Nonlinear Forecasting Model regarding Evolutional Risk of the …downloads.hindawi.com/journals/jat/2018/3870285.pdf · 2019-07-30 · titatively analyze the correlation among variables,

Research ArticleNonlinear Forecasting Model regarding EvolutionalRisk of the PPP Project

Wu Gao

Department of Management Hunan City University Yiyang 413000 China

Correspondence should be addressed to Wu Gao gw740620sinacom

Received 10 June 2018 Revised 13 September 2018 Accepted 30 September 2018 Published 14 October 2018

Guest Editor Michela Longo

Copyright copy 2018 Wu Gao This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The special topic of this paper is to build a nonlinear measuring model between PPP project risk and multiple variables andtest it through case analysis Nonlinear regression method was used in this research to study the risk mutation of public-private partnership (PPP) projects without any significant events Risk evolution is influenced by three factors which include (1)macroscopic environment (2) micro environment and (3) subjectrsquos capacity and their cooperative relationship First it revealsthree main drive variables of project risk evolution through case analysis Second it builds a nonlinear time-varying measurementmodel which is then transformed to a classical regression model Lastly it estimates and tests the model parameter by an exampleThe study shows that there is an integral negative correlation among the three independent variables within a certain thresholdrange revealing macro environment as the most significant factor of project risk Analyzing the complex relationship betweenmultiple impact variables and risk evolution of PPP projects can provide a basic tool for forecasting and control of risk

1 Introduction

Under the current macroeconomic downturn pressureinfrastructure investment is still the main power promotingthe growth of economyThe PPPmodel can effectively mergethe resources and abilities of the public sector (government)and the private sector (enterprise) lower the unilateralrisks of government and enterprise and at the same timegenerate enthusiasm [1 2] Thus nonprofit quasi-operationalinfrastructure projects with certain cash inflows are idealWith the complex resonance of both internal and externalenvironment changes and subject behavior evolution [3]the risk formation and evolution process of PPP projectsis extremely complex for big investment scale long con-struction operation cycle and multiple interest subjectsAccording to input variable changes project risk evolutionhas two basic conditions One is stability evolution owing tothe inertia or continuity of PPP project risk evolution thecurrent project risk is highly correlated not only with thecurrent environment and the height of subject variable to acertain extent but also with the risk in past periods [4ndash7]When PPP project risk forms an intrinsic motivation drives

its evolution until input variable changes within a certaingradual range resulting in the characteristics of smooth andgradual evolution The other basic condition is mutabilityevolution wherein shock waves reach a certain point andthe nature and structure of the project risk mutates rapidlychanging among different conditions so that the risk ofvolatility is relatively violent [8] this type of situation usuallyoccurs after a major sudden event

C Zhang et al (2012) analyzed the dynamic evolutionof PPP project risk from two aspects of endogenous andexogenous dynamics F Zo and Y Zhang (2014) analyzedinteractive evolution about risk elements of PPP project LLi (2014) analyzed the behavioral game between multiplesubjects of PPP project and its impact on evolution of risk[9] The evolution of PPP project risk is highly complexand nonlinear and this therefore poses a challenge to theprediction of PPP project risk Many scholars have studiedthe nonlinear evolution of financial risk and have introducedthis method into the field of engineering with a nonlineartime-varying measurement model for PPP project risk soas to help project owners better predict and manage risks[10ndash13] The use of nonlinear science tools for analysis based

HindawiJournal of Advanced TransportationVolume 2018 Article ID 3870285 9 pageshttpsdoiorg10115520183870285

2 Journal of Advanced Transportation

SocietyPolitical

Nature

Market

Management

Macro environment

Microenvironment

Subject ability and cooperation

Corruption

Conflict

Corporation

Economy

CognitionBehavior abilityTechnology

Competition

Finance

Law Operation

Figure 1 The main driving variables of PPP project risk evolution

on the complicated nonlinear evolution of PPP project issuitable We looked at existing research results of examplesof the method of nonlinear regression model includingthe variable regression model [14] time-varying parametermodel [15] and stochastic volatility model [16] and built anonlinear time-varying measurement model to measure therelationship between PPP project risk and variables such asmacro environment micro environment and the capacityand cooperative relationship of the subjects as well as toestimate and inspect the regression coefficient combinedwithcases [17 18] In the model transformation the logarithmand finite difference method not only simplify the nonlin-ear regression model to the multivariate linear regressionmodel but also basically eliminate the lagged effects ofthe previous risk by the finite difference method [19] Inorder to avoid the phenomenon of ldquofalse returnrdquo [20] andensure the validity of parameter estimation we conductedthe stationarity test cointegration test and Granger test [21]respectively before the regression analysis of time series dataTo obtain accurate parameter estimation the least squaresregression is used after ensuring the stable cause-and-effectrelationship between effect variables In previous studiesthe nonlinear time-varying measurement model is mainlyused to study the macroeconomic variables and the riskevolution of the financial market whereas with this paperwe introduce it to provide concise practical analysis tools forproject measurement and risk management

The main goal of this study is to predict risk change bybuilding a nonlinear model between PPP project risk andmultiple variables The main research methods are modelbuilding questionnaire survey statistical data analysis andexample analysis The theoretical assumptions are as follows

Hypothesis 1 Themain influence variables of PPP project riskevolution include macro environment micro environmentand subjects of PPP project

Hypothesis 2 There is a complex nonlinear relationshipbetween PPP project risk and multiple impact variables

Hypothesis 3 The better the environment and the more thecooperation between the subjects the lower the risk for PPPproject

2 Main Driving Variables and Mechanism ofPPP Project Risk Evolution

The size of the PPP project risk is mainly codetermined bythree variables including (1) the macro environment (2)micro environment and (3) the subjectrsquos capacity and gamesituation [22] The interaction between internal elements asshown in Figure 1 [23] reveals that the macro environmentvariables are basically independent and not affected by othervariables while the micro environment and the subjectvariables are interactive

21 Main Driving Variables of PPP Project Risk EvolutionReferring to the research results of B Mohammad (2010) andothers this paper divides the main sources of PPP projectrisk into three aspects (1) macro environment (2) microenvironment and (3) the subjectrsquos capacity and cooperationrelationship Macro environment andmicro environment areobjective factors whereas the subjectrsquos capacity and cooper-ation relationship is the subjective factor There are certaininteractions between the two variables of micro environment

Journal of Advanced Transportation 3

Macro environment (X)

Micro environment (Y)

Cognitive level behavior ability and cooperation (Z)

Risk variables and interaction

changeRisk changes

Construction period

Quality

Input

Cost

Output

Revenue

The deviation of the expected values

rarr

Figure 2 The mechanism of three risk variables of the PPP project

and project subjects Through case analysis [24] the maindriving variables of the risk evolution are as follows(1)Macro environment variables (X) including political

economic social legal and natural variables A politicalenvironment variables include government industrial policyadjustment project examination and approval procedureschanges etc B economic environment variables includefiscal policy and monetary policy changes financial marketvolatility macroeconomic slowdown inflation etcC socialenvironment variables include publicrsquos opposition to theproject construction major public security issues or anincident of violence at the location of the project etcD legalenvironment variables mainly refer to the legitimacy of thePPP projects market demand productservice charge andthe validity of the contract changes due to the change of lawsand regulations thus leading to normal damage failure oreven the suspension of the project and E natural environ-ment variables include major natural disasters deteriorationof geological and hydrological conditions continuous badweather etc(2)Micro environment variables (Y) including competi-

tion market operation finance management technologyand other variables A competition environment variablesare similar projects built by government investors formingsubstantial business competition to this project B marketenvironment variables are when the market demand changeleads to differences between actual demand and marketforecasts C operating environment variables include theactual price of PPP products or services being lower thanexpected and possible emergencies in operations D finan-cial environment variables can include investors unable toallocate funds in a timely manner cash flow not being ableto meet the target difficulty financing rising financial costsetcEmanagement environment variables include decision-making errors caused by substandard project managementsystem bureaucracy and lack of operating experience andability etc and F technical environment variables mayinclude the inappropriate use of technology and outdatedtechnology led by fast technology update(3) Project subject variables (Z) including the cognitive

level behavior ability and cooperation variables of the mainassociated subjects A investment subject variables includethe inability to pay or fulfill the contract responsibility causedby main operation deterioration or bankruptcy temporarywithdrawal of funds or change of investment direction

etc B the contractor subcontractor subject variables maybe insufficient technology and management ability lackof proper technical experts and managers interruption orhidden quality control issues caused by technology andmanagerial errors in the construction misunderstanding ofownerrsquos intentions and the bidding documents improperpricing etc C supplier subject variables would include theinability to supply the quality or quantity of materials ontime D design subject variables include errors in designincomplete design documents untimely delivery of drawingsor inability to complete the design work etcE supervisionsubject variables may be poor management and organiza-tional skills lack of work enthusiasm professional ethics andintegrity incorrect execution of contracts and instructionsetcF government subject variables include staff corruptionuntimely payment of project funds improper interventionetc and G public subject variables may be a lack of publicsupport for the project construction the lodging of a protestor the imposing of strict requirements etc

22 TheMechanism ofThree Risk Variables of the PPP ProjectThe public-private partnership (PPP) project risk variablesmentioned above will continue to change the level of projectrisk so as to change the combinational losses of the wholeproject value The value losses brought by project risk aremultidimensional mainly shown as A project delays pro-longed local (engineering activities subdivisional work) orthe construction and use time of the whole projectB highercosts including additional cost overruns and investment Cquality reduction of materials technology or engineeringthat does not pass approval levels unqualified trial produc-tion and evaluation engineering quality or the completeproject not being able tomeet the design production capacityand D low revenue less income and return on investment(ROI) The mechanism of three risk variables of the PPPproject is shown in Figure 2 where the changes of the inputand output variables are evident whereas the middle processis a ldquoblack boxrdquo

3 Nonlinear Time-Varying MeasurementModel Construction about SmoothEvolution Risk of the PPP Project

The time series data of PPP project risk is nonlinear andirregular due to many factors therefore it is difficult for the


traditional linear model to accurately measure and describethe complex relation between multiple variables Hence weneed to build a nonlinear time-varying measurement modelwhich contains random fluctuations and will be relativelystable within certain threshold parameters

31 The Construction of a Basic Model Combined with theconstruction idea and method of stochastic volatility modeland production function nonlinear time-varying model thestochastic evolution model (formula (1)) of PPP projectrisk is built which is used to describe the evolution ruleand the sensitivity of PPP project risk under the action ofenvironment evolution and subjectrsquos capacity and cooperativerelationship changes

119877119905 = 119883120572119905 sdot 119884120573119905 sdot 119885120574119905 sdot 119890120585119905 119905 = 1 2 3 119899 (1)

In formula (1) 119877119905 represents the size of the project risk inphase t119883119905 means the quality and stability of macro environ-ment119884119905 is the quality and stability ofmicro environment and119885119905 is the cognitive level behavior ability and cooperation ofassociated subjects assuming that macro environment (119883)micro environment (119884) and the cognitive level behaviorability and game relation (119885) are basically independent andadditive and multicollinearity does not exist 120572 120573 and 120574are elasticity coefficients which reflect the relative changesof explained variables to variables being explained 120585119905 is anunobservable random disturbance

32 The Transformation of the Model Formula (1) belongsto a linearized nonlinear time-varying model replacingvariables into multiple linear time-varying models and bytaking the logarithm from formula (1) on both sides it canbe transformed into

ln119877119905 = 120572 ln119883119905 + 120573 ln119884119905 + 120574 ln119885119905 + 120585119905 (2)

In order to eliminate the heteroscedasticity and multi-collinearity caused by lagged variables the following (for-mula (3)) is formed by further differential treatment

ln119877119905 minus ln119877119905minus1 = 120572 (ln119883119905 minus ln119883119905minus1)

+ 120573 (ln119884119905 minus ln119884119905minus1)

+ 120574 (ln119885119905 minus ln119885119905minus1) + 120585119905 minus 120585119905minus1

(3)

which can be expanded further

Δ ln119877119905 = 120572Δ ln119883119905 + 120573Δ ln119884119905 + 120574Δ ln119885119905 + Δ120585119905 (4)

119889 (1) ln119877119905 = 120572119889 (1) ln119883119905 + 120573119889 (1) ln119884119905 + 120574119889 (1) ln119885119905

+ 120575119905(5)

The above variables in differential correction modelsappear in the form of difference due to the low autocorrela-tion degree there will be less multicollinearity to capture thelong-term equilibrium relationship between variables Thevariable substitution does not involve the use of regressioncoefficients so the regression coefficients remain unchangedand can be calculated by the least square method

4 The Empirical Analysis

The PPP project of xx highway stretches about 63 km with 4years of construction a 30-year operation period and a totalinvestment of 105 billion RMB During the construction thelocal government became a shareholder by land demolitionand invested 5 million RMB Social investors are responsiblefor the remaining capital and financing During the oper-ation the local government provides guaranteed subsidiesfor the project which means when annual operation incomedoes not reach a certain proportion of the total investmentthe government will supplement the insufficient share Nowwewill analyze the relationship between risks in the construc-tion period and the main variables by the nonlinear time-varying econometric model

41 The Source and Processing of Original Data Lackingdirect data of project environment and subject we used thequestionnaire method [25] to obtain the original data of thefour main variables The evaluation criterion of variables isthat if the evaluation body thinks an index is better it shouldgive it the higher score Project risk value is equal to theweighted average of the actual values of four indexes that is(1) construction time (2) cost (3) quality and (4) revenue

Δ119879= extension of construction timeoriginal comple-tion timeΔ119862= cost overruns and additional investmentamountoriginal cost or amountΔ119876= engineering quantity which is unqualified orfailed tomeet the design production capacity after thecompletiontotalΔ119872= the reduced amount of cash flow to expectedearningsoriginal expected earnings1198771015840 = (Δ119879 + Δ119862 + Δ119876)3

119877 = |1198771015840 times 100|

The data of the macro environment (119883) micro environ-ment (119884) and behavior ability and game relation (119885) comesfrom the average value of 120 staffs of The Yiyang-LoudiHigh Speed PPP Project according to the 100-grade pointwhich includes government investors and contractors 120questionnaires were distributed through the mobile networkplatform and 112 valid questionnaires were recovered Timeseries data of each quarter from 2014 to 2017 is obtained bycalculation regarding the overall risk macro environmentmicro environment and the subject ability and relation andis shown in Table 1

Using SPSS software calculation the variation coefficientsof four groups of data shown in Table 1 are 119877119905 = 119883

minus6146119905 sdot

119884minus2559119905 sdot 119885minus0658119905 sdot 11989044293 119881119883 = 0034 119881119884 = 0086 and119881119885 = 0069 among which 119881119877 is between 01 and 10 andbelongs to medium variation and the other three variationcoefficients are less than 01 belonging to weak variationwhile the data range differences of the four groups are smallTo eliminate possible heteroscedasticity of original timeseries data and obtain the classical regressionmodel variableswe took respectively the logarithm and first-order difference


Table 1 The original risk data of The Yiyang-Loudi High Speed PPP Project

YearQuarter

The observed value ofoverall risk (119877)

The superiority andstability evaluationvalue of macroenvironment (119883)

The superiority andstability evaluation valueof micro environment

(119884)

The evaluation value ofsubject ability and

cooperation level (119885)

20141 |-42times100|=42 981 919 93820142 |-55times100|=55 993 922 86620143 |-33times100|=33 996 915 94320144 |-94times100|=94 954 835 86920151 |-127times100|=127 914 793 81820152 |-133times100|=133 909 766 76520153 |-141times100|=141 912 719 78420154 |-68times100|=68 945 869 87120161 |-57times100|=57 962 891 85520162 |-62times100|=62 946 885 86220163 |-109times100|=109 933 807 83720164 |-122times100|=122 924 812 81520171 |-128times100|=128 911 789 83920172 |-153times100|=153 892 722 73120173 |-131times100|=131 908 773 79620174 |-143times100|=143 919 734 789

Table 2 The original logarithm data of The Yiyang-Loudi High Speed PPP Project

YearQuarter ln R lnX ln Y ln Z20141 144 459 452 45420142 170 460 452 44620143 119 461 452 45520144 224 456 442 44620151 254 452 436 44020152 259 451 433 43420153 265 451 428 43620154 192 455 446 44720161 174 457 449 44520162 182 455 448 44620163 239 454 439 44320164 250 453 437 44020171 255 452 436 44320172 273 450 427 42920173 257 451 433 43820174 266 452 429 437

of the project risk evaluation value (119877) the superiority andstability evaluation value of macro environment (119883) microenvironment superiority and stability evaluation value (119884)and subject ability and cooperation level evaluation value (119885)with the results shown in Tables 2 and 3

42 The Correlation Analysis of Variables To analyze thecorrelation among variables from the intuitive perspectiveFigure 3 is output throughEviews80 showing that the changetrend correlation among ln119877 and ln119883 ln119884 and ln119884 is notobvious whereas the negative correlation among 119889(1) ln119877

and 119889(1) ln119883 119889(1) ln119884 and 119889(1) ln119885 is obvious through thefirst difference

43 The Smoothness Test of Variables To further quan-titatively analyze the correlation among variables regres-sion analysis of the time series data is needed beforewhich variables data should pass the smoothness testso as to exclude ldquospurious regressionrdquo phenomenon andmake sure of the validity of regression model parametersUsing ADF test methods [26] the results are shown inTable 4


Table 3 The first-order difference of ln119877 ln119883 ln119884 and ln119885

YearQuarter d(1)ln R d(1)ln X d(1)ln Y d(1)ln Z20142 026 001 0 -00820143 -051 001 0 00920144 105 -005 -01 -00920151 03 -004 -006 -00620152 005 -001 -003 -00620153 006 0 -005 00220154 -073 004 018 01120161 -018 002 003 -00220162 008 -002 -001 00120163 057 -001 -009 -00320164 011 -001 -002 -00320171 005 -001 -001 00320172 018 -002 -009 -01420173 -016 001 006 00920174 009 001 -004 -001

10

15

20

25

30

35

40

45

50

I II III IV I II III IV I II III IV I II III IV2012 2013 2014 2015

lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12


d(1)lnR d(1)lnXd(1)lnY d(1)lnZ

Figure 3 The change trend correlation analysis of risks and variables

44TheCointegrationTest of theVariables As seen inTable 4the data is still unsmooth by logarithm while the data bythe first difference is smooth which means that although thesequence data of a single variable is unstable there may bea stable equilibrium relationship between independent vari-ables and dependent variables Therefore the cointegrationtest of variables can be undertaken so as to conduct theGranger testThe results of analyzing data of four groups aftertaking the logarithm by Eviews80 are shown in Table 5

Line 3 in Table 5 shows trace test value 119875 = 00001 andthe Max-Eigen test value 119875 = 00018 are less than 005 thesevalues deny the null hypothesis and show that there exists acointegration relationship between variables In Table 5 line4 the trace test value 119875 = 00581 and the Max-Eigen testvalue 119875 = 02831 are greater than 005 which accepts thenull hypothesis and indicates there exists one cointegrationequation The test values of P in line 5 and line 6 of Table 5are less than 005which denies the null hypothesis and showsthat the number of cointegration equation is less than 2 To

sum up there is only one long-term equilibrium relationshipamong the four variables

45 The Granger Test of the Variables The cointegrationrelationship among four variables indicates that there is atleast one direction of Granger causality As to what kind ofGranger causality exists multivariable Granger test is neededfor further analysis [27 28] The results achieved by usingEviews80 software analysis are shown in Table 6

The values of P in lines 1 3 and 5 of Table 6 are lessthan 005 showing that the change of macro environmentmicro environment and subject capacity and cooperativerelationship is the Granger cause of the project risk in thesecond lag period But in return the project risk is notthe Granger cause of the change of macro environmentmicro environment and subject capacity and cooperativerelationship

46 The Parameter Estimation and Validity Test of the ModelAfter the above three tests we used the linear least square


Table 4 The smoothness test of The Yiyang-Loudi High Speed PPP Project risks and variables

Variables t-Statistic Problowast Results under Significance Level1 5 10

ln119877 -1834031 03504 -4004425 -3098896 -2690439Unsmooth Unsmooth Unsmooth




119889 (1) ln119877 -4339817 00081 -4200056 -3175352 -2728985Smooth Smooth Smooth




Table 5 The results of Johansen cointegration test on the variables

Trace Test Max-Eigen TestNull Hypothesis Problowastlowast Null Hypothesis ProblowastlowastNone lowast 00001 None lowast 00018At most 1 lowast 00581 At most 1 lowast 02831At most 2 lowast 00179 At most 2 lowast 00432At most 3 lowast 00154 At most 3 lowast 00154

Table 6 The results of Granger test on the variables

Null Hypothesis Obs Lags Probln X is not the Granger cause of ln R 14 2 00480ln R is not the Granger cause of ln X 14 2 04984ln Y is not the Granger cause of ln R 14 2 00359ln R is not the Granger cause of ln Y 14 2 05812ln Z is not the Granger cause of ln R 14 2 00377ln R is not the Granger cause of ln Z 14 2 00780

(LLS)method to estimate parameters and the results obtainedby SPSS software calculation are shown in Table 7

The VIF of three variables shown in Table 7 are lessthan 10 revealing that the three influencing variables of PPPproject risk are independent and there is no approximatelinear relationship among them therefore amulticollinearityproblem does not exist in this model In addition thesignificant coefficient model calculated by SPSS software119878119894119892 = 0000 lt 0005 shows that the model is significantand credible 2 lt 119863119882 = 2241 lt 4 minus 119889119906 (when n =16 k = 4 119889119906 = 1664) shows that there is no first-ordersequence autocorrelation the fitting degree 1198772 = 0930shows that 930 of the model can be predicted and theregression equation has a high fitting degree Thus in thiscase the nonlinear time-varying measurement model of the

PPP project risk passes the parameter test and the parameterestimation is valid Therefore the relationship between theproject risk andmacro environmentmicro environment andthe subject ability and cooperation level can be quantitativelydescribed as 119877119905 = 119883

minus6146119905 sdot 119884

minus2559119905 sdot 119885minus0658119905 sdot 119890

44293 suggestingthat when macro environment index changes a unit toward apositive direction project risk changes 6146 units toward thenegative direction whenmicro environment index changes aunit toward a positive direction project risk changes 2259units toward the negative direction and when the subjectability and cooperation level index changes a unit toward apositive direction project risk changes 0658 units towardthe negative direction It shows that project risk is negativelyrelated to three influencing variables being most sensitive tothemacro environment and least sensitive to the subject body

5 Conclusion and Prospect

With this research we introduce an econometrics model intoproject risk analysis and evaluation We studied the dynamicevolution relationship between the overall risk of large PPPprojects and three variables without any significant eventsthrough model building and empirical analysis The mainresearch conclusions are as follows(1) When the PPP project risk steadily evolves within

a certain threshold (eg the impact of project risk on the


Table 7 The regression coefficient of the model

Model Unstandardized Coefficients Standardized Coefficients t Sig Multicollinearity StatisticsB Standard Error Trial Version Tolerance VIF

1

(Constant) 44293 9102 4866 000ln X -6146 3151 -432 -1950 075 114 8745ln Y -2559 1308 -463 -1957 074 100 9996ln Z -658 1325 -092 -497 628 163 6135

project value is within 20 which belongs to the lowerlevel and the nature of the project risk is not radicallychanged) the complex relationship between PPP project riskandmultiple variables can bemeasured by nonlinearmultipleregression model Although the linearized model parametersshare a certain approximation it can simulate the interactiverelationship between project risk and variables under stableconditions(2)There exists a nonlinear negative correlation relation-

ship among the size of the PPP project risk and the qualityand smoothness of macro environment the quality andsmoothness ofmicro environment and the subject ability andcooperation levelTherefore project risk can be controlled byinput variables such as the internal and external environmentand the subject ability and cooperation relation Becausethe relationship among variables is a complex nonlinearcombination a single independent variable and a dependentvariable are not necessarily negatively correlated at someperiod of time (eg when an influencing variable slightlyweakens and the other two variables significantly strengthenit can decrease the whole project risk)(3) Among three variables the coefficient absolute value

of macro environment variable is maximum showing thatproject risk is most sensitive to macro environment changesthat being said the macro environment is relatively stablewith small fluctuation and out of control by the subject soit is not the main object of project risk control Howeverthe coefficient absolute value of micro environment and thesubject is small while their volatility and controllability arestrong Therefore focus should be put on improving themicro environment enhancing cognition level and behaviorability strengthening the subject cooperation and reducingthe game conflict etc In addition it would be useful tocontrol the risk to clear the risk management responsibilityof the main body in the PPP project contract and give fullplay to their respective advantages(4)The PPP project risk data predicted by this model is

the same as the risk value obtained from actual observationregardingThe Yiyang-Loudi High Speed PPP Project It showsthat the model has good prediction function It also showsthat the complex nonlinear influence relationship amongvariables can be measured by a certain exponential modelIndeed the research presented here is limited to the smoothtrend of PPP project risk thus for complex situations suchas smooth evolution mixed with risk mutation nonlinearapproaches such as time-varying parameter model Markovaprobability matrix and the BP neural network would berequired to further expand the risk evolution measurementmodel so as to improve its scientific and applicable scope

This paper builds a risk evolution prediction model forPPP project It provides a useful tool for risk forecasting andcontrolThe research is limited to the risk of PPPprojectswithstable trends In the case of mutations the model needs to bemodified

Data Availability

The data used to support the findings of this study areincluded within the article Raw data was obtained throughquestionnaires Other data were calculated by SPSS

Conflicts of Interest

The author declares that they have no conflicts of interest

Acknowledgments

This paper is funded by Research project of HunanSocial Science Achievement Review Committee in 2018(XSP18YBC048)

References

[1] D Tsamboulas A Verma and P Moraiti ldquoTransport infras-tructure provision and operations Why should governmentschoose private-public partnershiprdquo Research in TransportationEconomics vol 38 no 1 pp 122ndash127 2013

[2] E E Ameyaw and A P C Chan ldquoA fuzzy approach forthe allocation of risks in public-private partnership water-infrastructure projects in developing countriesrdquo Journal ofInfrastructure Systems vol 22 no 3 2016

[3] C Tang and X Li ldquoThe stability of evolution strategy in finitepopulationsrdquo Journal of University of Electronic Science andTechnology of China no 6 pp 821ndash824 2012

[4] K B Salling ldquoA new approach to feasibility risk assessmentwithin transport infrastructure appraisalrdquo Procedia - Social andBehavioral Sciences vol 74 pp 468ndash477 2013

[5] Z-Q Hou and Y-M Zeng ldquoResearch on risk assessmenttechnology of themajor hazard in harbor engineeringrdquoProcediaEngineering vol 137 pp 843ndash848 2016

[6] J Park B Park Y Cha and C Hyun ldquoRisk factors assessmentconsidering change degree for mega-projectsrdquo Procedia - Socialand Behavioral Sciences vol 218 pp 50ndash55 2016

[7] F Saleh and M P Weinstein ldquoThe role of nature-basedinfrastructure (NBI) in coastal resiliency planning A literaturereviewrdquo Journal of Environmental Management vol 183 pp1088ndash1098 2016

[8] Y Jiang ldquoThe new progress based on the time series of structuremutation research and its prediction methodrdquo Statistics andDecision no 19 pp 8ndash11 2011


[9] L Li Z Liu and K Zhang ldquoParticipants status asymmetricgamemodel under the condition of PPP project risk allocationrdquoSystems Engineering Theory and Practice no 8 pp 1940ndash19482013

[10] Y L Xu J F Y Yeung A P C Chan DWM Chan S QWangandY Ke ldquoDeveloping a risk assessmentmodel for PPP projectsin Chinamdasha fuzzy synthetic evaluation approachrdquo Automationin Construction vol 19 no 7 pp 929ndash943 2010

[11] H Thamhain ldquoManaging risks in complex projectsrdquo ProjectManagement Journal vol 44 no 2 pp 20ndash35 2013

[12] L Ma Y Li L Liang M Li and L Cheng ldquoA novel method ofquantitative risk assessment based on grid difference of pipelinesectionsrdquo Safety Science vol 59 pp 219ndash226 2013

[13] S Lua and Y Hong ldquoA comparative study of the measurementsof perceived risk among contractors in Chinardquo InternationalJournal of Project Management vol 31 no 2 pp 307ndash312 2013

[14] W Cheng ldquoThe practical problems analysis of regressionmodelrdquo The Journal of Quantitative and Technical Economicsno 1 pp 86ndash89 2006

[15] J Zhang Y Shen and W Lu ldquoChinarsquos real estate investmentresearch based on time-varying parameter modelrdquo HumanGeography no 6 pp 84ndash88 2010

[16] Q Liu and R Hua ldquoBig risk events impact on Chinarsquos commod-ity futures market effect - based on stochastic volatility modelof the students distributionrdquo The Journal of Quantitative andTechnical Economics no 5 pp 89ndash103 2015

[17] X Zhou and Z Pan ldquoLinear regression model of the nonlinearrobust estimation-based on the theory of experience in theprocess of researchrdquo SystemEngineeringTheory and Practice no4 pp 1014ndash1024 2016

[18] Z Ye ldquoThe research of nonlinear regression model parameterestimation-taking c-d production function for examplerdquo Statis-tics and Information Forum no 1 pp 41ndash45 2010

[19] H Zhang ldquoThe improvement of estimationmethodwhen existsautocorrelationrdquo The Journal of Quantitative and TechnicalEconomics no 11 pp 155ndash161 2010

[20] L Tian ldquoThe interpretation on non-stationary data spuriousregressionrdquo Statistics and Decision no 3 pp 17ndash21 2014

[21] J Zhang and X Gong ldquoStudy on the relationship between thescience and technology input and economic growth in XinJiang - based on empirical co-integration analysis and Grangercausality testrdquo Scientific Management Research no 4 pp 43ndash472009

[22] H P Krane N O E Olsson and A Rolstadas ldquoHow projectmanager-project owner interaction can work within and influ-ence project risk managementrdquo Project Management Journalvol 43 no 2 pp 54ndash67 2012

[23] M Baydoun ldquoRisk management of large-scale developmentprojects in developing countries Cases from MDIs projectsrdquoInternational Journal of Technology Management and Sustain-able Development vol 9 no 3 pp 237ndash249 2010

[24] X Qi Y Ke and S Wang ldquoThe analysis of major risk factorsbased on the case of the Chinarsquos P-projectsrdquo China Soft Scienceno 5 pp 107ndash113 2009

[25] J Liu ldquoFamily social capital and higher education participationan attempt of indirectmeasurementrdquo Journal Science Educationno 3 pp 49ndash53 2011

[26] W Deng andQ Tang ldquoThe unit root processrdquoDevelopment andComparison of TheTheory no 2 pp 132ndash141 2014

[27] Y Li and C Wu ldquoBased on multivariate Granger causality testmethodrdquo Journal of Applied Statistics andManagement no 1 pp50ndash58 2014

[28] Z Li and Y Liu ldquoThe analysis of modern econometric modelsystemrdquo Economics Information no 5 pp 22ndash25 2010

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


SocietyPolitical

Nature

Market

Management

Macro environment

Microenvironment

Subject ability and cooperation

Corruption

Conflict

Corporation

Economy

CognitionBehavior abilityTechnology

Competition

Finance

Law Operation

Figure 1 The main driving variables of PPP project risk evolution

on the complicated nonlinear evolution of PPP project issuitable We looked at existing research results of examplesof the method of nonlinear regression model includingthe variable regression model [14] time-varying parametermodel [15] and stochastic volatility model [16] and built anonlinear time-varying measurement model to measure therelationship between PPP project risk and variables such asmacro environment micro environment and the capacityand cooperative relationship of the subjects as well as toestimate and inspect the regression coefficient combinedwithcases [17 18] In the model transformation the logarithmand finite difference method not only simplify the nonlin-ear regression model to the multivariate linear regressionmodel but also basically eliminate the lagged effects ofthe previous risk by the finite difference method [19] Inorder to avoid the phenomenon of ldquofalse returnrdquo [20] andensure the validity of parameter estimation we conductedthe stationarity test cointegration test and Granger test [21]respectively before the regression analysis of time series dataTo obtain accurate parameter estimation the least squaresregression is used after ensuring the stable cause-and-effectrelationship between effect variables In previous studiesthe nonlinear time-varying measurement model is mainlyused to study the macroeconomic variables and the riskevolution of the financial market whereas with this paperwe introduce it to provide concise practical analysis tools forproject measurement and risk management

The main goal of this study is to predict risk change bybuilding a nonlinear model between PPP project risk andmultiple variables The main research methods are modelbuilding questionnaire survey statistical data analysis andexample analysis The theoretical assumptions are as follows

Hypothesis 1 Themain influence variables of PPP project riskevolution include macro environment micro environmentand subjects of PPP project

Hypothesis 2 There is a complex nonlinear relationshipbetween PPP project risk and multiple impact variables

Hypothesis 3 The better the environment and the more thecooperation between the subjects the lower the risk for PPPproject

2 Main Driving Variables and Mechanism ofPPP Project Risk Evolution

The size of the PPP project risk is mainly codetermined bythree variables including (1) the macro environment (2)micro environment and (3) the subjectrsquos capacity and gamesituation [22] The interaction between internal elements asshown in Figure 1 [23] reveals that the macro environmentvariables are basically independent and not affected by othervariables while the micro environment and the subjectvariables are interactive

21 Main Driving Variables of PPP Project Risk EvolutionReferring to the research results of B Mohammad (2010) andothers this paper divides the main sources of PPP projectrisk into three aspects (1) macro environment (2) microenvironment and (3) the subjectrsquos capacity and cooperationrelationship Macro environment andmicro environment areobjective factors whereas the subjectrsquos capacity and cooper-ation relationship is the subjective factor There are certaininteractions between the two variables of micro environment






changeRisk changes

Construction period

Quality

Input

Cost

Output

Revenue


rarr













119877119905 = 119883120572119905 sdot 119884120573119905 sdot 119885120574119905 sdot 119890120585119905 119905 = 1 2 3 119899 (1)



ln119877119905 = 120572 ln119883119905 + 120573 ln119884119905 + 120574 ln119885119905 + 120585119905 (2)



+ 120573 (ln119884119905 minus ln119884119905minus1)


(3)


Δ ln119877119905 = 120572Δ ln119883119905 + 120573Δ ln119884119905 + 120574Δ ln119885119905 + Δ120585119905 (4)

119889 (1) ln119877119905 = 120572119889 (1) ln119883119905 + 120573119889 (1) ln119884119905 + 120574119889 (1) ln119885119905

+ 120575119905(5)






119877 = |1198771015840 times 100|







YearQuarter




(119884)













10

15

20

25

30

35

40

45

50


lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12




























minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







changeRisk changes

Construction period

Quality

Input

Cost

Output

Revenue


rarr













119877119905 = 119883120572119905 sdot 119884120573119905 sdot 119885120574119905 sdot 119890120585119905 119905 = 1 2 3 119899 (1)



ln119877119905 = 120572 ln119883119905 + 120573 ln119884119905 + 120574 ln119885119905 + 120585119905 (2)



+ 120573 (ln119884119905 minus ln119884119905minus1)


(3)


Δ ln119877119905 = 120572Δ ln119883119905 + 120573Δ ln119884119905 + 120574Δ ln119885119905 + Δ120585119905 (4)

119889 (1) ln119877119905 = 120572119889 (1) ln119883119905 + 120573119889 (1) ln119884119905 + 120574119889 (1) ln119885119905

+ 120575119905(5)






119877 = |1198771015840 times 100|







YearQuarter




(119884)













10

15

20

25

30

35

40

45

50


lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12




























minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





119877119905 = 119883120572119905 sdot 119884120573119905 sdot 119885120574119905 sdot 119890120585119905 119905 = 1 2 3 119899 (1)



ln119877119905 = 120572 ln119883119905 + 120573 ln119884119905 + 120574 ln119885119905 + 120585119905 (2)



+ 120573 (ln119884119905 minus ln119884119905minus1)


(3)


Δ ln119877119905 = 120572Δ ln119883119905 + 120573Δ ln119884119905 + 120574Δ ln119885119905 + Δ120585119905 (4)

119889 (1) ln119877119905 = 120572119889 (1) ln119883119905 + 120573119889 (1) ln119884119905 + 120574119889 (1) ln119885119905

+ 120575119905(5)






119877 = |1198771015840 times 100|







YearQuarter




(119884)













10

15

20

25

30

35

40

45

50


lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12




























minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




YearQuarter




(119884)













10

15

20

25

30

35

40

45

50


lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12




























minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





10

15

20

25

30

35

40

45

50


lnRlnX

lnYlnZ

minus08

minus04

00

04

08

12




























minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




















minus6146119905 sdot 119884









1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1







Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Nonlinear Forecasting Model regarding Evolutional Risk of the …downloads.hindawi.com/journals/jat/2018/3870285.pdf · 2019-07-30 · titatively analyze the correlation among variables,