Research Article Multiscale Combined Model Based on Run...

Research ArticleMultiscale Combined Model Based on Run-Length-JudgmentMethod and Its Application in Oil Price Forecasting

Wang Shu-ping Hu Ai-mei Wu Zhen-xin Liu Ya-qing and Bai Xiao-wei

School of Economics and Management North China University of Technology Beijing 100144 China

Correspondence should be addressed to Wang Shu-ping dwangshuping163com

Received 30 December 2013 Revised 15 April 2014 Accepted 14 May 2014 Published 12 June 2014

Academic Editor Jianping Li

Copyright copy 2014 Wang Shu-ping et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Forecasting of oil price is an important area of energy market research Based on the idea of decomposition-reconstruction-integration this paper built a new multiscale combined forecasting model with the methods of empirical mode decomposition(EMD) artificial neural network (ANN) support vector machine (SVM) and time series methods While building the model weproposed a new idea to use run length judgment method to reconstruct the component sequences Then this model was applied toanalyze the fluctuation and trend of international oil price Oil price series was decomposed and reconstructed into high frequencymedium frequency low frequency and trend sequences Different features of fluctuation can be explained by irregular factorsseason factors major events and long-term trend Empirical analysis showed that the multiscale combined model obtained thebest forecasting result comparedwith singlemodels including ARIMA Elman SVM andGARCH and combinedmodels includingARIMA-SVMmodel and EMD-SVM-SVMmethod

1 Introduction

International commodity price fluctuates sharply and risesin the long run Commodity pricesrsquo fluctuation creates largeimpact on global economy for example surging the cost ofimports triggering inflation slowing economic growth anddiminishing the effectiveness of fiscal and monetary policyTherefore analyzing the features of international commodityprice fluctuations so as to predict the price and trend has avery important significance for global economy

From the view of nations and governments commoditiesare indispensable for economic development and have majorstrategic impact onnational economic security If the prices ofcommodities can be predicted more accurately commoditiescan be imported when prices are low so that the importedinflation pressures will be greatly eased Due to lower importcosts government can reduce the subsidies for enterprisestherefore increasing the flexibility of fiscal policy What ismore due to the reduction in foreign exchange expenditurea countryrsquos foreign exchange reserves can be used to adjustthe stability of the exchange rate therefore increasing theflexibility of monetary policy

From the view of producers commodities are raw mate-rials for industries such as aviation transportation foodprocessing They are also products for industries such as oilexploration and nonferrous metals enterprises Commodityprice fluctuations have impact on business costs and profitsIf the price fluctuation of commodities can be predictedmore accurately producersmaymake production plansmoreprecisely thus reducing costs and obtaining higher profits

As for the trading companies sharp fluctuations incommodity prices often result in great loss However due tolack of research team operations team and correspondingdecision-making mechanism the risk of price fluctuationsis underdetermined Especially when dealing commodityfutures the predicted price deviates greatly with actual priceThrough building commodity price forecasting model andprice fluctuation warning system trading companies are ableto avoid the risk of price fluctuations and reduce trade losses

In general in order to provide rational support forgovernment and business decisionmakers it is necessary andurgent to research on commodity prices forecast

This paper is organized as follows Section 2 is a literaturereviewmainly discusses singlemodels and combinedmodels

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 513201 9 pageshttpdxdoiorg1011552014513201

2 Mathematical Problems in Engineering

of forecasting oil prices as well as the shortcomings ofthe existing multiscale combined model Section 3 gives thedetailed process of establishing a new multiscale combinedmodel and gives a new idea that is the run-length judgmentto reconstruct subsequences In Section 4 the empiricalresults of forecasting oil prices are reported and commentedSection 5 concludes the paper

2 Literature Review

Researchers have developed quite a lot of methods to ana-lyze and forecast oil price which can be roughly dividedinto single models and combined models Single modelsinclude qualitative methods causality regression methodstime series methods and mathematical methods Combinedmodels are formed by combining single models according tocertain rules

Abramson and Finizza [1] predicted the trend of oilprice based on OPEC member countriesrsquo output volumetransport capacity policy and expert judgment This qual-itative method is flexible easy and quick to use But it isof constraint to the knowledge experience and capacity ofpeople who use it and it lacks the quantitative descriptionYe et al [2] established a regression forecasting model basedon oil reserves oil output and oil import volumes As aprimitive constant coefficient regression model it has somelimitations On one hand the factors affecting oil pricesare numerous and complex It is impossible to include allthe influencing factors On the other hand this modelonly considers the linear impact on oil prices Howevermany studies showed that the fluctuation of commodityprices is nonlinear Gori et al [3] examined the evolutionof oil price and consumption of oil in the last decadesto construct a relationship between them and then pre-dicted the trend of oil price Lanza et al [4] used theECM specification to predict crude oil prices In additionsome researcher applied mathematical methods into oilprice forecasting Fan et al [5] proposed futures weightedoil price multistep prediction method based on PMRSGhaffari and Zare [6] applied a data filtering algorithmto predict daily oil price variation Meade [7] establishedan oil price forecasting model based on Gaussian processMathematical methods are outstanding in fitting complexnonlinear functions and make improvement in oil priceforecasting

Based on the above singlemodels Krogh andVedelsby [8]proved such a thought when the single models are accurateand diversified enough establishing a combined model withthem can obtain better forecasting result Combined modelshave become important for oil price forecasting after thatWang et al [9 10] integrated text mining techniques econo-metric models and artificial neural networks to establishTEII a new combined model and used it to predict oilprice Nguyen and Nabney [11] built a combined model byputting together wavelet decomposition adaptive machinelearning methods and adaptive GARCH and improvedthe prediction accuracy de Souza e Silva et al [12] usedwavelets and hidden Markov models to predict oil pricetrends Ahmad Kazem et al [13] built a combined model

based on chaotic map firefly algorithm and support vectorregressionTheir empirical results showed that the combinedmodel performed better than artificial neural network andsupport vector regression model based on genetic algorithmAzadeh et al [14] presented a flexible algorithm basedon artificial neural network (ANN) and fuzzy regression(FR) to cope with optimum long-term oil price forecast-ing

As oil price sequence showed characteristics of nonlin-ear nonstationary and multiscale researchers began to usemultiscale methods such as wavelet analysis empirical modedecomposition (EMD) to analyze the fluctuations of oil priceThese methods have good time resolution and frequencyresolution and can enhance the variation regularity Xie etal [15] demonstrated that EMD has remarkable effect intime series decomposition and provided a powerful toolfor adaptive multiscale analysis of nonstationary signals Atthe same time they proposed a bandwidth criterion forEMD and used bandwidth EMD to decompose electricityconsumption data into cycles and trend which help usrecognize the structure of the electricity consumption seriesZhang et al [16 17] used EMD to analyze the underlyingcharacteristics of international crude oil price movementsThey gave economic explanations to the reconstructioncomponents such as normal supply-demand disequilibriumthe shock of significant events and long-term trend Yu etal [18] decomposed oil price series with EMD predictedall components with FNN and then integrated them withALNN Li et al [19] proposed a decomposition hybridapproach (DHA) to predict country risk for oil exportersbased on the principle of ldquodecomposition and ensemblerdquoand the strategy of ldquodivide and conquerrdquo Experimentalresults with ten major oil exporters as study samplesdemonstrated that DHA with decomposition process wasstatistically proved to be much stronger and more robustthan other prediction models A hybrid ensemble learningparadigm integrating EEMD and LSSVR was proposed inTang et al [20] The hybrid ensemble method was helpful topredict time series with high volatility Mingming and Jin-liang [21] proposed a multiwavelet recurrent neural networkmodel

Currently the multiscale combined model is still in itsearly development stage but its application prospect canbe wide There are still some problems Firstly the decom-posed sequences are relatively numerous and the forecast-ing workload is large Many papers did not reconstructthe subsequences and some papers reconstructed the sub-sequences subjectively rather than objectively This paperputs forward run-length-judgment method to reconstructall subsequences based on the feature that it has unifiedcriterion and can reconstruct objectively Secondly the recon-structed sequences have little economic implications Thispaper explores relevant economic implication which willhelp us understand oil price fluctuations In addition theselection of prediction methods will affect the accuracy ofprediction This paper chooses different prediction methodsto predict different reconstructed sequences according totheir characteristics

Mathematical Problems in Engineering 3

3 The Establishing and Analysis ofMultiscale Combined Model

31 The Basic Idea of Multiscale Combined Model Generallyspeaking the fluctuations of commodities price sequenceshave showed features of nonlinear nonstationary and mul-tiscale Multiscale refers to multiple frequencies These fea-tures bring difficulties to the forecast of oil price Somegeneral prediction methods failed to grasp the complexcharacteristics and the laws of the data fluctuation thereforethe prediction accuracy was reduced In order to excavatethe rules behind the commodity prices fluctuations it isa good idea to decompose the original data sequence andanalyze the features of each decomposed sequence Amongmany decomposition methods the multiscale method canmine inherent laws and essential features hidden in thedata fluctuations of different scales and can determine theeffect size of influencing factors It also has advantages suchas simple and low computation complexity Therefore themultiscalemethod is used in this paper to decompose the datasequences It is efficient to analyze the influencing factors ofprice sequences and to better predict the trend of price series

The basic idea ofmultiscale combinedmodel is as followsfirstly to decompose the sequence in different scales withmultiscale decomposition method secondly to reconstructthe subsequences then to predict reconstructed sequenceswith different predictionmethods and finally to integrate thepredictions and obtain the final prediction value

The process is shown in Figure 1

32 The Process of Multiscale Combined Model In detail thebasic process of model building is as follows

Firstly EMD is applied to decompose commodity pricesequence EMD is superior to wavelet analysis and Fourierdecomposition method in that it is direct and self-adaptiveEMD has better time resolution and frequency resolutionhighlighting the local characteristics of data and enhancingthe fluctuation rules of subsequence It is also helpful ingrasping the characteristic information of the original data infurther analysis With EMD decomposition the original datasequence will be decomposed to 119899 IMF components whosefrequency is from high to low and one residual component

Secondly a new method that is run-length-judgmentmethod is proposed in this paper to reconstruct these sub-sequences Generally price sequence can be reconstructedinto high frequency medium frequency low frequency andtrend part by run-length-judgment method But some com-modity price sequences may only be reconstructed into highfrequency low frequency and trend part Here we considerthe general case

Thirdly ANN SVM and time series methods are usedto predict the four parts The machine learning methodssuch as ANN and SVM have advantages for high vibrationfrequency sequences They have good learning ability andcapture the nonlinear features of the data The time seriesmethod such as ARIMA is a linear model and suitable fortrend part forecasting

Finally SVM is selected to integrate

The concrete steps of establishing multiscale model are asfollows

(1) The First Step Multiscale Decomposition by EMD Assumethe original price series are 119910(119905) (119905 = 1 2 119873) and it canbe decomposed into several IMFs by EMD these IMFs areobtained by ldquosievingrdquo

(a) Find out all maxima of 119910(119905) and use cubic splinefunction to interpolate them into the upper envelope of theoriginal data Find out all minima of 119910(119905) and interpolatethem into the lower envelope of the original data with cubicspline function The mean of upper and lower envelope oforiginal data is the average envelope 119898

1(119905) Subtracting the

average envelope from the original data 119910(119905)will obtain a newdata sequence ℎ

1(119905)

119910 (119905) minus 1198981(119905) = ℎ

1(119905) (1)

If ℎ1(119905) is an IMF it will be the first subsequence IMF

must satisfy two conditions Firstly the number of its extremepoints must be the same as or a different one at most withthe number of zero crossing points Secondly the upper andlower envelope must be locally symmetric about the axis

(b) If ℎ1(119905) is not an IMF put ℎ

1(119905) into the original data

then repeat process (a) 119896 times until the average envelopevalue tends to be 0 Then the first IMF component 119862

1(119905) is

obtained which represents the high frequency sequence(c) Subtracting the first IMF 119862

1(119905) from the original data

119910(119905) will obtain a new sequence 1198771(119905) Put 119877

1(119905) into the

original data and repeat the processes (a) and (b) we will getthe second IMF component 119862

2(119905) Repeat down until the last

119877119899(119905) is amonotonic function Finally the original data can be

expressed by n IMF components and a residual componentConsider

119910 (119905) =

119899

sum

119895=1

119862119895(119905) + 119877

119899(119905) (2)

In (2) 119877119899(119905) represents the trend of the original price

series 119910(119905) and119862119895(119905) (119895 = 1 119899) represent frequency com-

ponents from high frequency to low frequency respectively

(2) The Second Step Reconstruction by Run-Lengt-JudgmentMethod According to EMD decomposition theory 119877

119899(119905)

represents the trend of signal so we classify it as the trendterm at first Then how to reconstruct these IMF sequencesThis paper proposed a new idea as follows

For 119899 IMF sequences 1198621(119905) 1198622(119905) 119862

119899(119905) use run-

length-judgment method to calculate the run number ofeach IMF component Assume that the mean of 119862

119894(119905) is

119862119894 if the observed data is smaller than 119862

119894 we mark ldquominusrdquo

if the observed data is greater than 119862119894 we mark ldquo+rdquo Then

we obtain a symbol sequence Among the symbol sequenceeach continuous identical symbol sequence is a run thus wecan calculate the run number of each IMF The run numberreflects the volatility of data sequenceThe larger the numberis the higher the volatility is It is obvious that the run numberof any IMF component will not exceed 119873 the total numberof sample data


middot middot middot middot middot middotmiddot middot middotIMFkIMFk+1 IMFm IMFm+1

IMFnIMF1Rn

Medium frequency

SVM

Price sequence

EMD decomposition

Low frequency Trend partHigh frequency

Time series method

Integration

SVMANN

Figure 1 The process of establishing multiscale combined model

After that since the maximum possible run number isequal to the total number of samples we divided the run-length number [1 2 119873 minus 1119873] equally into n intervalsThen the IMFs whose run-length number falls in the sameinterval will be reconstructed into one item Those falling inthe interval of larger run number are high frequency itemsfollowed by medium frequency items and low frequencyitems Thus we can use run-length-judgment method toreconstruct IMFs into high frequency 119910

1(119905) medium fre-

quency 1199102(119905) and low frequency 119910

3(119905) The residual compo-

nent 119877119899(119905) is the long trend item 119910

4(119905)

It can be seen that with the run-length-judgmentmethodthe run interval number is determined by the number ofIMF components and the interval length is determined bythe number of samples and the number of IMF componentsTherefore the reconstruction method is completely depen-dent on characteristics of data fluctuation and data length andit is objective

(3) The Third Step Prediction of Different Subsequences withDifferent Methods According to different scale features ofreconstructed items differentmethods are selected to predict

(a) It can be learned from previous literatures [9 10 18]and our research work Elman neural network is a suitableforecasting approach for high frequency data So here Elmanmethod is selected to predict high frequency sequences 119910

1(119905)

and its predicted value is assumed as 1199101(119905)

(b) SVM is selected to predict medium frequency 1199102(119905)

and low frequency 1199103(119905) SVMmodel maps the input variable

119910(119905) to the high feature space through a nonlinear mapping0 then runs linear regression in the feature space andconstructs the optimal learning machine According to theprinciple of minimizing structural risk the Duality theory

and Saddle Point condition we will obtain the followingoutput variables

119910 (119905) =

119899

sum

119905=1

(120572lowast

119894minus 120572119894) 119896 (119910 (119905)) + 119887 (3)

Therefore we will get the predicted values of mediumfrequency 119910

2(119905) and low frequency 119910

3(119905) which we assumed

as 1199102(119905) and 119910

3(119905)

(c) ARIMA is selected to predict trend item 1199104(119905)

We firstly determine the order of the model and estimatethe unknown parameters Then we establish ARIMA (119901 119902)

model 119910(119905) = 119888 + 1205931119910(119905 minus 1) + 120593

2119910(119905 minus 2) + sdot sdot sdot +120593

119901119910(119905 minus 119901) +

120576(119905) + 1205791120576(119905 minus 1) + sdot sdot sdot + 120579

119901120576(119905 minus 119901) Finally we will obtain the

predicted value of trend item 1199104(119905) which is assumed as119910

4(119905)

(4) The Fourth Step Integration of Prediction Results ofAll Subsequences with SVM Model The method of SVMintegration is to set all predicted results as input and actualprice as output After learning certain amount of samples itwill build a mapping function between component predictedresults and actual price For a trainedmodel when the inputsare predicted results of four components the output is thefinal predicted value 119910(119905)

We can get the final predictive value 119910(119905) by integratingthe predicted values of the four components with SVM Theequation of this multiscale combined model is

119910 (119905) = svm (1199101(119905) 1199102(119905) 1199103(119905) 1199104(119905)) (4)


Table 1 The run number of each IMF

IMF IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7Run number 186 77 32 13 8 5 3

Table 2 The cycle and variance contribution rate of each sequence

High frequency Medium frequency Low frequency TrendCycle 16 4 13 312Variance contribution rate () 04 18 145 822

4 International Oil Price Forecasting

In this paper we use the abovemultiscale combinedmodel toanalyze the characteristics of oil price fluctuation and forecastthe oil price trend

41 Data Selection and Evaluation Criteria This paper selectsmonthly spot price of the USWest Texas international (WTI)crude oil from January 1986 to November 2013 335 data intotal The unit of price is US dollarbarrel Data from January1986 to December 2011 are used as the training set anddata from January 2012 to November 2013 are used as testset All oil price data are from the US Energy InformationAdministration (httpwwweiadoegov)

NMSE and MAPE are used to measure the predictionaccuracy and DS are used to measure the trend predictionabilityThese three evaluation index are calculated as follows

NMSE = 1

1198991205752

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))2

1205752=

1

119899 minus 1

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))

2

MAPE = 1

119899

119899

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910 (119905) minus 119910 (119905)

119910 (119905)

10038161003816100381610038161003816100381610038161003816

DS = 1

119899

119899

sum

119894=1

119889119894

119889119894=

1 (119910 (119905) minus 119910 (119905 minus 1)) (119910 (119905) minus 119910 (119905 minus 1)) ge 0

0 (119910 (119905) minus 119910 (119905 minus 1)) (119910 (119905) minus 119910 (119905 minus 1)) le 0

(5)

The smaller NMSE and MAPE are the larger DS is andthe prediction method is better MATLAB and EVIEWS areused in this paper to process the data The core part ofSVM modeling was finished based on LIBSVM designed byLin EMD and Elman were developed in MATLAB ARIMAmodeling was done in EVIEWS

42 Oil Price Sequence Decomposition and Reconstruction Inthis part of the training set data 312 in total from January1986 to December 2011 are decomposed and reconstructed

Firstly EMD is applied to decompose WTI oil spot priceseries into seven IMF components and a residual componentThe result is shown in Figure 2

According to the EMD theory we firstly classify 119877 as thetrend component Then we calculate the run number of theseven IMF components The result is shown in Table 1

The run-length-judgment method is used to reconstructthe seven IMF components Firstly we divide the run-lengthnumber [1 2 311 312] into 7 equal intervals that is[1 44] [45 88] [89 132] [133 176] [177 220] [221 264]and [264 312] It is obvious that IMF1 falls in the fifthinterval [177 220] IMF2 falls in [45 88] and IMF3 IMF4IMF5 IMF6 and IMF7 fall in [1 44] Therefore according tothe run-length-judgment method IMF1 is classified as highfrequency item IMF2 as medium frequency and IMF3 toIMF7 as low frequency after summation The WTI oil pricesand the four reconstructed sequences are shown in Figure 3

43 Fluctuation Features of Reconstructed Sequences Toobserve the fluctuation features of the four sequences thecycle and variance contribution rate are calculated The cycleis determined by the data number of each sequence dividedby the number of extreme point The variance contributionrate is the ratio of the variance of each sequence divided by theoverall variance of the original data that is119860

119894= 120585119894120585 120585119894is the

variance of the 119894 sequence and 120585 is the variance of the originaloil prices series Statistical results are shown in Table 2

It is shown from the table that the four reconstructedsequences have different features

For trend component its variance contribution ratereaches 822 and its cycle is 312 Trend component isthe most important component of oil price and plays adecisive role for long-term fluctuation The rising trendcomponent is synchronous with the world economy growthwhich indicates that the long-term trend of oil price isfundamentally determined by world economy Although oilprice may fluctuate heavily by the influence of some majorevents such as wars it will return to trend price in the longrun In a word trend component represents the long-termtrend of oil price without the influence of other factors

For low frequency component its variance contributionrate reaches 145 and its cycle is 13 months It is shownin Figure 3 that the shape of the low frequency sequence isconsistent with oil price sequence Specially every volatilitypoint is correspondent with major event influencing the oilprice For example oil price rise from 1990 to 1991 (at 58point in Figure 3) resulted from the Gulf War High volatilityin 2008 (at 270 point in Figure 3) was caused by the USsubprime crisisThese illustrate that low frequency sequencesreflect oil price volatility affected by major events Therefore


Table 3 Oil price forecasting in short-term one year forecasting (Jan 2012 to Dec 2012)

Multiscale combined model ARIMA Elman SVM GARCH ARIMA-SVM EMD-SVM-SVMNMSE 05594 17079 08756 21201 20306 1733 07999MAPE 00506 00927 00728 01017 00999 00963 00579DS () 75 6667 6667 6667 6667 50 75

Table 4 Oil price forecasting in long-term 23 months forecasting (Jan 2012 to Nov 2013)


it is believed that low frequency component represents thesignificant impact of major events It is important to separatelow frequency to predict oil price

For medium frequency its variance contribution rate is18 and its cycle is about 4 months In Figure 3 mediumfrequency sequence shapes as sine wave or cosine wave andits cycle is about one season In general economic time seriesis vulnerable to seasonal factors It is believed that mediumfrequency mainly reflects seasonal factors

For high frequency component its variance contributionrate is 04 and its cycle is 1-2 months Although high fre-quency component has little effect on oil price its cumulativeeffect is not neglectable With the financialization of interna-tional crude oil market the impact of speculation on short-term fluctuation is on the rise High frequency componentis highly volatile and its regularity is not obvious This paperargues that high frequency term represents the impact ofpsychological factors speculation and other irregular factorson oil price

44 Oil Price Forecasting and Comparative Analysis Weselect oil price data from January 1986 to December 2011 asa training set to train the multiscale combined model

ANN is used to predict high frequency component SVMto predict medium frequency and low frequency componentand ARIMA to predict trend componentThe prediction andintegration methods are as follows

(1) Predict high frequency component 1199101(119905) with Elman

Neural Network Input layer node is 3 output layernode is 1 and hidden layer node is 10

(2) Predict medium frequency component with SVMUse cross-validation method to find the optimalparameters 119888 = 6 120574 = 05 and 120576 = 005

(3) Predict low frequency component with SVM Usecross-validation method to find the optimal param-eters 119888 = 3 120574 = 5 and 120576 = 005

(4) Predict trend component with ARIMA model Afterrepeating attempts we chose ARIMA (5 1 3)

(5) Integrate the prediction results of the four compo-nents with SVM Use cross-validation method to findthe optimal parameters 119888 = 4 120574 = 2 and 120576 = 005

To further prove the validity of the proposed multi-scale combined model we select oil price data from Jan-uary 2012 to December 2013 as a test set Then we makecomparative analysis with single models including ARIMAElman SVM and GARCH as well as combined modelsincluding ARIMA-SVM model EMD-SVM-SVM methodwhich is a decomposition ensemble model without ldquorun-length-judgment methodrdquo (ie using a uniform tool of SVMto forecast all of IMFs) and the EMD-SVM-SVM methodadvocated in the literatures [16 17]

The short-term and long-term forecasting effects areshown in Tables 3 and 4

It can be seen from Tables 3 and 4 that the multiscalecombined model improves the prediction accuracy anddirection accuracy of oil prices forecasting No matter inshort-term or in long-term according to the three evaluationindicators including NMSE MAPE and DS the multiscalecombined model established in this paper performs betterthan the single models such as ARIMA Elman SVM andGARCH as well as the combined model such as ARIMA-SVM model and EMD-SVM-SVM method For examplesin short-term forecasting the most precise model amongprevious models is the EMD-SVM-SVM method Its NMSEand MAPE are 07999 and 579 respectively and the DSis 75 However for the multiscale combined model NMSEand MAPE are 05594 and 506 respectively and the DS is75 It is even better than EMD-SVM-SVMmethod In long-term forecasting the NMSE and MAPE of the multiscalecombined model are smaller than those of other methodsmeanwhile the DS of the multiscale combined model is notsmaller than that of any other methods

Overall the multiscale combined model is a good fore-casting method and suitable to forecast international oilprices

45 A Description of the Model Application Comparing withother existing prediction model including single model andcombinedmodel themultiscale combinedmodel establishedin this paper has several characteristics as follows


0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7

Figure 2 EMD decomposition of WTI oil spot price

(1) According to the different scale characteristics of datathe model decomposes the data into seven subse-quences and a trend component These subsequencesare independent with each other So this model cangrasp the datarsquos features from different scales andreveal the underlying rules

(2) Instead of analyzing the components sequencesobtained by EMD decomposition this paper applies

the run-length-judgment method to reconstruct thecomponents sequences The reconstruction has threeadvantages Firstly the main feature of data fluctua-tion is revealed and the movement pattern of recon-structed sequences is found out Secondly the run-length-judgment method is only dependent on thedata fluctuation features and the data length so thereconstruction of component sequences is objective


minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date

Oil pricesHigh frequencyMedium frequency

Low frequencyTrend term

Figure 3 The fluctuation graph of oil prices and the four recon-structed sequences

Thirdly it is easy to find out influencing factorsaccording to the fluctuation features of reconstructedsequences and give economic explanations If thereare too many sequences it is impossible to analyzeand explain

(3) This model applies ANN SVM and time seriesmethod to predict the four reconstructed sequencesrespectively which take the advantages of each pre-diction method It is different from other existingcombined forecasting model such as the literatures[16ndash18] which use the same method to predict thereconstructed sequences

(4) Comparing with the simple linear integration thismodel prevails for using SVM to integrate and capturethe nonlinear relationship between variables

Based on the above characteristics the multiscale com-bined model established in this paper has obvious advantagein forecasting the oil price and improves the predictionaccuracy

When using this model to predict commodity pricesattention needs to be paid to several aspects One is that thismodel is suitable for the economic time series which havecharacteristics of nonlinear nonstationary multiscale But itis not suitable for the high frequency financial time series (forexample there is a data in one minute or several seconds)This model is established through a complex process ofldquodecomposition-reconstruction-prediction-integrationrdquo It isnecessary to give economic explanation to reconstructedsequence However for the high frequency financial timeseries data it is hard to give the economic meaning to thereconstruction sequencesThe second point is that the sampledata need to be above certain length which is required bythe multiple methods For the small sample (no more than30 data) this model is not appropriate

5 Conclusions

Forecasting of oil price is a challenging problem This paperestablishes a new multiscale combined model to analyzeoil price fluctuations and predict its trend EMD is usedto decompose nonstationary oil price sequence into sev-eral IMFs and a residual component For the IMFs wepropose a new run-length-judgment method to reconstructthem Empirical test shows that oil price sequences canbe reconstructed into high frequency sequence mediumfrequency sequence low frequency sequence and trendsequence By analyzing the fluctuation features of these fourcomponents and referring to existing researches we point outthat high medium and low frequency and trend sequencesrespectively reflect the irregular factors seasonal factorsmajor events and the world economyrsquos impact on oil priceThenElman neural networkmethod support vectormachine(SVM) and time series method are applied to forecast thefour components Finally SVM is used to integrate the fourpredicted results and obtained the final prediction valueEmpirical analysis shows that both in short-term and long-term forecasting the multiscale combined model is betterthan single models including ARIMA Elman and SVM aswell as combinedmodels including ARIMA-SVMmodel andEMD-SVM-SVMmethod

This multiscale combined model not only enhances theprediction accuracy but also confers certain economic impli-cations to reconstructed sequences The proposed multiscalecombined model is a combination of ldquodata-driven modelingrdquoand ldquotheory-driven modelingrdquo and is suitable for commodityprice volatility analysis and prediction

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by the Funding Project for Aca-demic Human Resources Development in Institutions ofHigher Learning Under the Jurisdiction of Beijing Munici-pality (PHR20110869) the Special Fund of Subject and Grad-uate Education of Beijing Municipal Education Commission(PXM2013 014212 000005) and theNationalNatural ScienceFoundation Project of China (71301002) as well as Fundingfor training talents in Beijing (401053711403)

References

[1] B Abramson andA Finizza ldquoProbabilistic forecasts from prob-abilistic models a case study in the oil marketrdquo InternationalJournal of Forecasting vol 11 no 1 pp 63ndash72 1995

[2] M Ye J Zyren and J Shore ldquoA monthly crude oil spotprice forecastingmodel using relative inventoriesrdquo InternationalJournal of Forecasting vol 21 no 3 pp 491ndash501 2005

[3] F Gori D Ludovisi and P F Cerritelli ldquoForecast of oil price andconsumption in the short termunder three scenarios parabolic


linear and chaotic behaviourrdquo Energy vol 32 no 7 pp 1291ndash1296 2007

[4] A Lanza M Manera and M Giovannini ldquoModeling and fore-casting cointegrated relationships among heavy oil and productpricesrdquo Energy Economics vol 27 no 6 pp 831ndash848 2005

[5] Y Fan Q Liang and Y-M Wei ldquoA generalized pattern match-ing approach for multi-step prediction of crude oil pricerdquoEnergy Economics vol 30 no 3 pp 889ndash904 2008

[6] A Ghaffari and S Zare ldquoA novel algorithm for predictionof crude oil price variation based on soft computingrdquo EnergyEconomics vol 31 no 4 pp 531ndash536 2009

[7] NMeade ldquoOil pricesmdashBrownianmotion ormean reversion Astudy using a one year ahead density forecast criterionrdquo EnergyEconomics vol 32 no 6 pp 1485ndash1498 2010

[8] A Krogh and J Vedelsby ldquoNeural network ensembles crossvalidation and active learningrdquo Neural Computing and Applica-tions vol 25 pp 231ndash238 1995

[9] S Y Wang L A Yu and K K Lai ldquoA novel hybrid AI systemframework for crude oil price forecastingrdquo in Data Mining andKnowledge Management Y Shi W Xu and Z Chen Eds vol3327 of Lecture Notes in Computer Science pp 233ndash242 2004

[10] S Y Wang L A Yu and K K Lai ldquoCrude oil price forecastingwith TEII methodologyrdquo International Journal of SystemsScience and Complexity vol 18 pp 145ndash166 2005

[11] H T Nguyen and I T Nabney ldquoShort-term electricity demandand gas price forecasts using wavelet transforms and adaptivemodelsrdquo Energy vol 35 no 9 pp 3674ndash3685 2010

[12] E G de Souza e Silva L F L Legey and E A de Souza e SilvaldquoForecasting oil price trends using wavelets and hiddenMarkovmodelsrdquo Energy Economics vol 32 no 6 pp 1507ndash1519 2010

[13] AKazem E Sharifi F KHussainM Saberi andOKHussainldquoSupport vector regression with chaos-based firefly algorithmfor stock market price forecastingrdquo Applied Soft ComputingJournal vol 13 no 2 pp 947ndash958 2013

[14] A AzadehMMoghaddamMKhakzad andV EbrahimipourldquoA flexible neural network-fuzzy mathematical programmingalgorithm for improvement of oil price estimation and forecast-ingrdquo Computers and Industrial Engineering vol 62 no 2 pp421ndash430 2012

[15] Q Xie B Xuan S Peng J Li W Xu and H Han ldquoBandwidthempirical mode decomposition and its applicationrdquo Interna-tional Journal of Wavelets Multiresolution and InformationProcessing vol 6 no 6 pp 777ndash798 2008

[16] X Zhang K K Lai and S-YWang ldquoA new approach for crudeoil price analysis based on empirical mode decompositionrdquoEnergy Economics vol 30 no 3 pp 905ndash918 2008

[17] X Zhang L Yu S Wang and K K Lai ldquoEstimating the impactof extreme events on crude oil price an EMD-based eventanalysis methodrdquo Energy Economics vol 31 no 5 pp 768ndash7782009

[18] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[19] J P Li L Tang X L Sun L A Yu W He and Y Y YangldquoCountry risk forecasting for major oil exporting countriesa decomposition hybrid approachrdquo Computers and IndustrialEngineering vol 63 no 3 pp 641ndash651 2012

[20] L Tang L Yu S Wang J Li and S Wang ldquoA novel hybridensemble learning paradigm for nuclear energy consumptionforecastingrdquo Applied Energy vol 93 pp 432ndash443 2012

[21] T Mingming and Z Jinliang ldquoA multiple adaptive waveletrecurrent neural network model to analyze crude oil pricesrdquoJournal of Economics and Business vol 64 no 4 pp 275ndash2862012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


of forecasting oil prices as well as the shortcomings ofthe existing multiscale combined model Section 3 gives thedetailed process of establishing a new multiscale combinedmodel and gives a new idea that is the run-length judgmentto reconstruct subsequences In Section 4 the empiricalresults of forecasting oil prices are reported and commentedSection 5 concludes the paper

2 Literature Review

Researchers have developed quite a lot of methods to ana-lyze and forecast oil price which can be roughly dividedinto single models and combined models Single modelsinclude qualitative methods causality regression methodstime series methods and mathematical methods Combinedmodels are formed by combining single models according tocertain rules

Abramson and Finizza [1] predicted the trend of oilprice based on OPEC member countriesrsquo output volumetransport capacity policy and expert judgment This qual-itative method is flexible easy and quick to use But it isof constraint to the knowledge experience and capacity ofpeople who use it and it lacks the quantitative descriptionYe et al [2] established a regression forecasting model basedon oil reserves oil output and oil import volumes As aprimitive constant coefficient regression model it has somelimitations On one hand the factors affecting oil pricesare numerous and complex It is impossible to include allthe influencing factors On the other hand this modelonly considers the linear impact on oil prices Howevermany studies showed that the fluctuation of commodityprices is nonlinear Gori et al [3] examined the evolutionof oil price and consumption of oil in the last decadesto construct a relationship between them and then pre-dicted the trend of oil price Lanza et al [4] used theECM specification to predict crude oil prices In additionsome researcher applied mathematical methods into oilprice forecasting Fan et al [5] proposed futures weightedoil price multistep prediction method based on PMRSGhaffari and Zare [6] applied a data filtering algorithmto predict daily oil price variation Meade [7] establishedan oil price forecasting model based on Gaussian processMathematical methods are outstanding in fitting complexnonlinear functions and make improvement in oil priceforecasting

Based on the above singlemodels Krogh andVedelsby [8]proved such a thought when the single models are accurateand diversified enough establishing a combined model withthem can obtain better forecasting result Combined modelshave become important for oil price forecasting after thatWang et al [9 10] integrated text mining techniques econo-metric models and artificial neural networks to establishTEII a new combined model and used it to predict oilprice Nguyen and Nabney [11] built a combined model byputting together wavelet decomposition adaptive machinelearning methods and adaptive GARCH and improvedthe prediction accuracy de Souza e Silva et al [12] usedwavelets and hidden Markov models to predict oil pricetrends Ahmad Kazem et al [13] built a combined model

based on chaotic map firefly algorithm and support vectorregressionTheir empirical results showed that the combinedmodel performed better than artificial neural network andsupport vector regression model based on genetic algorithmAzadeh et al [14] presented a flexible algorithm basedon artificial neural network (ANN) and fuzzy regression(FR) to cope with optimum long-term oil price forecast-ing

As oil price sequence showed characteristics of nonlin-ear nonstationary and multiscale researchers began to usemultiscale methods such as wavelet analysis empirical modedecomposition (EMD) to analyze the fluctuations of oil priceThese methods have good time resolution and frequencyresolution and can enhance the variation regularity Xie etal [15] demonstrated that EMD has remarkable effect intime series decomposition and provided a powerful toolfor adaptive multiscale analysis of nonstationary signals Atthe same time they proposed a bandwidth criterion forEMD and used bandwidth EMD to decompose electricityconsumption data into cycles and trend which help usrecognize the structure of the electricity consumption seriesZhang et al [16 17] used EMD to analyze the underlyingcharacteristics of international crude oil price movementsThey gave economic explanations to the reconstructioncomponents such as normal supply-demand disequilibriumthe shock of significant events and long-term trend Yu etal [18] decomposed oil price series with EMD predictedall components with FNN and then integrated them withALNN Li et al [19] proposed a decomposition hybridapproach (DHA) to predict country risk for oil exportersbased on the principle of ldquodecomposition and ensemblerdquoand the strategy of ldquodivide and conquerrdquo Experimentalresults with ten major oil exporters as study samplesdemonstrated that DHA with decomposition process wasstatistically proved to be much stronger and more robustthan other prediction models A hybrid ensemble learningparadigm integrating EEMD and LSSVR was proposed inTang et al [20] The hybrid ensemble method was helpful topredict time series with high volatility Mingming and Jin-liang [21] proposed a multiwavelet recurrent neural networkmodel

Currently the multiscale combined model is still in itsearly development stage but its application prospect canbe wide There are still some problems Firstly the decom-posed sequences are relatively numerous and the forecast-ing workload is large Many papers did not reconstructthe subsequences and some papers reconstructed the sub-sequences subjectively rather than objectively This paperputs forward run-length-judgment method to reconstructall subsequences based on the feature that it has unifiedcriterion and can reconstruct objectively Secondly the recon-structed sequences have little economic implications Thispaper explores relevant economic implication which willhelp us understand oil price fluctuations In addition theselection of prediction methods will affect the accuracy ofprediction This paper chooses different prediction methodsto predict different reconstructed sequences according totheir characteristics
















1(119905)

119910 (119905) minus 1198981(119905) = ℎ

1(119905) (1)






1(119905) is




1(119905) into the





119910 (119905) =

119899

sum

119895=1

119862119895(119905) + 119877

119899(119905) (2)





119899(119905)



119899(119905) use run-


119894(119905) is







IMFnIMF1Rn

Medium frequency

SVM

Price sequence

EMD decomposition


Time series method

Integration

SVMANN







4(119905)




1(119905)






119910 (119905) =

119899

sum

119905=1

(120572lowast

119894minus 120572119894) 119896 (119910 (119905)) + 119887 (3)




as 1199102(119905) and 119910

3(119905)



model 119910(119905) = 119888 + 1205931119910(119905 minus 1) + 120593


119901119910(119905 minus 119901) +




4(119905)



119910 (119905) = svm (1199101(119905) 1199102(119905) 1199103(119905) 1199104(119905)) (4)










NMSE = 1

1198991205752

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))2

1205752=

1

119899 minus 1

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))

2

MAPE = 1

119899

119899

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910 (119905) minus 119910 (119905)

119910 (119905)

10038161003816100381610038161003816100381610038161003816

DS = 1

119899

119899

sum

119894=1

119889119894

119889119894=



(5)







119894= 120585119894120585 120585119894is the



























0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7






minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























1(119905)

119910 (119905) minus 1198981(119905) = ℎ

1(119905) (1)






1(119905) is




1(119905) into the





119910 (119905) =

119899

sum

119895=1

119862119895(119905) + 119877

119899(119905) (2)





119899(119905)



119899(119905) use run-


119894(119905) is







IMFnIMF1Rn

Medium frequency

SVM

Price sequence

EMD decomposition


Time series method

Integration

SVMANN







4(119905)




1(119905)






119910 (119905) =

119899

sum

119905=1

(120572lowast

119894minus 120572119894) 119896 (119910 (119905)) + 119887 (3)




as 1199102(119905) and 119910

3(119905)



model 119910(119905) = 119888 + 1205931119910(119905 minus 1) + 120593


119901119910(119905 minus 119901) +




4(119905)



119910 (119905) = svm (1199101(119905) 1199102(119905) 1199103(119905) 1199104(119905)) (4)










NMSE = 1

1198991205752

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))2

1205752=

1

119899 minus 1

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))

2

MAPE = 1

119899

119899

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910 (119905) minus 119910 (119905)

119910 (119905)

10038161003816100381610038161003816100381610038161003816

DS = 1

119899

119899

sum

119894=1

119889119894

119889119894=



(5)







119894= 120585119894120585 120585119894is the



























0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7






minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











IMFnIMF1Rn

Medium frequency

SVM

Price sequence

EMD decomposition


Time series method

Integration

SVMANN







4(119905)




1(119905)






119910 (119905) =

119899

sum

119905=1

(120572lowast

119894minus 120572119894) 119896 (119910 (119905)) + 119887 (3)




as 1199102(119905) and 119910

3(119905)



model 119910(119905) = 119888 + 1205931119910(119905 minus 1) + 120593


119901119910(119905 minus 119901) +




4(119905)



119910 (119905) = svm (1199101(119905) 1199102(119905) 1199103(119905) 1199104(119905)) (4)










NMSE = 1

1198991205752

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))2

1205752=

1

119899 minus 1

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))

2

MAPE = 1

119899

119899

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910 (119905) minus 119910 (119905)

119910 (119905)

10038161003816100381610038161003816100381610038161003816

DS = 1

119899

119899

sum

119894=1

119889119894

119889119894=



(5)







119894= 120585119894120585 120585119894is the



























0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7






minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















NMSE = 1

1198991205752

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))2

1205752=

1

119899 minus 1

119899

sum

119905=1

(119910 (119905) minus 119910 (119905))

2

MAPE = 1

119899

119899

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910 (119905) minus 119910 (119905)

119910 (119905)

10038161003816100381610038161003816100381610038161003816

DS = 1

119899

119899

sum

119894=1

119889119894

119889119894=



(5)







119894= 120585119894120585 120585119894is the



























0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7






minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra































0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

50

minus50

0

1 51 101 151 201 251 301

minus005

0

1 51 101 151 201 251 301

50

100

R

0

1 51 101 151 201 251 301

20

minus20

0

1 51 101 151 201 251 301

20

minus20

0

minus10

10

1 51 101 151 201 251 301

0

1 51 101 151 201 251 301

50

minus50

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF7






minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus40

minus20

0

20

40

60

80

100

120

140

160

1 41 81 121 161 201 241 281

US

dol

lar

barr

el

Relative date









5 Conclusions





Acknowledgments


References































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Multiscale Combined Model Based on Run...

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