Unit Root Test를 기반으로 한 장기 시계열 데이터의 Non-Stationary 발생에 따른 구조 변화 검정 및 시각화 연구

A Study on the Test and Visualization of Change in Structures Associated with the Occurrence of Non-Stationary of Long-Term Time Series Data Based on Unit Root Test

Abstract

시계열의 구조 변화란, 전체 시계열 자료를 구성하는 기간에서 관측치들의 분포가 상대적으로 안정적이다가, 특정 시점에서 분포 특성의 급격한 변화를 보이는 것을 의미한다. 비정상(non-stationary) 장기 시계열 안에서도, 단기적인 추세의 변화가 일시적인 것인지, 아니면 구조적으로 변한 것인지를 적시에 판단하는 것은 중요하다. 이는 시계열 추세의 변화를 상시 감지하여, 변화에 맞는 적정한 대응을 할 필요가 있기 때문이다. 본 연구에서는 단위근 검정법을 기반으로 한 검정 결과를 시각화함으로써, 의사결정자가 시계열의 구조 변화를 손쉽게 파악할 수 있는 방안을 제시하였다. 특히 시계열을 분할한 후 검정하는 방법을 통해, 장기 시계열일 때에도 단기 구조 변화를 파악할 수 있도록 하였다.

Structural change of time series means that the distribution of observations is relatively stable in the period of constituting the entire time series data, but shows a sudden change of the distribution characteristic at a specific time point. Within a non-stationary long-term time series, it is important to determine in a timely manner whether the change in short-term trends is transient or structurally changed. This is because it is necessary to always detect the change of the time series trend and to take appropriate measures to cope with the change. In this paper, we propose a method for decision makers to easily grasp the structural changes of time series by visualizing the test results based on the unit root test. Particularly, it is possible to grasp the short-term structural changes even in the long-term time series through the method of dividing the time series and testing it.

Fig. 1. Seasonal-trend Variation Decomposition using Loess by Cleveland et al.

Fig. 2. Three Main Patterns of the Auto-correlation (A) The Case of Indicates that There is an Autoregressive Term in the Data, (B) The Case of Indicates that There is a Higher Order Autoregressive Term in the Data, (C) The Case of Indicates that There is a Moving Average Term in the Data

Fig. 3. Changes due to Variation Elements of Time Series Data, (A) Long-term trend, (B) (A) with Cyclical Variations, (C) (B) and Seasonal Variations, (D) (C) with Random Variations

Fig. 4. Short-term Structural Changes in Long-term Time Series. Short-term Trends before and after Structural Changes Tend to Change

Fig 5. Procedure of Unit Root Test

Fig. 6. Segmentation using Partial Data Length and Step Size of Time Series Data

Fig. 7. Based on the Results of the unit Root Test, some Partial Data are Emphasized

Fig. 8. Synthetic Data using the Base Model (n=35,040)

Fig. 9. An Example of Type 1 Synthetic Data (n = 35,040, ξ = 1000)

Fig. 10. An Example of Type 2 Synthetic Data (n = 35,040, ξ = 1000)

Fig. 11. Power Consumption Data of Montenegro by ENTSO-E

Fig. 12. Visualizations of Analysis of [A] Type 1(F), [B] Type 2(F) and [C] Type 3(B)

Fig. 13. Power Consumption Data of Montenegro by ENTSO-E

Fig. 14. Outliers and Structure Breaks Intuitively Confirmed from Power Consumption(kWh) Data of Montenegro by ENTSO-E

Fig. 15. Visualizations of Analysis of Power Consumption(kWh) Data of Montenegro by ENTSO-E

Table 1. Definition of 5 Types Outliers

Table 2. Parameters for analysis of Type 1^(F), Type 2^(F) and Type 3^(B) (CV is critical value)

Table 3. [A] IDX Gap of Results by Analysis and [B] Sum of IDX Gap of Results by 100 Times Analysis (right) for Type 1^(F), Type 2^(F) and Type 3^(B)

Table 4. Parameters for Power Consumption of Montenegro by ENTSO-E (CV is critical value)