Analysisofeconometricmethods1 xForecastingconstructionindustrydemandpriceandproductivityinSingaporetheBoxJenkinsapproach1 InterestRatesandConsumptionBE19901
Running head: ANALYSIS REPORT ON ECONOMETRIC METHODS 1
ANALYSIS REPORT ON ECONOMETRIC METHODS 2
Analysis report on econometric methods
Student’s Name
Institution
Analysis report on econometric methods
Economic researchers and authors present the approaches of econometric methods using diversified approaches. This is due to the diversified nature of econometric methods. The methods are a combination of statistical tools and economic theory that are used to analyze, structure and explain economic relations. The diversity of the variables and the linkages among the variables in an economic system forces different writers to use the models in their own unique way and describe a phenomenon, answer a research question and test a hypothetical relationship. These paper summarizes three different research articles and examines how thee different economic researchers perceive econometric methods
In the article Forecasting construction industry demand, price and productivity in Singapore: The Box–Jenkins approach, Hua & Pin (2000) examines the versatility of the Box–Jenkins approach as n analysis and forecast univariate models. The study is done in the constructions industry and two forecasting measures of accuracy: the root-mean-square-error and the mean absolute percentage error were adopted to test the approach. The researchers conclude the model to have great predictive strength and is consistent. The researcher lists the demand model as the most accurate and the productivity model as the least accurate.
The article Nominal interest rate effects on real consumer expenditure, James (1990) challenges the current economic models that measure the purchase of durable household goods as a factor of the variables expected and after-tax interest rates. Instead, the researcher shows that although there is a powerful effect of interest rates on household purchases, the interest rates operate on nominal not real rates. Furthermore, the effects of the nominal interest rates are not only on durable consumables but nondurables as well. The writer feels that the current econometric models fail to factors that affect the non-durables as well as those that arise as a result of excess borrowing constraints caused by rising nominal interest rates and the imposition of repayments limits as a percentage of income by lenders. As a result, consumer spending is more dependent on the nominal interest rates instead of the actual cash flow to households.
References
Hua, G. B., & Pin, T. H. (2000). Forecasting construction industry demand, price and productivity in Singapore: the BoxJenkins approach. Construction Management and Economics, 18(5), 607-618.
Wilcox, J. A. (1990). Nominal interest rate effects on real consumer expenditure. Business Economics, 31-37.
Introductio
n
In the construction industry, regression techniques
have been used often to model and forecast construc-
tion variables such as demand and price owing to their
relative simplicity in both concept and application. Goh
(1999) evaluated the accuracy of the multiple regres-
sion approach in forecasting sectoral construction
demand in Singapore. In the UK, Akintoye and
Skitmore (1994) produced regression models to predict
private-sector construction demand. Tang et al. (1990)
also applied regression analysis to project values of
total construction activities for the Thai construction
industry. In the USA, Killingsworth (1990) developed
a demand forecasting model based on a regression
analysis of the leading indicators of industrial con-
struction. Regression models, using leading indicators
of construction workload, were also built to forecast
UK contractors’ total new orders (Oshobajo and
Fellows, 1989). For construction cost prediction, linear
and loglinear regression methods were explored for
public school buildings in Jordan (Al-Momani, 1996).
Flanagan and Norman (1983) applied simple linear
and curvilinear regressions to obtain extrapolated fore-
casts of tender price, while McCaffer et al. (1983)
developed a regression model to predict construction
price movements. The feasibility of econometric cost
modelling was examined by Bowen (1982) as an alter-
native estimating approach for reinforced concrete
frame structures.
In essence, regression techniques are concerned with
the modelling of relationships among variables, and
they quantify how a response variable is related to a
set of explanatory variables. The strength of a causal
model as a forecasting tool is that it allows the impact
of various alternative inputs to be evaluated. However,
the dif� culty of this approach is that it requires infor-
mation on several variables in addition to the variable
Construction Management and Economics (2000) 18, 607–618
Forecasting construction industry demand, price and
productivity in Singapore: the Box–Jenkins approach
GOH BEE HUA* AND T EO HO PIN
School of Building and Real Estate, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Received 12 July 1999; accepted 13 January 2000
In academic research, the traditional Box–Jenkins approach is widely acknowledged as a benchmark technique
for univariate methods because of its structured modelling basis and acceptable forecasting performance.
This study examines the versatility of this approach by applying it to analyse and forecast three distinct
variables of the construction industry, namely, tender price, construction demand and productivity, based
on case studies of Singapore. In order to assess the adequacy of the Box–Jenkins approach to construction
industry forecasting, the models derived are evaluated on their predictive accuracy based on out-of-sample
forecasts. Two measures of accuracy are adopted, the root mean-square-error (RMSE) and the mean absolute
percentage error (MAPE). The conclusive � ndings of the study include: (1) the prediction RMSE of all
three models is consistently smaller than the model’s standard error, implying the models’ good predictive
performance; (2) the prediction MAPE of all three models consistently falls within the general acceptable
limit of 10%; and (3) among the three models, the most accurate is the demand model which has the lowest
MAPE, followed by the price model and the productivity model.
Keywords: Box–Jenkins approach, forecasting, construction demand, tender price, productivity, accuracy
* Author for correspondence. e-mail: bemgohbh@nus.edu.sg
Construction Management and Economics
ISSN 0144–6193 print/ISSN 1466-433X online © 2000 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
that is being predicted. By contrast, a univariate model
predicts future values of a time series solely on the
basis of its historical values. It treats the system as a
black box and makes no attempt to discover the factors
affecting its behaviour. The time-series model always
assumes that some pattern or combination of patterns
is recurring over time. Hence, by identifying and
extrapolating that pattern, forecasts for subsequent
time periods can be obtained. However, one limitation
of such simpler methods is that they are suitable for
making only short term forecasts. It is also disadvan-
taged by the black box characteristics, whereby
explanatory capabilities are lacking, and hence it is not
suitable for applications where explanation of reasoning
is critical.
Nevertheless, empirical studies dealing with fore-
casting accuracy (Slovic, 1972; Armstrong, 1978; and
Makridakis and Hibon, 1979) have shown that ‘more
complex or statistically sophisticated methods are
not necessarily more accurate than simpler methods’
(Makridakis et al., 1982, p. 112). Greene (1997,
p. 823) notes that ‘researchers have observed that the
large simultaneous equations macroeconomic models
constructed in the 1960s frequently have poorer
forecasting performance than fairly simple, univariate
time-series models based on just a few parameters and
compact speci� cations’. Similarly, in construction-
related studies, researchers have found that a higher
level of accuracy can be achieved by using time-series
methods as they are based upon a stochastic rather
than deterministic approach (McCaffer et al., 1983;
Fellows, 1987; Taylor and Bowen, 1987; and Goh,
1998). As a new approach, Wang and Mei (1998)
presented a time-series model for forecasting construc-
tion cost indices in Taiwan.
Univariate time-series forecasting techniques range
from simple smoothing methods such as moving aver-
ages and exponential smoothing to more advanced
techniques such as decomposition and the Box–Jenkins
approach. The simpler techniques are often applied
in practice in situations where clearly it is not worth
the time or the money to develop and apply more
sophisticated ones, for instance, preparing daily fore-
casts for a number of different variables. However,
in academic research, the traditional Box–Jenkins
approach is used widely as a benchmark technique for
univariate methods because of its structured modelling
basis and acceptable forecasting performance. For
immediate and short term forecasts, ‘the Box–Jenkins
method is probably the most accurate of the time-series
models’ (O’Donovan, 1983, p. 9). Taylor and Bowen
(1987), and Fellows (1987, 1991) have found the tech-
nique to be satisfactory in modelling construction
tender price movements as it permits judgment, models
the changing process adequately and provides a
class of models of stationary stochastic processes. Its
strength lies in its generality, as it can handle virtually
any time-series data, partly owing to its strong theo-
retical foundations and partly to its success in empir-
ical comparisons which have found it to be as accurate
as many complex econometric models (Wheelwright
and Makridakis, 1985). Abdelhamid and Everett
(1999) found this technique, in particular, useful in
analysing construction productivity data, as order and
dependence are the exact two properties that are
found in data collected for productivity improvement
� eld experiments. The versatility of the Box–Jenkins
approach is examined in this paper, where it is used
to analyse and forecast three distinct variables of the
construction industry, namely, price, demand and
productivity, based on case studies of Singapore.
Objectives and scope
This paper constitutes a culmination of empirical
studies on the application of an advanced univariate
time-series technique to model and forecast construc-
tion demand, tender price and industry-level produc-
tivity in Singapore. More speci� cally, these studies, or
rather the objectives of this paper, include the use
of the Box–Jenkins approach to analyse and forecast:
1. public industrial building tender prices (case study
I); 2. residential construction demand (case study II);
and 3. construction productivity at industry level (case
study III). These case studies were undertaken consec-
utively over a period of six years, each serving a
different purpose to cater to speci� c needs of the
Singapore construction industry. For case study I, the
intention of developing a tender price index forecasting
model for public industrial buildings in the early 1990s
was in anticipation of a rise in demand for such devel-
opments to support a booming manufacturing
industry. This was in line with Singapore’s new
economic thrust ‘to adopt a global strategy and become
a competitive total business centre’ (Jurong Town
Corporation, 1988, p. 2). For case study II, a model
to produce accurate demand forecasts was needed in
the mid-1990s to cater to a rapidly growing residen-
tial sector where it had a share of 32–50% in the total
value of construction contracts awarded between 1986
and 1994 (CIDB, 1994). Case study III was under-
taken most recently, as there has been an urgent need
to look into ways of improving industry productivity
as Singapore enters into the next millennium. If
productivity levels can be predicted with reasonable
accuracy, future levels of competitiveness in the
industry could be raised through proper planning of
its workload and better use of its limited resources to
achieve national targets.
608 Goh and Teo
Time-series data
For case study I, the Singapore public industrial
building tender price index series, constructed by Goh
(1992), was used as the time-series data set. The
SBEM Modal House approach (Goh and Teo, 1993)
to index construction was adapted from the concepts
of the New Zealand Institute of Valuers Modal House
approach (NZIV, 1967a, b, 1972). Figure 1 shows a
plot of the quarterly compiled index series from the
� rst quarter of 1980 to the � rst quarter of 1992, giving
a total of 49 data points. With the intention of utilizing
as many data points as possible to build the forecasting
model, the � rst 47 quarters formed the modelling data
set, while the remaining 2 quarters were used to test
the accuracy of the model for out-of-sample forecasts.
For case study II, ‘gross � oor area (GFA) of devel-
opments commenced’ was used to represent demand
for residential construction. A study on construction
statistics in the UK has singled out its usefulness
as a forward indicator of demand (MPBW, 1968).
Alternative series, such as the ‘gross � xed capital
formation’ and ‘value of contracts awarded’, were
considered, but deemed less suitable because the
former is an output rather than a demand measure,
while the latter had data starting from only 1986. A
graphical plot of the time series from the � rst quarter
of 1975 to the � rst quarter of 1994, comprising a
total of 77 data points, is shown in Figure 2. The � rst
72 quarters formed the modelling data set and the
remaining 5 quarters were used for model testing.
For case study III, ‘value added per worker’ was
chosen as the industry-level productivity measure for
two reasons. First, a longer time series was required
for modelling purposes and the alternative measure,
‘square metres of built-up area per man-day’, had data
starting from only 1991. Second, the output and input
measures, ‘GDP at 1990 market prices, by industry:
Construction’, and ‘Employed persons aged 15 years
and above, by industry: Construction’, respectively,
used for its computation were published national statis-
tics compiled by the Department of Statistics, which
could be obtained readily. Data for these two series
were abstracted from statistical yearbooks from 1975
to 1996 and comprising a total of 22 data points. Based
on the same intention of utilizing more data for model-
ling, the � rst 20 periods were used for modelling, with
the last two periods for testing. Figure 3 shows a plot
of the time series for ‘value added per worker’.
The Box–Jenkins approach
The general methodology suggested by Box and
Jenkins (1976) for applying autoregressive-integrated-
moving-average (ARIMA) models to time-series
analysis, forecasting and control has come to be known
as the Box–Jenkins approach for time-series analysis
and forecasting. It is a systematic approach for iden-
tifying characteristics of a time series such as station-
arity and seasonality, and eventually it provides a class
of models of stationary stochastic processes. It relies
on an iterative approach for identifying a possible
useful model from a general class of models. The
chosen model is then checked against the historical
data to see whether it describes the series accurately.
The model presents a good � t if the residuals between
the forecasting model and the historical data are small,
randomly distributed and independent. If the speci� ed
model is not satisfactory, the process is repeated by
using a different model that is designed to improve on
the original one. This process is repeated until a satis-
factory model has been identi� ed.
Forecasting tender price, demand and productivity 609
Figure 1 Time series of public industrial building tender
price index in Singapore (1980 Q1 = 100)
Figure 2 Time series of gross � oor area (GFA in sq. m)
of residential developments commenced in Singapore
This approach divides the forecasting problem into
three stages. Initially, a general class of forecasting
models is postulated. Stage 1 involves identifying a
speci� c model that can be tentatively entertained as
one that best suits the characteristics of the time series.
This model is � tted to the historical data in stage 2,
and a check is carried out to determine whether it is
adequate. If the tentative model is not satisfactory, the
approach returns to stage 1, where an alternative model
is identi� ed. Once an adequate model is determined,
it will be used to generate forecasts for the variable
concerned in stage 3.
The stages of identi� cation, estimation and diag-
nostic checking, and application can be carried out via
statistical analysis software, such as SPSS for Windows
or SAS for PC. However, skilled user intervention is
required at the stage of identifying the best-� t model.
Also substantial knowledge in time-series analysis is
necessary for this approach, such as analysing the time
series for stationarity, seasonality, and identifying and
specifying the form of the time-series model using the
autocorrelations and partial autocorrelations. Once the
model has been identi� ed, � tting and forecasting are
automatic.
Case study I: public industrial building
tender price index forecasting in Singapore
Autoregressive-integrated-moving-average (ARIMA)
models are designed for stationary time series. A
stationary series is one whose basic statistical proper-
ties, such as the mean or variance remain constant over
time. To build ARIMA models, � rst periodic varia-
tions and systematic changes in these properties must
be identi� ed and removed. One method of checking
for stationarity is the use of the autocorrelation func-
tion (ACF). Typically, the ACFs for nonstationary data
are signi� cantly different from zero for the � rst several
time lags. Figure 4 plots the pattern of the autocorre-
lations of the time series for ‘public industrial building
tender price index’. It was con� rmed that the time
series was nonstationary in the mean since the ACF
died down very slowly. The series was transformed into
one that is stationary by the method of ‘differencing’.
It involved the process of taking � rst differences of the
series and creating a new time series of successive
differences. The results of the � rst differences of lag 1
are shown in Figure 5. The Box–Ljung test statistic
was used to test the null hypothesis that the residuals
of the differenced series are random. Based on the
‘Prob’ values given in Figure 5, the null hypothesis was
not rejected at the 5% signi� cance level for almost all
the lags. The ACF plot also resembled ‘white noise’,
that is, all of the autocorrelations were near zero,
con� rming that the differenced series was ready for
model � tting.
During model � tting, the behaviour of the ACF and
the partial ACF (PACF) served as the key to model
identi� cation as shown in Table 1. The simple corre-
lation coef� cient r between Yt and Yt-1 was derived by
means of the following equation:
n
S
t=2
(Yt – Y
]
)(Yt–1 –Y
]
)
rYtYt–1 = —————————n
S
t=1
(Yt – Y
]
)2
where Y
]
is the mean value of Y; and n is the number
of time periods.
Similarly, the autocorrelations for 1, 2, 3, 4, …, k time
lags can be found and denoted by rk, as
n –k
S
t =1
(Yt – Y
]
)(Yt–k –Y
]
)
rk = —————————n
S
t =1
(Yt – Y
]
)2
where D(q) means the function drops off to 0 after
lag q; D(p) means the function drops off to 0 after lag
p; T means the function tails off exponentially; and 0
means the function is 0 at all nonzero lags.
The ACF and PACF plots of the differenced series
did not give a clear indication of an autoregressive (AR)
or moving average (MA) model. On the one hand, the
ACF seemed to indicate an MA model, but on the
other, the PACF was consistent with an AR model.
However, based on the study by Fellows (1987) which
found that low-order AR models of differenced series
provide the best-� t models for tender price indices, a
tentative AR model was chosen.
At the estimation stage, the tentative AR(1) model
was � tted to the differenced series and the model para-
meters were estimated. Table 2 provides the results of
the AR(1) model � t. It was found that the parameter
610 Goh and Teo
Figure 3 Time series of value added per worker (in S$) in
Singapore
estimate for the constant term, was statistically insig-
ni� cant at the 10% level and, hence, was removed
from the model. The AR(1) model was re� tted but
without a constant term and the results are given in
Table 3. It was con� rmed that the removal of the
constant term did not affect the signi� cance of the
parameter estimate of the AR(1) term.
Diagnostic checking involved either checking for
random residuals or, by ‘over� tting’, to determine the
adequacy of the � tted AR(1) model without a constant
term. In this case, both procedures were conducted to
test for consistency of result. First, the residuals were
checked for randomness by observing the pattern of
the autocorrelations, together with their respective
Box–Ljung test statistics. As shown in Figure 6, all the
autocorrelations were highly insigni� cant, indicating
that the residuals were random and the � tted model
was adequate. Second, the series was ‘over� tted’ with
a higher order AR model. The parameter estimate for
the AR(2) term was found to be insigni� cant at the
10% level (t-ratio = –0.280). Hence both procedures
have con� rmed that an AR(1) model best � ts the data
series for Singapore’s public industrial building tender
price index.
Then the equation for the best-� t model, ARIMA
(1,1,0), can be expressed as
Yt = Yt–1 + f 1Yt–1 – f 1Yt–2 + et
where Yt is the variable to be forecast at current time
t; Yt–1 and Yt–2 are past values of Yt at time lags 1 and
2, respectively; f 1 is the � rst-order autoregression
coef� cient; and et is the random error term. From the
analysis, the parameter estimate of the AR(1) term, f 1,
was found to be –0.3864. The forecasts generated for
the validation period (1991 Q4–1992 Q1) are given in
Table 4.
Case study II: residential construction
demand forecasting in Singapore
The data series for ‘GFA of developments commenced’
was � rst checked for stationarity. The pattern of the
autocorrelations is plotted in Figure 7. The ACF
con� rmed that the data series was nonstationary in the
mean since it died down very slowly. Once again,
‘differencing’ was performed to transform the series
Forecasting tender price, demand and productivity 611
Figure 4 ACF of ‘public industrial building tender price index’
Table 1 Summary of model identi� cationa
MA (q) AR (p) ARMA (p,q) White noise
ACF D(q) T T 0
PACF T D(p) T 0
a Source: Brocklebank and Dickey (1986).
Autocorrelations: TPI
Auto- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1 Box-Ljung Prob.
+—-+—-+—-+—-+—-+—-+—-+—-+
1 .812 .141 . I*****.********* * 33.026 .000
2 .726 .140 . I*****.******** * 59.971 .000
3 .604 .138 . I*****.***** * 79.062 .000
4 .489 .137 . I****.**** * 91.894 .000
5 .433 .135 . I****.**** 102.154 .000
6 .335 .133 . I****.** 108.445 .000
7 .222 .132 . I****. 111.291 .000
8 .156 .130 . I*** . 112.725 .000
9 .050 .128 . I* . 112.876 .000
10 –.005 .127 . * . 112.878 .000
11 –.074 .125 . *I . 113.229 .000
12 –.112 .123 . **I . 114.061 .000
13 –.164 .122 . ***I . 115.889 .000
14 –.187 .120 . ****I . 118.342 .000
15 –.210 .118 . ****I . 121.505 .000
16 –.213 .116 . ****I . 124.888 .000
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 47 Computable � rst lags: 46
612 Goh and Teo
Figure 5 ACF and PACF of � rst differences of ‘public industrial building tender price index’
Autocorrelations: TPI
Transformations: difference (1)
Auto- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1 Box-Ljung Prob.
+—-+—-+—-+—-+—-+—-+—-+—-+
1 –.416 .143 **. *****I . 8.490 .004
2 .090 .141 . I** . 8.901 .012
3 .102 .140 . I** . 9.439 .024
4 –.020 .138 . * . 9.460 .051
5 –.009 .136 . * . 9.465 .092
6 .090 .135 . I** . 9.915 .128
7 –.168 .133 . ***I . 11.505 .118
8 .213 .131 . I****. 14.142 .078
9 –.154 .129 . ***I . 15.562 .077
10 .079 .128 . I** . 15.947 .101
11 –.016 .126 . * . 15.963 .143
12 –.008 .124 . * . 15.967 .193
13 –.082 .122 . **I . 16.413 .228
14 .066 .120 . I* . 16.710 .272
15 –.165 .118 . ***I . 18.641 .230
16 .212 .117 . I****. 21.959 .145
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 47 Computable � rst lags after differencing: 45
Partial Autocorrelations: TPI
Transformations: difference (1)
Pr–Aut- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1
+—-+—-+—-+—-+—-+—-+—-+—-+
1 –.416 .147 **. *****I .
2 –.100 .147 . **I .
3 .125 .147 . I** .
4 .101 .147 . I** .
5 .015 .147 . * .
6 .081 .147 . I** .
7 –.133 .147 . ***I .
8 .108 .147 . I** .
9 –.042 .147 . *I .
10 .032 .147 . I* .
11 –.005 .147 . * .
12 –.009 .147 . * .
13 –.105 .147 . **I .
14 –.045 .147 . *I .
15 –.134 .147 . ***I .
16 .117 .147 . I** .
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 47 Computable � rst lags after differencing: 45
into a stationary one. The ACF of the differenced series
generally resembled ‘white noise’, except for the � rst
few lags, and model � tting was initiated.
At the model identi� cation stage, it was observed
that the ACF tailed off exponentially while the PACF
dropped off to zero after lag 1. Hence, a tentative
AR(1) model was chosen and � tted to the differenced
series. The results of the model � t are provided in
Table 5, which indicates that the parameter estimate
of the constant term is insigni� cant at the 10% level.
Based on this observation, the constant term was
dropped and the results of the re� tting are given in
Table 6, con� rming that the parameter estimate of the
AR(1) term is still highly signi� cant.
For diagnostic checking, the residuals were exam-
ined for randomness to test for goodness of � t of the
AR(1) model without a constant term. The ACF plot
of the residuals indicated that all the autocorrelations
were highly insigni� cant, and this was re-con� rmed by
Forecasting tender price, demand and productivity 613
Table 2 Results of the AR(1) model � t with a constant
term
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
AR(1) –0.4172 0.136 –3.059 0.0038
Constant 2.8406 1.778 1.597 0.1173
Table 3 Results of the AR(1) model � t without a constant
term
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
AR(1) –0.3864 0.1368 –2.824 0.0071
Figure 6 Autocorrelations of residuals of the � tted ARIMA (1,1,0) model
Table 4 Details of forecasts generated by the ARIMA (1,1,0) model
Period Actual Forecast Error Lower 95% Upper 95%
values A values F (A–F) con� dence limit con� dence limit
1991 Q4 224 236 –12 201 270
1992 Q1 240 228 12 194 262
Auto- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1 Box-Ljung Prob.
+—-+—-+—-+—-+—-+—-+—-+—-+
1 –.072 .143 . *I . .253 .615
2 –.024 .141 . * . .283 .868
3 .176 .140 . I**** . 1.878 .598
4 .022 .138 . * . 1.904 .753
5 .021 .136 . * . 1.928 .859
6 .045 .135 . I* . 2.041 .916
7 –.090 .133 . **I . 2.498 .927
8 .150 .131 . I*** . 3.808 .874
9 –.075 .129 . **I . 4.146 .902
10 .034 .128 . I* . 4.217 .937
11 .015 .126 . * . 4.231 .963
12 –.059 .124 . *I . 4.457 .974
13 –.081 .122 . **I . 4.896 .977
14 –.025 .120 . *I . 4.940 .987
15 –.100 .188 . **I . 5.646 .985
16 .135 .117 . I*** . 6.994 .973
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 47 Computable � rst lags: 45
the Box–Ljung test statistics generated for each lag.
The best-� t univariate time-series forecasting model
for Singapore’s residential construction demand has
been identi� ed as ARIMA(1,1,0) and the equation can
be expressed as
Yt = Yt–1 + f 1Yt–1 – f 1Yt–2 + et
where Yt is the variable to be forecast at current time
t; Yt–1 and Yt–2 are past values of Yt at time lags 1 and
2, respectively; f 1 is the � rst-order autoregression coef-
� cient; and et is the random error term. For this study,
the parameter estimate of the AR(1) term f 1 was found
to be 0.7279 in the analysis. The forecasts generated
for the validation period (1993 Q1–1994 Q1) are given
in Table 7.
Case study III: construction industry
productivity forecasting in Singapore
To study the characteristics of the time series ‘value
added per worker’ for Singapore’s construction indus-
try productivity the ACF plot was generated as shown
in Figure 8. It was con� rmed that the data series was
nonstationary in the mean since the ACF drops off
exponentially to zero. When � rst differences of the
series were taken it was suspected that the series had
not achieved stationarity, since the ACF plot did not
behave much differently from the earlier plot.
Essentially, the autocorrelations did not drop to zero
rapidly, suggesting that nonstationarity was still present
in the � rst-order differenced data series. In this
instance, it was necessary to take � rst differences of the
� rst-order differenced series. The ACF of the second-
order differenced series indicated stationarity and,
hence, was ready for model � tting.
At the model identi� cation stage, the behaviour of
the ACF and the PACF indicated a tentative MA(1)
614 Goh and Teo
Table 5 Results of the AR(1) model � t with a constant
term
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
AR(1) 0.7237 0.0812 8.914 0.0000
Constant 18.0252 30.731 0.587 0.5594
Table 6 Results of the AR(1) model � t without a constant
term
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
AR(1) 0.7279 0.0803 9.063 0.0000
Figure 7 ACF of ‘GFA of residential developments commenced’
Autocorrelations: DEMAND Demand
Auto- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1 Box-Ljung Prob.
+—-+—-+—-+—-+—-+—-+—-+—-+
1 .955 .115 . ý****.************* * 68.446 .000
2 .873 .115 . ý****.*********** * 126.432 .000
3 .873 ,115 . ý****.********* * 172.432 .000
4 .655 .113 . ý****.******* * 205.684 .000
5 .547 .112 . ý***.****** * 229.435 .000
6 .445 .111 . ý***.**** * 245.438 .000
7 .348 .110 . ý***.*** 255.345 .000
8 .249 .110 . ý***.* 260.502 .000
9 .144 .109 . ý***. 262.268 .000
10 .038 .108 . ý* . 262.390 .000
11 –.065 .107 . *ý . 262.758 .000
12 –.157 .106 .***ý . 264.949 .000
13 –.242 .105 *.***ý . 270.234 .000
14 –.328 .104 ***.***ý . 280.105 .000
15 –.418 .103 ****.***ý . 296.412 .000
16 –.507 .103 ******.*** ý . 320.891 .000
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 72 Computable � rst lags: 71
model. The PACF tailed off exponentially while the
ACF dropped off to zero after lag 1. Table 8 gives the
results of the MA(1) model � t. The MA(1) parameter
estimate was highly signi� cant at the 10% level,
implying that the correct model might indeed be a � rst-
order moving average. The constant term was not
necessary, in this case, since the process of differencing
would have transformed the data to have a series mean
about zero.
Diagnostic checking was carried out by observing
the pattern of the autocorrelations of the residuals
of the MA(1) model. The ACF plot, together with their
respective Box–Ljung test statistic, indicated
that all the autocorrelations were highly insigni� cant
and, hence, the residuals were random and the � tted
model was adequate. The series was also ‘over� tted’
with an MA(2) model and the results are given in Table
9. They show clearly that the parameter estimates for
MA1 and MA2 are insigni� cant at the 10% level.
The best-� t model was con� rmed to be an ARIMA
(0,2,1) and the derivation of the model’s equation is
detailed below.
By using the backward shift operator B, in the form
BYt = Yt–1
a second-order difference is represented as
Y 0 t = (1 – B)
2Yt
If the second-order difference, Y0t, forms an MA(1)
model, then the appropriate equation is
Forecasting tender price, demand and productivity 615
Table 7 Details of forecasts generated by the ARIMA (1,1,0) model
Period Actual Forecast Error Lower 95% Upper 95%
values A values F (A–F) con� dence limit con� dence limit
1993 Q1 1638 1642 –4 1500 1785
1993 Q2 1681 1622 59 1479 1764
1993 Q3 1724 1712 12 1569 1854
1993 Q4 1752 1755 –3 1612 1898
1994 Q1 1760 1772 –12 1630 1915
Figure 8 ACF of ‘value added per worker’
Autocorrelations: VADDPWK
Auto- Stand.
Lag Corr. Err. –1 –.75 –.5 –.25 0 .25 .5 .75 1 Box-Ljung Prob.
+—-+—-+—-+—-+—-+—-+—-+—-+
1 .617 .208 . ý*******.*** * 8.826 .003
2 .135 .202 . ý*** . 9.268 .010
3 –.312 .197 . ******ý . 11.780 .008
4 –.506 .191 **.*******ý . 18.831 .001
5 –.395 .185 *.******ý . 23.410 .000
6 –.246 .178 . *****ý . 25.305 .000
7 –.073 .172 . *ý . 25.484 .001
8 .107 .165 . ý** . 25.906 .001
9 .247 .158 . ý*****. 28.347 .001
10 .261 .151 . ý*****. 31.342 .001
11 .093 .143 . ý** . 31.762 .001
12 –.084 .135 . **ý . 32.148 .001
13 –.289 .126 *.****ý . 37.399 .000
14 –.298 .117 *.****ý . 43.909 .000
15 –.133 .107 .***ý . 45.475 .000
16 .021 .095 . * . 45.525 .000
Plot Symbols: Autocorrelations * Two Strand Error Limits .
Total Cases: 22 Computable � rst lags: 19
(1 – B)2 Yt = (1 – u 1B)et
and substituting B into the above equation gives
Yt = 2Yt–1 – Yt–2 + et – u 1et–1
Here Yt is the variable to be forecast at current time
t; Yt–1 and Yt–2 are past values of Yt at time lags 1 and
2, respectively; u 1 is the � rst-order moving average
coef� cient; and et and et–1 are the random error term
at current time t and lag 1, respectively. For this study,
the parameter estimate of the MA(1) term u 1 was found
to be 0.8134 in the analysis. The forecasts generated
for the validation period (1995–1996) are given in
Table 10.
Evaluation of forecasting accuracy
The forecasts generated by the models were evaluated
on two measures of accuracy, namely, the root-mean-
square error (RMSE) and the mean absolute
percentage error (MAPE). The characteristics of these
measures have been elaborated in other studies
(Akintoye and Skitmore, 1994; Fitzgerald and
Akintoye, 1995). In brief, these measures can be
explained as follows.
Root-mean-square error
RMSE = !
n
S
t=1
———
e2t / n
where et = At – Pt, et is the forecast error at current
time t; At is the actual value at current time t; and Pt
is the predicted value at current time t.
Mean absolute percentage error
1 |et|MAPE = –
n
S
t=1
— 3 100
n At
These two measures were used because the prediction
RMSE could be evaluated against the model RMSE,
while the magnitude of the prediction MAPE could be
gauged by the general acceptable limit of 10%. Based
on the models’ out-of-sample forecasts, the computed
values for these measures are given in Table 11.
Discussion of � ndings
There are basically two types of forecast, the point
forecast and the prediction interval forecast (Newbold
and Bos, 1990). The three models have been used to
generate the two types of forecast, as shown in Tables
4, 7 and 10, and their predictive performance has been
evaluated on the point forecast by applying the RMSE
and MAPE. Essentially, a prediction interval forecast
is an interval of values that is calculated based on a
speci� ed level of con� dence that the actual value will
be contained in the interval. For example, in case study
I the prediction interval for 1991 Q4 implies that there
is 95% con� dence level that the actual tender price
index for Singapore’s public industrial projects will fall
between 201 and 270.
Based on the point forecasts, the evaluation of the
models’ forecasting accuracy has produced two posi-
tive results. For the three models, the prediction
RMSE is consistently smaller than the model’s stan-
dard error (or RMSE) and also the prediction MAPE
is consistently within the acceptable limit of 10%.
Generally speaking, assessing the predictive ability of
models based on out-of-sample forecasts is considered
as an objective and stringent test. This is because the
data set used to build the model is distinct from that
used to test its accuracy.
In this instance, both absolute and relative measures
of accuracy have been used in the evaluation. The stan-
dard error is generated automatically as a descriptive
statistic of a model and often it is useful to compare
it with the prediction’s RMSE. As such, it serves as
616 Goh and Teo
Table 10 Details of forecasts generated by the ARIMA (0,2,1) model
Period Actual Forecast Error Lower 95% Upper 95%
values A values F (A–F) con� dence limit con� dence limit
1995 66598 67505 –907 50715 84295
1996 78111 70755 7356 44700 96811
Table 8 Results of the MA(1) model � t
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
MA1 0.8134 0.2112 3.8519 0.0013
Table 9 Results of the MA(2) model � t
Parameter Coef� cient u SE (u ) t-ratio Approx.
estimate prob.
MA1 0.7071 0.5224 1.3536 0.1947
MA2 0.2361 0.3465 0.6813 0.5055
an absolute measure of accuracy for each model. On
the other hand, the relative measure, MAPE, provides
a basis for comparing among different models, as well
as against the general acceptable limit. For example,
it is observed that among the three models, the
one generated in case study II to predict residential
construction demand is the most accurate as its
prediction MAPE is the lowest (1.07%). However, all
three models have high predictive ability since their
prediction MAPE is within the 10% acceptable limit.
Conclusion
This paper presents an empirical study of the use of
a benchmark univariate time-series forecasting tech-
nique, the Box–Jenkins approach, to model and
forecast three distinct construction industry variables,
price, demand and productivity. The derived models
have been used to generate out-of-sample forecasts to
provide a basis for assessing the predictive performance
of the models and, hence, adequacy of the approach.
The results of the evaluation can be summarized as
follows. 1. The prediction RMSE of all three models
is consistently smaller than the model’s standard error,
implying the models’ good predictive performance.
2. The prediction MAPE of all three models consis-
tently falls within the general acceptable limit of 10%.
Among the three models, the most accurate is the
demand model (MAPE = 1.07%), followed by the
price model (MAPE = 5.18%) and the productivity
model (MAPE = 5.39%).
Despite the favourable results of the study, it has
to be highlighted that the derived models are suitable
for producing only short-term forecasts, that is, one to
� ve periods ahead. In this respect, the choice to build
a complex econometric model or a simple univariate
model has to be based on considerations such as time,
data and cost. In any case, even if conditions permit
the building of a larger model, the need for a simpler
and easier-to-use model is still justi� able, since it
would serve as a benchmark or control model to check
on the larger model’s performance.
Broadly speaking, the purpose of building an indus-
try-level forecasting model is to treat its predictions as
targets for the industry to plan its future workload and
use of limited resources, such as land, � nancial capital
and manpower. In essence, the tender price index fore-
casting model allows the industry to assess current
against future prevailing price levels in order to achieve
higher price competitiveness by either lowering costs or
increasing productivity. Having a construction demand
forecasting model would assist the industry in antici-
pating any future changes and constraints, with the
objective of maintaining a healthy balance between
demand and supply of construction items such as resi-
dential buildings. The ability to predict industry pro-
ductivity enables future levels of competitiveness in the
industry to be raised through increasing value added in
construction or reducing manpower utilization.
Although the Box–Jenkins technique has been
proved in the study of Singapore to be a reliable time-
series forecasting approach to construction industry
forecasting, its inherent shortcomings should not be
ignored. Recent studies in empirical macroeconomics
involving nonstationary and trending variables, such
as income, consumption and exchange rates, have
explored more interesting and appropriate methods of
trend analysis. Granger causality analysis has the ability
to test for signi� cant short run causal relationship
between two trending variables, while a technique
known as ‘cointegration’ analyses the long run rela-
tionship of such variables. Essentially, these new
techniques have combined the principles of causality
and time series to produce a more comprehensive
approach to analysing related trending variables.
A report by the Royal Institution of Chartered
Surveyors (RICS, 1996) has presented a review of the
application of non-traditional forecasting techniques
and, in the process, highlighted the works of Barras
and Ferguson (1987a, b). Their progressive studies
have culminated in the development of a theoretical
model that incorporates an error correction term into
a transfer function model to capture both short run
dynamics and long run behaviour of the private prop-
erty market. In concurrence, the RICS undertook a
pilot study to examine the use of a vector error correc-
tion model (VECM), incorporating a vector of six
variables, to forecast construction orders and output.
Despite promising results from the VECM approach,
it was acknowledged that the major dif� culty had been
in the interpretation of the coef� cients of the derived
equations. To assess the performance of the VECM,
it was suggested that a comparison be made with some
traditional structural equation models. This is, in fact,
necessary since there has to be a formalized way of
evaluating state-of-the-art techniques against conven-
tional ones which serve as appropriate benchmarks.
Further adoption of such new techniques would have
to rely on more conclusive � ndings in future studies
of construction industry forecasting.
Forecasting tender price, demand and productivity 617
Table 11 Measures of accuracy for out-of-sample forecasts
Model Prediction Prediction
RMSE RMSE MAPE
Case study I 17.27 12.00 5.18
Case study II 73.79 27.55 1.07
Case study III 7955.47 5240.87 5.39
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