are considered in this experimental study. The parameters are estimated from the component series of SSA. Each DGP is decomposed into trend, periodic and irregular components. All these components except the irregular one are fitted by appropriate deterministic function separately. Based on the numerical simulation results, the estimated parameters are closer to the true values as the sample size increases. As the illustrative example of the real data set implementation, we used the monthly atmospheric concentrations of CO2 from Moana Loa observatory for period January 1959 to June 1972. The proposed method produces better forecast values than the results of SSA-LRF (Linear Recurrent Formula) and TLSAR (Two Level Seasonal Autoregressive). The results encourage the improvement in the time series modeling on the more complex pattern.

Page(s): 945-960

DOI: DOI not available

Published: Journal: Pakistan Journal of Statistics and Operation Research, Volume: 14, Issue: 4, Year: 2018

Keywords:

Trend , Deterministic , Periodic , Seasonal

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