Trend test for Korean climate data using wavelets

Abstract

Trend, i.e., large scale variations in the series that are best modeled outside of a stochastic framework, is highly relevant for the discussion of potential impacts in time series . We consider the problem of testing the existence of the trends for a time series. The trend is assumed to be a slowly varying deterministic component caused e.g. by human impact like global warming. In this paper, wavelet decomposition is used as a tool for identifying trends in climatic time series. Wavelets are fairly new approach in analysing data that is becoming increasingly popular for a wide range of applications. Especially, it is useful in studying time series climate data. This method decomposes a time series into low frequency (trend) and high frequency (noise) components. Therefore, we will apply the wavelet methodology in analyzing a time series and will study this alternative approach for testing whether the trend exists or not among time series. The test is following F distribution when the normality assumption is supposed. Otherwise, the distribution of the test is unknown. For wide conditions, empirical critical values will be generated for this test by using Monte Carlo simulations and the results will be compared with those results from applying the original least square methods for testing trend of the data. This methodology will be applied to real Korean temperature data for the period 2007-2011.

이 논문에서 우리는 기후 자료와 같은 시계열 자료에서 추세를 파악하고 검정하기 위해서 웨이블릿을 기초로 한 방법을 제안한다. 제안된 방법은 이산웨이블릿변환과 다중해상도분석이라는 웨이블릿 분석 방법을 기반으로 한다. 최근 2008년에 A. Almasri와 Hakan L., Shukur G.가 스웨덴의 기후 자료를 이용하여 이러한 방법을 통한 자료의 추세 분석을 연구하였다. 우리는 이러한 방법을 국내 데이터에 적용하였다.