상관성 분석을 통한 비정상 시계열 연구
Study of Nonstationary Time Series Based on Correlation Analysis
- 주제(키워드) nonstationary time series , correlation analysis
- 발행기관 강릉원주대학교 일반대학원
- 지도교수 김재화
- 발행년도 2015
- 학위수여년월 2015. 2
- 학위명 박사
- 학과 및 전공 일반대학원 물리학과
- 세부전공 통계물리
- 원문페이지 86
- 실제URI http://www.dcollection.net/handler/kangnung/000000006848
- 본문언어 한국어
초록/요약
Most of the real nonstationary time series observed various fields like physics, economics, methodology and medical science appear statistical correlation, fractal and multifractal characteristics. The correlation of nonstationary time series are very important in understanding of dynamic system. Therefore, this analysis study has been carried out by using various correlation analysis method sustainedly. In this study, we analyze the nonstationary time series based on correlation-analysis methods using ACF(Autocorrelation Function Analysis), R/S Analysis(Rescaled Range Analysis), DFA(Detrended Fluctuation Analysis), DCCA(Detrended Cross-Correlation Analysis), and . We apply the method to those nonstationary time series such as gamma exposure rates, temperature, relative humidity, rainfall, hours of daylight, amount of clouds and average wind speed. Through this methods, we obtained scaling exponents. In the first application part, we investigate the statistical properties of gamma exposure rates using well-known analysis methods, such as ACF, R/S Analysis, and DFA. Our data are measured by Gangneung regional radiation monitoring station over the period of 1998 to 2011. We find a crossover indicating two different governing regimes in fluctuations of gamma exposure rates. Within a year, they show a strong long-ranged memory while this property vanishes over the range of time period longer than one year. Our finding is very securely supported by a variety of analysis tools. Those tools yield many relevant exponents which satisfies the well known relation between them. In the second application part, we analyze the cross correlation between gamma exposure rates and rainfall, hours of daylight, average wind speed using method. Our data are measured simultaneous in Gangneung regional. We find the between gamma exposure rates and rainfall is in Day(3~7days) 0.57~0.48, Month(30days) 0.39, Season(90days) 0.34, Year(360days) 0.26, between Gamma exposure rates and Hours of daylight is Day -0.20~-0.23, Month -0.22, Season -0.17, Year -0.13, between Gamma exposure rates and average wind speed is Day -0.10~-0.12, Month -0.11, Season -0.05, Year -0.05. Second, our finding is cross-correlation between gamma exposure rates and rainfall, is no cross-correlation between gamma exposure rates and hours of daylight, average wind speed. In the third application part, we analyze the cross correlation between temperature, relative humidity, hours of daylight, amount of clouds and average wind speed using method. Our data are obtained simultaneously in ten cities(Gangneung, Gwangju, Seoul, Wonju, Busan, Sokcho, Daejeon, Jeju, Chuncheon, Daegu). We idenfied local characteristics not only of average wind speed in Gangneung but also hours of daylight in Jeju. In the final application part, we analyze the correlation of meteorological data with a periodic trend by using the recently proposed correlation-analysis methods. In order to make the time series stationary, we apply the varying polynomial order detrending method to the nonstationary time series. By using this method, we obtained stable scaling exponents different from those obtained by using the ordinary detrending method, which showed a cross over around the periodic time point. We chose three locations in the Korean peninsula and found the autocorrelation and the cross-correlation exponents between the temperature and the relative humidity. From the obtained scaling exponents, we conclude that there are universal properties in the correlation, the so-called long-range memories in autocorrelations and cross-correlations. In addition to these scaling exponents associated with the correlations, we found that the cross-correlation coefficients, which quantify the level of cross-correlation, are somewhat different according to the area.
more목차
I. 서론 . 10
II. 이론 . 12
1. 상관성 분석 방법 . 13
1.1 ACF(Auto-Correlation Function) . 13
1.2 R/S Analysis(Rescaled Range Analysis) 13
1.3 DFA(Detrended Fluctuation Analysis) . 14
1.4 DFA- 16
2. 교차 상관성 분석 방법 . 17
2.1 DCCA(Detrended Cross-Correlation Analysis) . 17
2.2 DCCA- 18
2.3 교차 상관 계수 . 19
2.4 변동 차수 교차 상관 계수 20
3. ARFIMA . 21
III. 응용 연구 23
1. 강릉 지역 공간 감마선량률의 시계열 분석 24
1.1 서론 24
1.2 분석 대상 25
1.3 결과 및 고찰 . 25
1.4 결론 . 27
2. 강릉 지역 공간 감마선량률과 강수량, 일조시간, 평균풍속 사이 교차 상관성 분석 33
2.1 서론 33
2.2 분석 대상 34
2.3 실험 결과 34
2.4 고찰 36
2.5 결론 38
3. 전국 10개 도시의 5개 기상요소 사이 교차 상관성 분석 . 42
3.1 서론 42
3.2 분석 대상 43
3.3 분석 결과 43
3.4 결론 45
4. 변동차수 탈경향 방법을 통한 기상데이터의 상관성분석 62
4.1 서론 62
4.2 이론 64
4.3 분석 결과 66
4.4 결론 68
IV. 결론 . 75
참고문헌 . 77
