cost forecasting

KSCE Journal of Civil Engineering (2018) 22(5):1626-1633

Copyright ⓒ2018 Korean Society of Civil Engineers

DOI 10.1007/s12205-017-0452-x

− 1626 −

pISSN 1226-7988, eISSN 1976-3808

www.springer.com/12205

Construction Management

Forecasting Construction Cost Index Using Interrupted Time-Series

Taenam Moon* and Do Hyoung Shin**

Received April 5, 2017/Accepted June 19, 2017/Published Online August 9, 2017

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Abstract

The Construction Cost Index (CCI) provided by the Engineering News-Record (ENR) is frequently used in predicting the cost of construction projects because it reflects a comprehensive trend in the construction costs. In previous studies, the CCI was forecasted using the time-series analysis methods. However, the effects of specific intervening factors such as economic recession and policy changes on the CCI data were neglected, thus compromising the reliability and accuracy of the forecast models. In this study, an interrupted time-series forecasting model was developed wherein the economic recession of 2008 was reflected in the forecasting model, which is an outlier identified to have significant impact on the CCI. The forecast result obtained using the interrupted time- series forecasting model was better than that using the conventional forecast models such as the ARIMA and Holt–Winters exponential-smoothing models. The accurately forecasted CCI using the presented model will help in budget and bid planning as well as assessing the risk of future businesses.

Keywords: Construction Cost Index (CCI), interrupted time-series, forecast, outlier detection, intervention analysis

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1. Introduction

The cost associated with a construction project is an important

parameter that needs to be analyzed by all parties, including the

project owner, contractor, and subcontractor. An increase in the

construction costs during the project period can have a negative

impact on the overall project such as delay or termination of the

project, high project costs, and quantitative and qualitative

degradation of bid competition. Predicting the trend in construction

costs is crucial in estimating the cost of construction projects as

well as assessing the risks associated with budget planning and

coordination and costs (Xu and Moon, 2013). However, since

the past few decades, many construction companies and project

owners have suffered huge losses because the final construction

costs were considerably higher than those initially anticipated at

the planning phase despite having made significant efforts to

accurately predict the construction costs (Touran and Lopez, 2006).

This problem exists largely because it is not easy to accurately

predict the construction costs because of the volatility and

uncertainty in the factors such as transportation and construction

material costs, which directly influence the construction market,

and socioeconomic factors such as macroeconomic environments.

In addition, there is considerable difficulty in predicting the

actual construction costs of a few months or several years into

the future during the planning process because the time gap

between the project planning process and the actual construction

period is considerable (Shane et al., 2009).

The Construction Cost Index (CCI) can be effectively used to

estimate the construction costs of a construction project by

employing it to the temporal correction of cost data, cost planning,

price fluctuation, comparison with relevant costs, and evaluation

of market trend (Seeley, 1972; Fleming and Tysoe, 1991). In

particular, the US construction industry widely employs the CCI,

provided by the Engineering News-Record (ENR), because the

trend in the construction costs can be studied comprehensively

(Lewis and Grogan, 2013). The ENR conducts various surveys

and studies on construction economics, including US construction

materials and labor costs, to provide statistical information based

on their findings. The CCI is published in the first week of every

month with 1913 as the reference year. The ENR discloses the

individual CCIs, as well as the average of the CCIs, of 20 cities

in the United States. However, the CCIs are often predicted

because the published CCI does not reflect the actual time

required for project completion. Thus, the CCI cannot be employed

satisfactorily to estimate the cost, prepare the bids, and plan the

investments required for a project. In particular, for construction

projects where millions of dollars are invested, it is very important to

increase the accuracy of forecasting the CCI because a mere 1%

error in the construction cost forecast translates to considerable

losses (Shahandashti and Ashuri, 2013).

Many studies have suggested CCI-forecasting methods largely

based on causality analysis or time-series analysis. In recent years, in

most of the studies, the time-series-analysis-based methods were

preferred because the independent variables must be precisely

selected and such variables must be accurately predicted for

causality analysis. The data used in the time-series analysis have

TECHNICAL NOTE

*Graduate Student, Dept. of Civil Engineering, Inha University, Incheon 22212, Korea (E-mail: [email protected])

**Member, Associate Professor, Dept. of Civil Engineering, Inha University, Incheon 22212, Korea (Corresponding Author, E-mail: [email protected])

Forecasting Construction Cost Index Using Interrupted Time-Series

Vol. 22, No. 5 / May 2018 − 1627 −

been observed over a relatively long period. These data are used

to develop the model and calculate the predicted values under an

assumption that the system based on this time-series data will be

maintained in the future. In the event of uncontrollable factors

such as policy changes, strikes, or wars, there is a possibility that

the time-series data over a long period may have different

patterns at different times because of the time-specific nature of

such factors. Hence, it is difficult to have confidence in the

analysis results if the data are affected by any event in the time-

series analysis, particularly when such effects are not reflected in

the model. Moreover, in most of the CCI-forecasting methods

based on the time-series analysis, necessary adjustments were

never made to consider these factors.

This study proposes an interrupted time-series model to

forecast the CCI, which helps in overcoming such limitations by

reflecting the intervening factors that influence the CCI to

improve the reliability and accuracy of the forecasting model.

The time-series data used in developing the forecasting model

are the CCI data obtained from the ENR, dating from January

1990 to February 2016. The analysis was performed using R

programming language.

2. Related Studies

Generally, the causality and time-series analyses have been

widely used in forecasting the construction costs (Touran and

Lopez, 2006). The CCI-based forecasting methods can be broadly

divided into the aforementioned methods.

2.1 Causality Analysis

The previous causality analysis methods used for forecasting

the CCI involved selecting independent variables that could best

explain the CCI and developing the model using these variables

with the help of linear-regression analyses. For example, Williams

(1994) predicted the CCI using the prime lending rate, housing

starts, and months of the year as the independent variables.

Hwang (2009) developed a model using prime-interest rate,

housing starts, and consumer price index. Ashuri et al. (2012)

predicted the CCI by determining the money supply and crude

oil prices as the significant variables having a long term correlation

with the CCI, among various variables. In these studies, the

causality analysis method was used to improve the predictability

of the model by using variables that were neglected in previous

studies or by using variables that coincided with the economic

conditions of the time. However, the causality analysis method

has disadvantages in that the independent variables associated

with the CCI must be identified and the predicted values of these

independent variables must be calculated. In particular, it is

difficult to select appropriate independent variables because

there are various factors affecting the construction costs in the

construction industry. Moreover, the degrees of such effects vary

with respect to time. In addition, predicting the future value of

the selected independent variables becomes a factor, as it

increases the error in the forecasted value of the CCI. Hence, the

causality analysis method has not been widely used in forecasting

the CCI in recent years (Joukar and Nahmens, 2015; Xu and

Moon, 2013).

2.2 Time-series Analysis

In many studies, the time-series analysis was used to overcome

the disadvantages of the causality analysis method in which the

CCI is explained with external factors. The time-series analysis

can be divided into two categories: a univariate time-series

analysis and a multivariate time-series analysis. The univariate

time-series analysis is used to predict the values of a dependent

variable by using its past values as an explanatory variable.

Unlike the causality analysis method, which helps in determining

the relationship between the various variables, the time-series

analysis method requires only the statistical information and

structure of the past values under an assumption that the past

time-series pattern continues to this day. As one of the most

representative CCI- forecasting studies using a univariate time-

series, Ashuri and Lu (2010) showed that seasonal Autoregressive

Integrated Moving Average (ARIMA) and Holt–Winters

exponential-smoothing models provided the most accurate

predictability by comparing the predictability of various univariate

time-series analyses. Additionally, Joukar and Nahmen (2015)

concluded that the variation values were not constant as the CCI

varies over time; moreover, in most of the previous CCI studies,

such variations over time were neglected. They forecasted the

CCI wherein they reflected the volatility of variance using

Autoregressive Conditional Heteroskedasticity (ARCH) and

Generalized Autoregressive Conditional Heteroskedasticity

(GARCH) with better results than the existing ARIMA model in

a one-step ahead forecast.

A multivariate time-series analysis is a time-series analysis

performed using multiple independent variables, which follows

the vector autoregression (VAR) approach. In recent years, the

multivariate time-series analysis of the CCI has been frequently

studied in comparison with the univariate analysis. For example,

Hwang (2011) developed a VAR model considering the CCI and

Consumer Price Index (CPI) as variables to forecast the CCI and

showed that this predictive model yielded more accurate predictions

than the univariate time-series models. Xu and Moon (2013)

predicted the CCI using the co-integrated vector autoregression

(C-VAR), considering not only the long-term effects of the two

variables but also the short-term interactions, with the CCI and

CPI as variables. In addition, they showed that this model

exhibited better results than a univariate time-series model such

as the ARIMA model. However, the VAR models have some

disadvantages in that the number of parameters to be estimated is

high compared to the dependent variable data. The results are

largely influenced by the method whereby the analyst chooses

the variable selection, lag length, and order of variables in the

model.

To date, the time-series analysis of the CCI has been performed

under an assumption that the time-series patterns of the past

continue to exist in both univariate and multivariate analyses.

Taenam Moon and Do Hyoung Shin

− 1628 − KSCE Journal of Civil Engineering

However, a considerable amount of real-world data, particularly

the time-series data observed over a long period, contains

outliers that influence such data with the change in the trend. In

previous CCI studies, because the time-series data were modeled

without considering the outliers, there are possibilities that

significant biases have occurred in the autocorrelations, partial

autocorrelations, and ARIMA parameters. As such, the biases

could have significantly influenced the predicted values by

distorting the results of statistical tests because they tend to

increase the confidence intervals of the model parameter (Guttman

and Tiao, 1978; Chang, 1982; Galeano and Peña, 2013). Hence,

in this study, the outliers that have influenced the CCI data were

identified and a CCI-forecasting model is proposed wherein such

outliers are accounted for as interventions. For the intervention

analysis, the multivariate time-series analysis is not generally

used because the multivariate time-series analysis is used to

estimate parameters using the cross-correlation of the variables,

making it difficult to apply various interventions to each variable.

Thus, the multivariate analysis was ruled out in this study. The

intervention model proposed in this study was developed based

on the interrupted ARIMA model (Box and Tiao, 1975), which

was a univariate model.

3. Development of CCI-Forecasting Model

To construct and validate the CCI-forecasting model, the CCI

data from January 1990 to January 2015 and from February 2015

to February 2016 were classified as training and test sets,

respectively. In the modeling process, the training set was first

used to test whether the CCI satisfied the stationarity condition,

which is the fundamental assumption of the time-series analysis,

and estimate the basic ARIMA model. The outliers were then

identified using this basic ARIMA model as the reference by

employing the outlier-detection method proposed by Tsay

(1988), breakpoint-estimation method proposed by Bai (1994),

and generalized Extreme Studentized Deviate (ESD) test suggested

by Rosner (1983). Among the identified outliers, appropriate

intervention points were selected and a predictive model was

developed by performing the intervention analysis. Additionally,

the CCI-forecast values, estimated through the intervention

analysis using the test set, were compared with the actual CCI

and forecast values to validate the model; these values were

derived from the ARIMA and Holt–Winters methods, which

were commonly used time-series models for forecasting the CCI.

3.1 Stationary Test

The CCI data used in this study are the monthly data dated

from January 1990 to February 2016 (a total of 314 months). In

the time-series analyses, a unit-root test such as the augmented

Dickey–Fuller test (Dickey and Fuller, 1979) is a commonly

used method for checking the stationarity condition. However,

Perron (1989) stated that if a structural break such as a sudden

increase or a trend change exists in the time-series data, it could

have an impact on the validity of the unit root. Fig. 1 shows the

lagged first difference of the CCI (∆CCIt = CCIt−CCIt-1, ∆: the

first difference operator). The figure shows that there are changes

in the CCI trend and variance in 1993, 2001, 2008, and 2013.

These changes can cause errors in the validation of the unit root

as well as influence the parameter estimation. In this case, it is

necessary to perform a unit root test wherein the structural breaks

are considered endogenously, thus reducing the bias in the unit-

root test (Zivot and Andrews, 1992; Perron and Vogelsang, 1992;

Perron, 1997). Table 1 lists the results of the Zivot–Andrews unit

root test for the CCI data, which is one of the most commonly

used unit-root tests. In a unit root test, the trends or the average

values must be considered depending on the types of data. Thus,

in this study, the trend term was considered in the unit-root test

for CCIt, and the intercept (the average value of the data) in the

unit-root test for ΔCCt. As listed in Table 1, the t-value of CCIt is

-3.838, and the null hypothesis could not be rejected at the 5%

significance level. However, when the t-value of ΔCCIt is

-15.3791, the null hypothesis was rejected at the 5% significance

level. Through this result, it was confirmed that the lagged first

difference of the CCI satisfied the stationarity condition.

Accordingly, further analysis in the study was conducted using

the lagged first difference of the CCI.

3.2 ARIMA Modeling

To confirm the degree of the ARIMA model for the CCI, the

autocorrelation between the time differences was checked by

investigating the Auto-Correlation Function (ACF) and Partial

Auto-Correlation Function (PACF) of the first lagged difference

Fig. 1. Lagged First Difference of CCI

Table 1. Results of Zivot–Andrews Unit-Root Test

Series Critical Value of t

(at 5% level of significance) t-Value

CCIt -4.42 -3.838

ΔCCIt -4.8 -15.3791

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Vol. 22, No. 5 / May 2018 − 1629 −

of the CCI (ΔCCIt). The ACF plot, shown in Fig. 2, exhibits a

significant shape in Lag 1 and a trend that gradually reduces into

a sine shape. In addition, the PACF plot presents a significant

shape in Lag 1. The first lagged difference of the CCI was

regarded at first place to have seasonality in Lag 5 because of the

weak significance in Lag 5 in its ACF and PACF. However, no

significant ACF or PACF patterns were observed in Lags 10 and

15, and no seasonality was observed when the ACF and PACF of

the CCI were examined. Thus, it was decided not to consider the

seasonality for the first lagged difference of the CCI in the

ARIMA modeling. The ACF shape in Lag 5 was considered an

error that could be accepted within a level of significance of 5%.

It was tentatively reasoned thorough this that it is appropriate to

forecast the CCI based on the lagged first-differenced Auto-

Regression (AR) model, i.e., ARIMA(1,1,0). Eq. (1) represents

the forecasting model of the CCI derived as ARIMA (1,1,0)

shape using the training set. Using the first lagged difference, this

model is used to forecast ΔCCIt+1, which is the change in the CCI

from the previous month to the next month. Hence, the forecast

value of the CCI, CCIt+1, can be calculated as CCIt + ΔCCIt+1 by

adding the CCI change compared to the previous month to the

CCI value of the previous month.

∆CCIt+1 = 17.6447 + 0.2127∆CCIt + εt+1 ~ WN(0,1) (1)

where ΔCCIt+1 is first lagged difference (CCIt+1 − CCIt), εt+1 ~

WN(0,1) is white noise (average 0, variance 1) error term.

To better determine the fitness of the ARIMA(1,1,0) model,

the model was compared to other models wherein overfitting

was employed by adding one degree at a time. Table 2 lists the

results obtained by comparing the ARIMA(1,1,0) derived from

the training set with the ARIMA(2,1,0) and ARIMA(1,1,1)

models, wherein the parameters were added to the ARIMA(1,1,0)

model. The Akaike Information Criterion (AIC), which is

generally used as the ARIMA-model selection criterion, reflects

the degree of fit of the model. The smaller the value, the better is

the degree of fit. By comparing of AIC for the fit of the ΔCCIt values, it was shown that the ARIMA(1,1,0) model is more

suitable for the CCI forecasting than the ARIMA(2,1,0) and

ARIMA(1,1,1) models. Moreover, the ARIMA(1,1,0) model

was determined to be most suitable in terms of the parameter

significance and principle of parsimony. Thus, the ARIMA(1,1,0)

model, which was derived using Eq. (1), was selected as the

basic ARIMA model for forecasting the CCI. However, the

intervention effects have not been considered in this basic model.

The outlier must be first detected to incorporate the intervention

effect into the forecasting model.

3.3 Outlier Detection

In this study, the outliers were detected to check whether there

is any intervention of specific factors in the CCI and determine

the timing of such intervention effect, if any. The following three

different outlier-detection methods were applied on the training

set to determine the outliers of the CCI in the study: 1) the

likelihood-ratio test, which is a probabilistic method proposed by

Tsay (1988); 2) the breakpoint-estimation method, which is a

robust method proposed by Bai (1994); and 3) the ESD test

proposed by Rosner (1983). These outlier-detection methods are

used to detect the outliers through different mechanisms. The

likelihood-ratio test is used to probabilistically detect the outliers

using the initially assumed ARIMA model. The breakpoint-

detection method is used to detect the outliers through the shift

and slope changes by dividing the time-series data into segments.

The ESD test is used to determine the outliers by setting the

normal distribution of the time-series data as the reference.

Because using both the detection method, through a probabilistic

model such as ARIMA, and the robust-detection method is

mutually supplementary (Martin, 1980), the likelihood of detecting

the outliers that are not identified using a specific method

increases. In this study, any outlier detected using one of the

aforementioned methods was treated as an outlier.

Table 3 and Figs. 3-5 present the results of the three outlier-

detection methods. A total of 15 outliers were detected. First, the

outliers of the CCI were detected by applying the likelihood-ratio

Fig. 2. ACF and PACF of Lagged First Difference of the CCI

Table 2. Comparison of ARIMA Model for CCI Forecast

ARIMA (1,1,0)

ARIMA (2,1,0),

ARIMA (1,1,1)

AR(1) Coefficient

0.2127*** (0.0564)

0.2096*** (0.0577)

0.2475 (0.1947)

AR(2) Coefficient

0.0147 (0.0576)

MA(1) Coefficient

-0.0364 (0.1969)

Drift 17.6447 ***

(1.9610) 17.6452***

(1.9897) 17.6452***

(1.9769)

AIC 2829.68 2831.61 2831.64

Note: *** represents the P-values, which satisfy the significance level of 0.1% or lower.

Taenam Moon and Do Hyoung Shin

− 1630 − KSCE Journal of Civil Engineering

test to the differences between the actual values and the

corresponding predicted values using ARIMA(1,1,0) model. The

outliers detected using the likelihood-ratio test are classified into

four types: Additive Outlier (AO), Innovational Outlier (IO),

Level Shift (LS), and Temporary Change (TC). Among these,

only the TC and LS were considered for the interrupted time-

series modeling in this study. The TC affects the time-series for a

short period; nevertheless, it comprehensively changes the time-

series, though the effect decreases after the occurrence point. The

LS constantly affects the time-series even after the occurrence

point. The IO was excluded because it does not lead to a

comprehensive change in the time-series, with the effect on the

time-series gradually diminishing after the occurrence point. It is

usually considered inappropriate to consider the IO in the

interrupted time-series modeling. The AO was excluded because

it affects the time-series only at the occurrence point, generally

resulting from exogenous factors such as measurement and

recording errors. The likelihood-ratio test helped in identifying

Table 3. Results of Outlier Detection

Method of Outlier Detection

Likelihood Ratio Test

Breakpoint-Estimation Method

ESD Test Cause of Outlier

Detection Point

1993.05 Jump in Steel Cost

1993.11

1999.06 Jump in Common Labor Cost

2004.03

Jump in Steel Cost2004.05

2004.09

2006.10 Jump in Steel Cost

2008.06

Recession2008.07 2008.07

2008.09

2012.06 Jump in Steel Cost

2013.10 2013.10 Jump in Common Labor Cost

2013.11

Fig. 3. Detection of CCI Outliers (using likelihood-ratio test)

Fig. 4. Detection of CCI Outliers (using breakpoint-estimation method)

Fig. 5. Detection of CCI Outliers (using ESD test)

Forecasting Construction Cost Index Using Interrupted Time-Series

Vol. 22, No. 5 / May 2018 − 1631 −

four outliers. The four outliers were TCs.

The outliers of the CCI were also detected using the breakpoint-

estimation method and ESD test. The number of outliers identified

using the breakpoint-estimation method and ESD test were five

and six, respectively. Because the slope of each segment is

compared in the breakpoint-estimation method, the outliers of

the CCI were effectively detected. In the ESD test, the lagged

first difference of the CCI (i.e., ΔCCI) was employed. The

normality of the data is required in the ESD test. The CCI was

not found to satisfy the normality whereas the normality was

satisfied by the lagged first difference of the CCI. Hence, in the

study, the ESD test was conducted on the lagged first difference

of the CCI instead of the CCI.

Even when the same outlier is detected using the three

detection methods, the occurrence points can be slightly different

depending on the detection method. For example, the three

detection methods were used to identify the outliers between

June 2008 and September 2008. The precise occurrence points

are slightly different; however, the outliers actually occurred at

the same point in time. In other words, the outliers between June

2008 and September 2008 are the same. However, slightly

different occurrence points were detected because of the differences

in the mechanisms of the outlier-detection methods. This issue is

dealt with in the interrupted time-series modeling. The approach

to address the issue is explained in section 3.4.

3.4 Interrupted Time-series Model

An intervention analysis was conducted using the detected

outliers to develop an interrupted time-series model wherein the

intervention effects are reflected. Through this analysis, an

interrupted time-series model was derived by adding the outlier

effects to the ARIMA(1,1,0) model shown in Eq. (1).

It is necessary to determine the intervention timing (occurrence

timing) of the outliers that have actually occurred at the same

point in time to validate the significance of the outlier effects in

the intervention analysis. Otherwise, it is possible to consider the

significance of the outlier effects by unnecessarily reflecting

outliers that are essentially the same. Accordingly, in this study,

identical outliers are indicated via the shaded boxes of similar

colors in Table 3, which were detected to have occurred at

similar time points obtained from the three detection methods.

Here, the intervention-timing points of the outliers occurring at

similar points detected using the different detection methods

were defined at the earliest of the occurrence points of the

outliers. This was done because latter points could have resulted

from the influences of a trend change or a jump in a short period.

Hence, when the intervention point is based on the latter points,

the model can be estimated without considering the outlier

effects between the earlier and latter points. By using this

approach, the following seven intervention timing points were

derived from the 15 outliers listed in Table 3: 1993.05, 1999.06,

2004.03, 2006.10, 2008.06, 2012.06, and 2013.10 (in YYYY.MM).

An interrupted time-series model was developed by adding the

effects of the seven intervention points to the ARIMA(1,1,0)

model, which was selected as the basic model in section 3.2.

Table 4 lists the results of the modeling performed by individually

adding the seven intervention points in the training set to

ARIMA(1,1,0). It can be seen that only model (1), obtained by

adding the intervention of March 2004, and model (2), obtained

by adding the intervention of June 2008, satisfy the significance

of the variable and exhibit a statistical fit. In March 2004, the

steel prices increased sharply to a point where the ENR had to

revise the CCI index after it had been released for the first and

last time in history. In June 2008, the subprime mortgage crisis

occurred, thus sharply increasing the labor and materials costs.

Hence, it is safe to say that the effects and causes of both the

intervention points are explicit. However, the model, which was

obtained by adding both March 2004 and June 2008 as the

interventions, failed to satisfy the significance of the variables.

Thus, the final interrupted time- series model was selected by

choosing the one having better predictability, between models

(1) and (2), wherein March 2004 and June 2008 were added as

the interventions, respectively. To compare the theoretical

predictability of the models, this study examined the AIC through

the change (ΔCCIt+1) in the CCI from the previous month to the

next month. The AIC values of models (1) and (2) were 2820.98

and 2810.42, respectively. Both the models provided better AICs

than the AIC value of ARIMA(1,1,0), which was 2829.68 (refer

to Table 2), where the outlier effects were not reflected. Additionally,

model (2) had a lower AIC value than model (1), showing that it

had better predictability. Moreover, no autocorrelation was

observed in the ACF of the residual nor was there any abnormality

of the residual in the post-hoc test of model (2). Thus, model (2)

was selected as the final interrupted time-series model to forecast

the CCI. Model (2) is represented in Eq. (2), which is obtained

by adding a dummy variable term Pt(T) to Eq. (1). This dummy

variable reflects the effect of the intervention that occurred at the

time point of June 2008. This intervention effect reduces the

statistical distortion due to the outlier that has existed in June

2008, enabling more accurate forecasting. Similar to the case in

Table 4. Statistical Results of Interrupted Time-series Models

AR(1) Coefficient

AR(1) (2004.03)

Coefficient-

MA(1) (2004.03)

Coefficient-

AR(1) (2008.07)- Coefficient

MA(1) (2008.07)

Coefficient Drift AIC

Model (1) 0.1857** (0.0568)

0.6111*** (0.1075)

17.0556*** (1.8841)

2820.98

Model (2) 0.1364* (0.0583)

0.5810*** (0.0521)

112.6052*** (24.1589)

16.3939*** (1.7400)

2810.42

Note : *, **, and *** show the p-values that satisfy the significance level of 5% or lower, 1% or lower, and 0.1% or lower, respectively.

Taenam Moon and Do Hyoung Shin

− 1632 − KSCE Journal of Civil Engineering

Eq. (1), the CCI forecast value CCIt+1 is calculated as CCIt +

DCCIt+1 by adding the changes in the CCI compared to the previous

month, calculated using Eq. (2), to the CCI value of the previous

month.

(2)

where ΔCCIt+1 is lagged first difference of CCIt+1 (CCIt − CCIt),

Pt(T) is dummy variable applied only for T point ( , T =

2008.06), B is Backshift operator (BΔCCIt+1 = ΔCCIt), εt+1 ~

WN(0,1) is white noise (average 0, dispersion 1) error term.

4. Model Validation

So far, the ARIMA and intervention analyses were performed

by setting the monthly time-series of the CCI dated from 1990.01

to 2015.01 as the training set. To validate the predictability of the

model, the test set (2015.02–2016.01) data were employed,

which were monthly time-series of the CCI obtained after the

training set. The interrupted time-series model (as in Eq. (2)),

ARIMA, and Holt–Winters exponential smoothing model were

tested on the test set to compare their predictability over a period

of 12 months (2015.02–2016.01). As the ARIMA and Holt–

Winters exponential smoothing models were frequently used in

previous CCI-forecasting studies, and showed relatively good

predictability for the CCI (Ashuri and Lu, 2010), they have been

included in the models to be compared. Each model helped in

forecasting the CCI value as of February 2015, which was the

first forecasting point, using the CCI value as of January 2015.

The forecasted values were then used to forecast the value as of

March 2015. The CCIs over a period of 12 months, until January

2016, which was the last point of the test set, were determined

similarly.

The forecasted values of the test set obtained using each model

were compared to the actual values. Table 5 lists the test results.

The error rate of each month is the ratio of the absolute value of

the error (the difference between the actual and forecasted

values) to the actual value in the percentage form. In addition,

Mean Absolute Error (MAE), Mean Absolute Percentage Error

(MAPE), and Root Mean Square Error (RMSE) were calculated

to evaluate the forecast error over the entire 12 months of each

model. The comparison-test results show that the MAE, MAPE,

and RMSE were lower in the interrupted time-series model

(interrupted ARIMA model) than those in the ARIMA and Holt–

Winters models. This implies that the interrupted time-series

model has better predictability than the other two models.

5. Conclusions

Forecasting the CCI can be very helpful in predicting the

trends in the future US construction market and determining the

direction of project budget planning. Because a small difference

in the prediction can translate into a significant amount of losses,

a forecast of index such as the CCI can play a crucial role in the

construction project market. When forecasting the CCI using a

time-series analysis, it is necessary to consider the intervention

effects due to events such as policy changes, sudden increase in

construction materials, and economic recessions. These factors

affect the construction market, because they can cause

comprehensive changes in the time-series of the CCI. To

develop a better forecasting model for the CCI, in this study,

stationarity validation and outlier detections were performed,

and necessary considerations were made for the identified

outliers. Finally, an interrupted time-series (interrupted ARIMA)

model was developed wherein the 2008 recession crisis was

incorporated as an intervention.

CCIt 1+Δ 16.3939 112.6052

1 0.5810B– ----------------------------P

t T( ) 0.1364 CCIt εt 1+ WN 0 1,( )∼+Δ+ +=

0 t T≠,

1 t, T=⎩ ⎨ ⎧

Table 5. Comparing the Predictability between CCI-forecasting Models

Month Actual Value

Interrupted ARIMA ARIMA Holt-Winters

Forecasted Value

Error (%) Forecasted

Value Error (%)

Forecasted Value

Error (%)

2015.02 9962 9991.068 0.2907 9993.549 0.3155 9978.792 0.1679

2015.03 9972 10007.826 0.3583 10012.024 0.4002 9988.709 0.1671

2015.04 9992 10024.270 0.3227 10029.845 0.3785 9994.417 0.0242

2015.05 9979 10040.670 0.6167 10047.527 0.6853 10041.459 0.6246

2015.06 10039 10057.065 0.1807 10065.180 0.2618 10070.876 0.3188

2015.07 10037 10073.459 0.3646 10082.826 0.4583 10102.959 0.6596

2015.08 10039 10089.853 0.5085 10100.471 0.6147 10134.876 0.9588

2015.09 10065 10106.247 0.4125 10118.116 0.5312 10171.459 1.0646

2015.1 10128 10122.641 0.0536 10135.761 0.0776 10183.668 0.5567

2015.11 10092 10139.035 0.4704 10153.406 0.6141 10214.335 1.2234

2015.12 10135 10155.429 0.2043 10171.050 0.3605 10218.460 0.8346

2016.01 10132 10171.823 0.3982 10188.695 0.5670 10231.502 0.9950

MAE 34.8420 43.8709 63.2956

MAPE (%) 0.3457 0.4346 0.6231

RMSE 37.8155 46.9538 54.73.7628

Forecasting Construction Cost Index Using Interrupted Time-Series

Vol. 22, No. 5 / May 2018 − 1633 −

The predictability between CCI-forecasting models over 12

months (2015.02–2016.01) in the test set was compared. The

results showed that the interrupted time-series model (MAPE =

0.3457%) provided better predictability than the ARIMA (MAPE

0.4346%) and Holt–Winters exponential-smoothing (MAPE =

0.6231%) models. The results indicate the need to consider the

interventions when developing a CCI-forecasting model to obtain

accurate forecasts. Additionally, it was possible to improve the

convincibility for the CCI forecast values because they were

explained by considering the intervention effects due to events

such as policy changes and economic recessions, which affect the

CCI, instead of explaining merely through characteristics of the

time-series structures. The intervention effects in the CCI not

only affect the future forecast but also have influences on the

normality as well as the autocorrelation, which are the basic

assumptions of the time-series analysis. Thus, it is necessary to

consider such influences to obtain forecasts with solid statistical

reasoning. As suggested in this study, the interrupted time-series

model, along with the interventions, will enable more accurate

forecasting of the construction costs and will be helpful in budget

planning as well as risk assessment for future projects.

Acknowledgements

This work was supported by an Inha University Research

Grant.

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