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    A new approach for crude oil price analysisbased on Empirical Mode Decomposition

    Xun Zhang a,b, K.K. Lai c, Shou-Yang Wang a,b,

    a Institute of Systems Science, Academy of Mathematics and Systems Science,

    Chinese Academy of Sciences, Beijing 100080, Chinab School of Management, Graduate University of Chinese Academy of Sciences, Beijing 100080, China

    c Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Received 22 September 2006; received in revised form 26 February 2007; accepted 26 February 2007

    Available online 4 May 2007

    Abstract

    The importance of understanding the underlying characteristics of international crude oil price movements

    attracts much attention from academic researchers and business practitioners. Due to the intrinsic complexityof the oil market, however, most of them fail to produce consistently good results. Empirical Mode

    Decomposition (EMD), recently proposed by Huang et al., appears to be a novel data analysis method for

    nonlinear and non-stationary time series. By decomposing a time series into a small number of independent

    and concretely implicational intrinsic modes based on scale separation, EMD explains the generation of time

    series data from a novel perspective. Ensemble EMD (EEMD) is a substantial improvement of EMD which

    can better separate the scales naturally by adding white noise series to the original time series and then treating

    the ensemble averages as the true intrinsic modes. In this paper, we extend EEMD to crude oil price analysis.

    First, three crude oil price series with different time ranges and frequencies are decomposed into several

    independent intrinsic modes, from high to low frequency. Second, the intrinsic modes are composed into a

    fluctuating process, a slowly varying part and a trend based on fine-to-coarse reconstruction. The economic

    meanings of the three components are identified as short term fluctuations caused by normal supply-demanddisequilibrium or some other market activities, the effect of a shock of a significant event, and a long term

    trend. Finally, the EEMD is shown to be a vital technique for crude oil price analysis.

    2007 Elsevier B.V. All rights reserved.

    JEL classification: C49; Q49

    Keywords: Empirical Mode Decomposition; Crude oil price; Forecasting; Composition; Volatility

    Available online at www.sciencedirect.com

    Energy Economics 30 (2008) 905918

    www.elsevier.com/locate/eneco

    Corresponding author. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy

    of Sciences, Beijing 100080, China.

    E-mail address: [email protected] (S.-Y. Wang).

    0140-9883/$ - see front matter 2007 Elsevier B.V. All rights reserved.

    doi:10.1016/j.eneco.2007.02.012

    mailto:[email protected]://dx.doi.org/10.1016/j.eneco.2007.02.012http://dx.doi.org/10.1016/j.eneco.2007.02.012mailto:[email protected]
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    1. Introduction

    Oil is one of the most important energy resources in the world and is known for wide price

    swings. It has significant effects on global economic activities. High oil prices often lead to anincrease in inflation and subsequently hurt economies of oil-importing countries. Low oil prices,

    on the other hand, may result in economic recession and political instability in oil-exporting

    countries since their economic development can get retarded. Besides the price levels, economic

    losses are also driven by volatility of oil price. A relatively small increase in price can result in

    sizeable losses. Studies show that a 10% increase in price of oil is equivalent to 0.6 to 2.5% GDP

    growth for US (Sauter and Awerbuch, 2003; Rotemberg and Woodford, 1996).

    There have been abundant studies on analysis and forecasting of crude oil price. The approaches

    can be grouped into two categories: structure models and data-driven methods. Standard structure

    models outline the world oil market and then analyze the oil price volatility in terms of a supply-

    demand equilibrium schedule (e.g. Bacon, 1991; Al Faris, 1991; Huntington, 1994; Mehrzad,2004; Yang et al., 2002). Data-driven models include linear models such as Autoregressive

    Moving Average (ARMA), Autoregressive Conditional Heteroscedasticity (ARCH) type models

    (e.g. Sadorsky, 2002; Morana, 2001) etc., and nonlinear models such as Artificial Neural Network

    (e.g. Mirmirani and Li, 2004; Moshiri, 2004; Nelson et al., 1994; Yu et al., 2006 ), Support Vector

    Regression (Xie et al., 2006), etc. A number of other references on this topic exist. (e.g. Abosedra

    and Baghestani, 2004; Abramson and Finizza, 1991; Abramson and Finizza, 1995; Chaudhuri,

    2001; Hagen, 1994; Maurice, 1994; Nelson et al., 1994; Pindyck, 1999; Stevens, 1995; Wang

    et al., 2005; Watkins and Plourde, 1994).

    The structure models can help understand the mechanisms of oil price determination and

    quantify each factor's impact on oil price. However, this approach has proved to be difficult due tosome specific characteristics of crude oil market. For example, supply is hard to model because oil

    is supplied by both a set of independent producers (non-OPEC nations) that act as price takers and

    an organization (OPEC) that uses myriad factors to determine levels of production, besides

    installed capacity (Desa et al., 2007). In addition, the dynamic and unstable market environment

    increases the difficulty of modeling. Data-driven methods often perform well when applied to short

    term forecasting but they lack economic meaning and can not explain the inner driving forces that

    move crude oil price.

    The dilemma between difficulties in modeling and lack of economic meaning can be solved by an

    objective data analysis method, i.e. Empirical Mode Decomposition (EMD), introduced by Huang

    et al. (1998). EMD is an empirical, intuitive, direct and self-adaptive data processing method which isproposed especially for nonlinear and non-stationary data. The core of EMD is to decompose data

    into a small number of independent and nearly periodic intrinsic modes based on local characteristic

    scale, which is defined as the distance between two successive local extrema in EMD. Each derived

    intrinsic mode is dominated by scales in a narrow range. Thus, according to the scale, the concrete

    implications of each mode can be identified. For example, an intrinsic mode derived from an

    economic time series with a scale of three months can often be recognized as the seasonal component.

    Since data is the only link we have with the reality, by exploring data's intrinsic modes, EMD not only

    helps discover the characteristics of the data but also helps understand the underlying rules of reality.

    EMD was initially proposed for study of ocean waves, and then successfully applied in many areas,

    such as biomedical engineering, structured health monitoring, earthquake engineering, and global

    primary productivity evolution. However, these applications are mainly limited to studies of nature

    science and engineering. There have been only two successful applications in social sciences so far.

    The first is to apply EMD to financial data, which is used to examine the changeability of the markets

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    by Huang et al. (2003b). The second is by Cummings et al. (2004), to use EMD to prove the existence

    of a spatial-temporal traveling wave in the incidence of dengue hemorrhagic fever in Thailand. We will

    show that EMD can be more widely used in social sciences, such as for crude oil price analysis, later.

    In this paper, we apply Ensemble EMD (EEMD, Wu and Huang, 2004), an improved EMD, tocrude oil price data and find that it can help interpret the formation of crude oil price from a novel

    perspective. First, three crude oil price series with different time ranges and frequencies are

    decomposed into several independent intrinsic modes, from high to low frequency. Second, the

    intrinsic modes are composed into a fluctuating process, a slowly varying part and a trend based

    on fine-to-coarse reconstruction. The economic meanings of the three components are identified

    as short term fluctuations caused by normal supplydemand disequilibrium or some other market

    activities, the effect or shock of a significant event, and a long term trend, according to their

    respective scales and characteristics. Finally, we define the features of the three components and

    the evolution of crude oil price. Some forecasting strategies for crude oil price are also discussed

    in the end of the paper, based on our conclusions.The rest of the paper is organized as follows: Section 2 gives a brief introduction to the basic

    theory and algorithm of EMD and EEMD. Section 3 introduces the data materials and decomposes

    them by EEMD. The derived intrinsic modes are also shown in this section. Detailed analyses based

    on a composition of intrinsic modes are presented in Section 4. Section 5 concludes the paper.

    2. Empirical Mode Decomposition

    2.1. EMD theory and algorithm

    EMD is a generally nonlinear, non-stationary data processing method developed by Huanget al. (1998). It assumes that the data, depending on its complexity, may have many different

    coexisting modes of oscillations at the same time. EMD can extract these intrinsic modes from the

    original time series, based on the local characteristic scale of data itself, and represent each intrinsic

    mode as an intrinsic mode function (IMF), which meets the following two conditions:

    1) The functions have the same numbers of extrema and zero-crossings or differ at the most by

    one;

    2) The functions are symmetric with respect to local zero mean.

    The two conditions ensure that an IMF is a nearly periodic function and the mean is set to zero.IMF is a harmonic-like function, but with variable amplitude and frequency at different times.

    In practice, the IMFs are extracted through a sifting process. The EMD algorithm is described

    as follows:

    1) Identify all the maxima and minima of time series x(t);

    2) Generate its upper and lower envelopes, emin(t) and emax(t), with cubic spline interpolation.

    3) Calculate the point-by-point mean (m(t)) from upper and lower envelopes:

    mt emint emaxt=2 14) Extract the mean from the time series and define the difference of x(t) and m(t) as d(t):

    dt xtmt 2

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    5) Check the properties of d(t):

    If it is an IMF, denote d(t) as the ith IMF and replace x(t) with the residual r(t) =x(t)d(t).

    The ith IMF is often denoted as ci(t) and the i is called its index;

    If it is not, replace x(t) with d(t);6) Repeat steps 1)5) until the residual satisfies some stopping criterion.

    One stopping criterion proposed by Huang et al. (2003a) for extracting an IMF is: iterating

    predefined times after the residue satisfies the restriction that the number of zero-crossings and

    extrema do not differ by more than one and the whole sifting process can be stopped by any of

    the following predetermined criteria: either when the component ci(t) or the residue r(t)

    becomes so small that it is less than the predetermined value of a substantial consequence, or

    when the residue r(t) becomes a monotonic function from which no more IMFs can be

    extracted. The total number of IMFs is limited to log2N, where Nis the length of data series. The

    original time series can be expressed as the sum of some IMFs and a residue:

    xt XN

    j1cjt rt: 3

    Where N is the number of IMFs, and r(t) means the final residue.

    In the sifting process, the first component, c1, contains the finest scale (or the shortest period

    component) of the time series. The residue after extracting c1 contains longer period variations in

    the data. Therefore, the modes are extracted from high frequency to low frequency. Thus, EMD

    can be used as a filter to separate high frequency (fluctuating process) and low frequency (slowingvarying component) modes. In practice, the following algorithm, based on fine-to-coarse

    reconstruction, i.e. high-pass filtering by adding fast oscillations (IMFs with smaller index) up to

    slow (IMFs with larger index) is adopted:

    1) Computing the mean of the sum of c1 to ci for each component (except for the residue);

    2) Using t-test to identify for which i the mean significantly departs from zero;

    3) Once i is identified as a significant change point, partial reconstruction with IMFs from this to

    the end, is identified as the slow-varying mode and the partial reconstruction with other IMFs

    is identified as the fluctuating process.

    The advantages of EMD can be briefly summarized as follows: first, it can reduce any data,

    from non-stationary and nonlinear processes, into simple independent intrinsic mode functions;

    second, since the decomposition is based on the local characteristic time scale of the data and only

    extrema are used in the sifting process, it is local, self-adaptive, concretely implicational and highly

    efficient (This characteristic makes EMD much different from wavelet (Daubechies, 1992). See

    Huang et al., 1998 for detailed comparisons between EMD and wavelet.); third, the IMFs have a

    clear instantaneous frequency as the derivative of the phase function, so Hilbert transformation can

    be applied to the IMFs, allowing us to analyze the data in a timefrequencyenergy space.

    2.2. Ensemble EMD

    EMD has proved to be quite versatile in a broad range of applications for extracting signals

    from data generated in nonlinear and non-stationary processes. However, the original EMD has a

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    drawback the frequent appearance of mode mixing, which is defined as a single IMF either

    consisting of signals of widely disparate scales, or a signal of a similar scale residing in different

    IMF components. To overcome the problem, Wu and Huang (2004) proposed EEMD. The basic

    idea of EEMD is that each observed data are amalgamations of the true time series and noise.Thus even if data are collected by separate observations, each with a different noise level, the

    ensemble mean is close to the true time series. Therefore, an additional step is taken by adding

    white noise that may help extract the true signal in the data. The procedure of EEMD is developed

    as follows:

    1) Add a white noise series to the targeted data;

    2) Decompose the data with added white noise into IMFs;

    3) Repeat step 1 and step 2 iteratively, but with different white noise series each time; and obtain

    the (ensemble) means of corresponding IMFs of the decompositions as the final result.

    The added white noise series present a uniform reference frame in the timefrequency and

    timescale space for signals of comparable scales to collate in one IMF and then cancel itself out

    (via ensemble averaging), after serving its purpose; therefore, it significantly reduces the chance

    of mode mixing and represents a substantial improvement over the original EMD. The effect of

    the added white noise can be controlled according to the well-established statistical rule proved by

    Wu and Huang (2004):

    en effiffiffiffiN

    p : 4

    Where Nis the number of ensemble members, is the amplitude of the added noise, and n isthe final standard deviation of error, which is defined as the difference between the input signal

    and the corresponding IMFs. In practice, the number of ensemble members is often set to 100 and

    the standard deviation of white noise series is set to 0.1 or 0.2.

    3. Decomposition

    Through EEMD, crude oil price data series can be decomposed into a set of independent IMFs

    with different scales, plus the residue. The analyses of these IMFs and the residue help explore the

    variability and formation of crude oil price from a new perspective.

    3.1. Data

    The monthly data of West Texas Intermediate (WTI) crude oil spot price, which is treated as

    the benchmark crude oil price for international oil markets, are used in our analysis.

    Fig. 1 shows the data series of WTI from Jan. 1946 to May 2006. In our experiments, three

    subdata sets of WTI are used. The first one is all the monthly data from Jul. 1946 to May 2005,

    512 data points in total. The long time range of this data set helps extract more information and

    analyze crude oil price from a long term view. The inclusion of crude oil price in different time

    periods, having different characteristics, does not affect the final results since EEMD is local. The

    other two data sets just cover the period from Jul. 2000 to May 2006, but one is weekly data of

    308 data points and the other is monthly data of 71 data points. The shorter period lets us focus on

    features of recent periods of high oil price and the different frequencies of data allow us to explore

    the features of crude oil price in different frequency ranges.

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    nonlinearity of the original time series and introduction of variance by the treatment of the cubic

    spline end conditions (Peel et al., 2005).

    For all the three decompositions, it is observed that the dominant mode of the observed data is

    not any IMF but the residue. Both Pearson and Kendall coefficients, between the residue and the

    observed data, reach a high level of more than 0.75, 0.66 and 0.80 in Tables 1, 2 and 3,

    respectively.

    At the same time, variances of the residue account for more than 75% of the total variability.

    The highest one is even more than 90%. As Huang et al. (1998) mentioned, the residue is often

    treated as the deterministic long term behavior.

    For the longer time series data, the second important mode is the lowest frequency IMF,

    IMF7, which has a mean period of nearly 30 years. Interestingly, the two correlation

    coefficients differ very much for IMF7 and also for IMF6. This is because these IMFs vary

    Fig. 2. The IMFs and residue for the WTI monthly data from Jan. 1946 to May 2006 derived through EEMD.

    Table 1

    Measures of IMFs and the residue for the WTI monthly data from Jan. 1946 to May 2006 derived through EEMD

    Mean period

    (month)

    Pearson

    correlation

    Kendall

    correlation

    Variance Variance as % of

    observed

    Variance as % of

    (IMFs + residual)

    Observed 181.41

    IMF1 3.09 0.10 0.06 0.66 0.36% 0.34%

    IMF2 6.90 0.07 0.05 0.66 0.36% 0.34%

    IMF3 13.43 0.14 0.07 0.89 0.49% 0.45%

    IMF4 26.85 0.17 0.00 2.97 1.64% 1.51%

    IMF5 60.42 0.29 0.03 2.55 1.41% 1.30%

    IMF6 145.00 0.23

    0.01 7.91 4.36% 4.04%IMF7 362.50 0.34 0.01 32.53 17.93% 16.61%

    Residue 0.81 0.75 147.76 81.45% 75.41%

    Sum 108.00% 100.00%

    : Correlation is significant at 0.05 level (2-tailed).

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    slowly. An up (down) movement can last for a long time before the direction changes.

    Therefore, the fluctuation is often reverse of the observed data, which is highly volatile.Although the residue also has the feature of a long cycle, the residue always maintains an

    increasing trend and this direction is the same in the observed data at most of the data points; so

    the Kendall correlation for it is still high. The sum of variances for the two most important

    components, the residue and IMF7, contribute 92.02% of total variance. On the other hand, the

    first two IMFs not only exhibit very low correlation coefficients with the observed data but

    also account for less than 1% of total variance. This means these IMFs do not have serious

    effect on crude oil price. For the two shorter time series, the second important mode is still the

    IMF of the lowest frequency, which is similar to the case of longer time series data. But the

    variance percentage is rather small, less than 4%.

    The two monthly data sets generate nearly the same high frequency IMFs. But IMFs for longperiods can not be extracted from the shorter monthly data sets due to the length restriction.

    Therefore, all the information of IMF4 to IMF7 and the residue of the longer monthly data set

    are contained in the residue of the shorter data set. This means when observing data series

    through a short time span, the long term factors in a longer time span will be treated as part of

    the trend.

    Decomposition results of weekly and monthly data in the same time range show consistency of

    EEMD. The monthly and weekly decomposition results have a good corresponding relationship,

    in accordance with their mean periods, and modes extracted from monthly data can be

    reconstructed roughly from modes generated by weekly data, one by one. We use the word

    roughlybecause there are some weekly data covering daily data in two successive months, which

    Table 3

    Measures of IMFs and the residue for the WTI weekly data from Jul. 2000 to May 2006 derived through EEMD

    Mean period

    (week)

    Pearson

    correlation

    Kendall

    correlation

    Variance Variance as %

    of observed

    Variance as % of

    (IMFs + residual)

    Observed 196.09

    IMF1 3.28 0.07 0.06 0.82 0.42% 0.46%

    IMF2 8.32 0.09 0.07 0.99 0.51% 0.56%

    IMF3 18.12 0.18 0.12 2.93 1.49% 1.65%

    IMF4 38.50 0.14

    0.10

    1.93 0.98% 1.08%IMF5 102.67 0.39 0.27 6.60 3.36% 3.71%

    Residue 0.96 0.80 164.50 83.89% 92.54%

    Sum 90.66% 100.00%

    : Correlation is significant at 0.05 level (2-tailed).

    Table 2

    Measures of IMFs and the residue for the WTI monthly data from Jul. 2000 to May 2006 derived through EEMD

    Mean period

    (month)

    Pearson

    correlation

    Kendall

    correlation

    Variance Variance as %

    of observed

    Variance as % of

    (IMFs+residual)

    Observed 195.02

    IMF1 3.38 0.16 0.12 3.16 1.62% 1.58%

    IMF2 7.89 0.01 0.01 2.36 1.21% 1.18%

    IMF3 14.20 0.19 0.22 7.32 3.75% 3.66%

    Residue 71.00 0.97 0.66 186.98 95.88% 93.58%

    Sum 102.46% 100.00%

    : Correlation is significant at 0.05 level (2-tailed).

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    results in errors in reconstruction. However, the first two modes in weekly data are so fluctuating,

    revealing information contained only in high frequency data.

    4. Composition

    In Section 3, decomposition results of three WTI price data sets and basic analysis of each IMFare provided. In this section, the IMFs are separated into high frequency parts and low frequency

    Fig. 3. The IMFs and residue for the WTI monthly data from Jul. 2000 to May 2006 derived through EEMD.

    Fig. 4. The IMFs and residue for the WTI weekly data from Jul. 2000 to May 2006 through derived EEMD.

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    parts, based on the algorithm mentioned in Section 2.1. The two components and residue have

    abundant economic meanings and reveal some new features of crude oil price.

    We focus only on the longest data set, for its decomposition provides more information about

    composing factors, owing to the longer time span. The mean of the fine-to-coarse reconstructionas a function of IMFs index K is shown in Fig. 5.

    The mean of the fine-to-coarse reconstruction departs significantly from zero at IMF 4.

    Therefore, the partial reconstruction with IMF1, IMF2 and IMF3 represents high frequency

    component and the partial reconstruction with IMF4, IMF5, IMF6 and IMF7 represents the low

    frequency component. The residue is treated separately. Fig. 6 shows the three components and

    Table 4 gives statistical measures, including Pearson and Kendall correlations between each

    component and the observed price, variance of each component and variance percentages.

    Each component has some distinct characteristics. The residue, as mentioned before, is slowly

    varying around the long term mean. Therefore, it is treated as the long term trend during the

    evolution of oil price; each sharp up or down of the low frequency component corresponds to asignificant event, which should be representative of the effect of these events; the high frequency

    component, with the characteristics of small amplitudes, contains the effects of markets' short

    term fluctuations.

    4.1. Trend

    The trend holds a high correlation with the original price and accounts for more than 70% of

    variability, suggesting it is a deterministic force for oil price evolution in the long run. The

    continuing increasing trend is consistent with the economic development of the world, which may

    imply that the long term trend of crude oil price is determined by global economic development.

    Fig. 5. The mean of the fine-to-coarse reconstruction as a function of index K. The vertical dash-line atK= 4 indicates that

    the mean departs significantly from zero (pb0.01).

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    In fact, from the comparison of the trend with the observed price, we can see that historically,

    although oil price would fluctuate dramatically due to significant events, it would return to the

    trend after the influence of the event is over. For example, the oil crisis in 1979 and 1980 made oil

    rise suddenly from $15.5/barrel to $39.5/barrel, but the price fell slowly after that and finally

    returned to the trend price of $22.5/barrel in 1986.

    4.2. Effects of significant events

    The effects of significant events are mainly described by IMF4 to IMF7. Looking at the mean

    periods of these IMFs, the shortest is more than two years and the longest can be as long as thirty

    years, suggesting that it is hard for the market itself to eliminate these effects soon; the duration of

    the effect of a significant event may be very long. In addition, the amplitudes at some data points

    could be more than $10 or even higher, suggesting that the effects of some significant events on

    oil price may be very serious. Since the trend changes slowly and the markets' normal fluctuation

    is small and happens at a high frequency, large fluctuations in medium term arise only from

    significant events. In fact, if we define change rate as the difference between prices for twoconsecutive months divided by the value of the earlier month, the change rate of the original price

    is consistent with that of the low frequency component. But this change rate for the low frequency

    Fig. 6. The three components of the WTI monthly data series from Jan.1946 to May 2006.

    Table 4

    The correlation and the variance of the components for the WTI monthly data series from Jan. 1946 to May 2006

    Pearson

    correlation

    Kendall

    correlation

    Variance Variance as %

    of observed

    Variance as % of

    (IMFs+residual)

    Observed 181.41

    High frequency component 0.16

    0.10

    2.90 1.60% 1.38%Low frequency component 0.43 0.13 59.65 32.88% 28.36%

    Trend 0.81 0.75 147.76 81.45% 70.26%

    Sum 115.93% 100.00%

    : Correlation is significant at the 0.05 level (2-tailed).

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    component often changes more slowly since it excludes the effects of very high frequency

    activities. This is also the reason why the curve generated by the significant event looks like a

    smoothed crude oil price series.

    By separating significant events as the low frequency component from the whole price, theeffect of every significant event can be measured and the result can then be a reference for

    forecasting the effect of the next significant event of the same type. For example, during the

    period of Iran revolution and IranIraq war in 1979 and 1980, this component resulted in a price

    increase of $22.05, which means the maximum effect of the two events was $22.05. This upward

    movement in price began at the beginning of 1979 and it did not return to zero until the end of

    1985. Since no serious event occurred during this period, we can conclude that the influence of

    the two events lasted for 7 years.

    4.3. Normal market disequilibrium

    Besides significant events and the intrinsic trend, crude oil prices are also influenced by many

    other factors, such as bad weather, strikes and depletion of inventory. Durations of these effects

    are often short. So they are classified into high frequency events and their effects are contained in

    the high frequency component. Although we call this component as effects of normal market

    disequilibrium for short, it should be treated as a collection of events with short term impact on oil

    price. Since the data used in our experiments are monthly data, the words short term should be

    described, in general, as less than one year.

    The normal market fluctuations, such as disequilibrium of supply-demand, have no serious

    impact on oil price it is generally within $5. But these events are becoming more and more

    frequent and have lately become the fundamental impetus for pushing oil prices up. Thus, normalmarket fluctuations can be neglected in long term trend prediction, but they are important for short

    term forecasting.

    The main finding of this section is that, assuming crude oil price is composed of the three

    components is reasonable, the residue, which is also described as the trend in EMD, represents

    the major trend of oil price in the long run. The low frequency component can be treated as the

    effects of significant events. It is the main reason for the dramatic oil price variability in the

    medium term. However, the high frequency component should be explained as normal market

    fluctuations or events which have only a short term impact on crude oil price. Through this

    method, the price of $70.94/barrel in May 2006 can be decomposed into a trend price ($33.42), a

    significant event price ($32.55), and a normal fluctuation of $4.86.

    5. Conclusion

    The data of West Texas Intermediate crude oil price are decomposed into several independent

    intrinsic modes with varying and different frequencies, bringing out some interesting features of

    crude oil price volatility. The IMFs and the residue are summed up into only three components,

    based on fine-to-coarse reconstruction. Then the crude oil price can be explained as the composite

    of a long term trend, effect of a shock from significant events, and short term fluctuations caused

    by normal supply-demand disequilibrium. Oil price in the long run is basically determined by the

    trend, which changes continuously and stays around the long term mean. The sharp downs or ups

    in oil prices are triggered by unpredictable and significant events, the impact of which may endure

    for several years. Otherwise, the small fluctuations in the short term are mainly driven by normal

    market activities or some small events which do not have a serious influence on oil markets.

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    By analyzing the composition of oil price, many forecasting strategies can be considered: the

    first is predicting every IMF based on its own characteristics, such as using a polynomial function

    to fit the residue, using a Fourier function to simulate low frequency IMFs, and applying

    nonlinear forecasting technology to deal with high frequency IMFs, and then integratingindividual parts to obtain a final result. The second might be grouping the IMFs into a nonlinear

    part and a linear part, forecasting each individually, and then summing them up together. While

    considering the concrete implications of each component, we suggest every part must be forecast

    based on both its concrete implications and data characteristics. The trend can be predicted by

    fitting the curve and the short term fluctuations can be dealt with nonlinear forecasting techniques

    such as Support Vector Regression and Artificial Neural Network. But significant events are hard

    to predict and evaluate. As people know, a significant event itself is influenced by many factors,

    such as political situation, weather and other complicated factors. No one knows when and where,

    what will happen. Even though an irregular event may be expected to happen, evaluating its

    influence is still very difficult. And even if the same event happens again, it may have a differentimpact on oil price, at different times. So there should be some new method or an integrated

    forecasting framework to handle these issues.

    Acknowledgements

    This work is supported by the NSFC, CAS and RGC of Hong Kong. The authors would like to

    thank the two anonymous referees for their many very helpful comments and suggestions.

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