MULTISCALE CHANGES AND A TREND ANALYSIS OF THE FLUCTUATION OF HOUSEHOLD CONSUMPTION GROWTH IN CHINA. GUO Yue-ting 1, XU Jian-gang 2

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1 DOI: /j.issn : (211) , (1., 2193;2., 2193) MULTISCALE CHANGES AND A TREND ANALYSIS OF THE FLUCTUATION OF HOUSEHOLD CONSUMPTION GROWTH IN CHINA GUO Yue-ting 1, XU Jian-gang 2 (1.School of Geographic and Oceanographic Sciences, Nanjing University, Nanjing 2193, China; 2.School of Architecture and Urban Planning, Nanjing University, Nanjing 2193, China) Abstract: This paper aims to reveal the growth of multi-scale fluctuations of household consumption growth during the process of economic development in China. Empirical Mode Decomposition (EMD) was developed in 1998 by Huang which facilitates the decomposition of climate records in terms of natural oscillatory patterns and trends. And this method was improved in The method can decompose any complicated data into a finite and small number of intrinsic mode functions (IMFs). EMD method decomposing a raw data series into different IMFs is a sifting process. In this paper, the EMD method is used to break down the data series of household consumption growth from 1953 to 29 in China into finite IMFs and trend at multiscale level. Each mode is represented as a function of both instantaneous frequency and amplitude. Thus it describes the scale and fluctuation characteristics at any time. The sum of all modes gives the full description of the frequency and time characteristics of the signal. The household consumption in China completely breaks down into three modes (IMFs) and a trend (Res) by EMD method. The first IMF is the component that has the smallest period and the periods turn bigger with the IMFs going on to IMF2. By calculating variance contribution and correlations test, the significant periodic fluctuation is researched. Based on the Mann-Kendall trend test, the trend of household consumption growth is studied. The analysis results show that the three IMFs of household consumption growth in China are 3-year period, 8-year period and 12.-year period. The main periodic fluctuation of household consumption growth in China is 8-year period. The secondary periodic fluctuation is 3-year period and the third one is 12.-year period.the purpose of the paper is to reveal the growth of multi-scale fluctuations of household consumption growth during the process of economic development in China. Key words: household consumption growth; Empirical Mode Decomposition; multiscale fluctuation; trend change : ( EMD) ,, IMF RES,, Mann-Kendall : , 8, 3 ; 56 : F12.8, 1978, : , 1983 : ; ; ; ; : A : guoyueting@126.com : ; : HUMAN GEOGRAPHY Vol.26.No.5 211/1

2 1 GDP 3 EMD " GDP EMD 2.3 Mann-Kendall Yue Trend Free Pre-Whitening [22-25] Theil Sen [1-3] β β=median x -x j l l<j 1 j-l 2. Mann-Kendall [] Mann-Kendall n x k Empirical Model DecompositionEMD S k = Σr i k=23 n 2 i = 1 x i >x j r i =1 r i = j=12 i Mann-Kendall UF k = S -E S k k k=12 n 姨 Var S k 2 EMD NASA Huang [1,15] EMD [16] [17-2] [21] [5] UF 1998 k UB k UF k UB k [6] 1999 [26] α=.5 EMD X t 3 Intrinsic Mode FunctionIMF IMF 3.1 RES EMD EMD IMF RES 1 IMF IMF [7] IMF [8,9] [1] [11,12] 23 IMF [13] [27] Huang EMD EMD IMF HUMAN GEOGRAPHY Vol.26.No.5 211/1 95 Σ Σ A 3 UF 1 =E S k Var S k S k x 1 x 2 x n 2.1 E S k = n n UF 29 i x x 1 x 2 x n α UF i >U α x x 2.2 n x n-1 x 1 UB k =-UF k k=nn-1 1UB 1 =

3 IMF 1 IMF 1963 IMF RES 1 IMF UF IMF1 IMF2 IMF3 UB 1978 RES.1 IMF 1 IMF IMF2 8 IMF IMF RES IMF 68.75% Z SPSS UF 1953 GDP UF.1 GDP I M F R E S IMF RES Fig.1 IMF and Residual Trend RES of Growth Rate of Household Consumption in China 96 HUMAN GEOGRAPHY Vol.26.No.5 211/1

4 % 2 Z 9.1% 1 IMF Tab.1 Variance Contribution of IMF 1- and Its Order IMF IMF1 IMF2 IMF3 IMF RES % M-K 23 Fig.2 M-K Check Curve Chart of Growth Rate of Household Consumption in China UF UB a=.5 3 EMD Mann-Kendall SPSS [1]. [J].,21, (1):21-2. [2]. [J]. 28 UF UB EMD Mann-Kendall ,21,(6):9-52. [3],,. [J].,22,23(6): [],. [J].,21,(): [5] Norden E Huang, Zheng Shen, Steven R Long, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis [J]. Proceedings of the Royal Society of London Series A, 1998,5(1971): % 5% 59% [6] Norden E Huang, Zheng Shen, Steven R Long. A New View of Nonlinear Water Waves: the Hilbert Spectrum[J]. Annual Review of Flu- % 9% 3% 39% id Mechanics, 1999,3l: [7] Chin-Hsiung Loh, Tsu-Chiu Wu, Norden E Huang. Application of the Empirical Mode Decomposition-Hilbert Spectrum Method to Identify Near-Fault Ground-Motion Characteristics and Structural % Re- HUMAN GEOGRAPHY Vol.26.No.5 211/1 97

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