Forecasting the Antwerp maritime traffic flows using transformations and intervention models

Journal of Forecasting, Vol. 15,395-412 (1996)

Forecasting the Antwerp Maritime Traffic Flows Using Transformations and Intervention Models

ANDRE KLEIN University of Amsterdam, The Netherlands

ABSTRACT This article uses univariate time-series models with data transformations and intervention models to forecast the volumes of twenty-two maritime traffic flows in the port of Antwerp which are expressed in tonnes. The models obtained produce forecasts that are a substantial improvement over those obtained with unadjusted data. The models also provide useful insight into the behaviour of maritime traffic flows during the period 1971 -82.

KEY WORDS intervention models; data transformations

INTRODUCTION

The presence of outliers in time series can cause severe distortions when the modelling procedure is implemented and the resulting forecasts are computed. This article analyses forecasting results in a situation where data transformation and intervention models are applied to a set of twenty-two maritime traffic flows at the port of Antwerp. The group of models studied is the univariate ARIMA. The Box and Cox (1964) family of transformations is considered even though other variants are introduced such as the one proposed by Ansley et al. (1977) and adapted with the effect of interventions. This article is implementing the approach outlined in Mklard (1981), where intervention effects are defined by using a piecewise linear function of time instead of the output response of a transfer function proposed by Box and Tiao (1975). The purpose of this article is to demonstrate the usefulness of transformations and interventions when forecasts are computed and to obtain insight into the time-series behaviour of the commodity flows at the port of Antwerp during the period 1971-82 and associate the forecasting results with identifiable events and with irregular ones in particular. It is shown that there is a considerable improvement in forecasting performance when appropriate data transformation and interventions are applied when compared with unadjusted data (without transformations and interventions).

Maritime traffic in Belgium and the Netherlands plays a very important role in these countries’ respective economies. The maritime trailic through the ports of these two countries alone accounts for more than 10% of the main world port traffic flow when expressed in tonnes. This means 10% of the registered amount loaded and unloaded at the ports of the world. Since the beginning of the CCC 0277-66931961050395- 18 Received August I995 0 1996 by John Wiley & Sons, Ltd. Accepted April 1996

396 Journal of Forecasting Vol. 15, Iss. No. 5

1970s an increased interest in forecasting port traffic flows has been witnessed. The Studiecentrum voor the Expansie van Antwerpen (1981) (SEA hereafter) investigated more than fifty commodity stream flows in the port of Antwerp and produced five-year forecasts on a non-quantitative basis. This study is carried out at a disaggregated level i.e. the focal point is a specific commodity stream flow rather than groups of commodities. A similar approach is followed in the paper, In the Gemeentelijke Havenbedrijf Rotterdam (198 1) long-term forecasts of maritime traEic flows are obtained for the years 1990 and 2000. The commodities are divided into nine commodity groups.

More recently, studies of port traffic flows have been a subject of interest in Klein and Verbeke (1987), Dagenais and Martin (1987) and De Gooijer and Klein (1989). The various traffic flows at the port of Antwerp, both outgoing and incoming, are described on the basis of figures registered monthly and expressed in tonnes from January 1971 to March 1982. Twenty- two commodity flows have been analysed (1 = loading, u = unloading):

1 chemical fertilizers 1 chemical products 1 crude and manufactured minerals, building materials 1 glass, glass ware, ceramics 1 machinery, apparatus, motors 1 motor vehicles 1 non-ferrous metals 1 iron and steel u feeding stuffs for animals and foodstuff waste u cellulose and paper waste u machinery, apparatus, motors u chemical fertilizers u chemical products u coal and coke (solid fuel) u crude and manufactured minerals, building materials u motor vehicles u natural fertilizers u non-ferrous metals u non-ferrous ores u iron and steel u wood and cork u natural and synthetic textile materials and waste

The article is organized as follows: The next section discusses the structure of the transformations and three intervention models, the third section specifies the modelling and forecasting study, the fourth section describes identifiable events which explain the forecasting results and conclusions follow in the final section.

TIME-SERIES METHODOLOGY

The time series realization 2, , . . . , 2, expressing the different maritime traffic flows are usually non-stationary but can be regarded as stationary after differencing:

(1) w, = VdzjA) = (1 - B ) d z / a )

A. Klein Forecasting the Antwerp Maritime Trafic Flows 397

Here d is the order of consecutive differencing, BZ, = Z,-l and t is the time index and d is the Box and Cox (1964) transformation parameter (see also Ansley et al. 1977) such that

(2) IGInZ, d = O

where G = ( 1 1 7 = 1 2,)”” is the geometrical mean of the original data. The presence of outliers is also to be taken into account. Intervention analysis deals with the

possible consequences of isolated events on the dynamic behaviour of a variable. The intervention will be applied to the original data Z, according to MClard (1981). The transformation then, takes the following form:

where y,! is the estimated reduction or increase for a given data point which underwent an intervention and zero for other values of the time series and G is then

and in case of a first difference to be applied for obtaining stationarity it will be applied to equation (3). Forecasting transformed time series is extensively studied in Granger and Newbold (1976)

where several forms of variable transformations are considered. The autocovariance and forecasting of the transformed series are examined. It is shown how to optimally forecast time series which have been transformed so that the forecasts are in the original metric. The forecast comparisons made in this paper are also in the original metric.

From time-series analysis it is well known that the behaviour of a stationary time series w, can be approximated by the SARMA model (Box and Jenkins, 1976):

w w w s ) t w , - P I = w w w , (4) where s is the seasonal periodicity, ,u represents the mean of the stationary process w, , E , is the noise component of the stochastic model to be NID(0, of), E(E ,E , . ) = 0 for t+ t‘ and w, is given by equation (1).

When differencing is applied to the original data in order to reach stationarity in the mean, the corresponding version of equation (4) is then referred as SARIMA.

The terms q5 ( B ) and O(B”) are the non-seasonal AR operator of order p and the seasonal AR polynomial of order Ps , respectively. Similarly, 8(B) and @(B’) are the non-seasonal and seasonal MA operators of order q and Qs, respectively:

(5 )

(6)

# ( W ) = 1 - $lmsB3D - Q ) p , s s p ” (7)

@(B’) = 1 - OI,,B“ - - 8Q,sBQs (8)

$ ( B ) = 1 - $ , B - * a * $pBP

e ( B ) = 1 - e ,B - ... eqBq

It is assumed that all roots of @ ( B ) = 0, O(Bs) = 0, B(B) = 0 and C9(B3) = 0 lie outside the unit circle .


Intervention models are convenient methods for modelling time series when one or more observations are inconsistent with the model, which is thought to be appropriate for the overwhelming majority of the observations. Consequently, the parameters in the model will be sensitive to its presence, as will the resulting forecasts.

In MClard (1981) the effect of an intervention is described by a piecewise linear function instead of a transfer function as outlined in Box and Tiao (1975). The effect of intervention leads to the following relationship:

where y, is an unknown deterministic function of time. The piecewise linear effect y, of the corresponding intervention can be seen as follows.

Assume that ti') is the intervention time and ty) , t\", ..., ry) are fixed instants such that tv )< t?< . d tz), where m = m ( j ) and

otherwise

Here, ah') has the meaning of the height of a jump and PI'), pi'), . . . ,By) are slopes. The quantities ag), B?, . . . , p'," are either fixed constants or unknown parameters. The net effect of all interventions, y f , is the sum of several piecewise linear effects defined by equation (10)

j - I

This is illustrated in Figure 1.

represented by the following equation: A general representation of the extended ARIMA model applied in this paper can be

where y : and y p are arbitrary time-dependent functions and y," is time dependent and strict positive. The process a, is Gaussian white noise, expected value zero and variance 0'. These operations allow us to write the process w, as

For the innovation we have


Figure 1. Illustration of a piecewise linear effect y,"' of the jth intervention

Let us point out that in our study d was chosen to be one when differencing was necessary for the maritime traffic flows at the port of Antwerp. The function yf is the intervention in the sense of Box and Tia. (1975) or Tsay (1988); y,' is zero for the instants of no intervention effects. The function y: is subtracted and is an intervention on the differenced data. The residuals are divided by the intervention function yP which acts on the standard deviation of the innovation and is of the form (10) and (1 1) (Mklard, 1981). The likelihood function used is based on model (12):

(15)

where w o = w - y , y = (y , ,...,Y:)~, r = 1 + d , y* =Vdy,, B consists of the ARIMA and transformation parameters and Tii = (r(/3, ly)), = cov(wO,, woj) i , j = 1, . .., n. The parameter vector yf is y" , yD' and yo' for the three intervention types, and each of them has the form (yl , . . . ,yJ, where

2 ( B , y; w) = (2x)-"/'(det l-)-n/2 exp( -f wJ'-'wo} * * *

The modelling procedure consists of having y: = 0 and yP = 1 in equation (12) when the y,'-type intervention is applied and the corresponding likelihood function (15) with just y" is used for estimation purposes. Analogously, when the yF-type intervention is considered, we then have y,' = 0 and y," = 1 in equation (12) resulting in a new parameter estimation, and finally for the y,"-type intervention, y:=O and y p = O in equation (12) yielded a corresponding parameter estimation (with just y'' in equation (15)). It is clear that a mixture of the different


intervention types in one single model can also be envisaged but this is not the case in this study. Here we limit ourselves to one intervention type in each model.

The identification problem consists of identifying the SARIMA parameters, the transformation parameter 1 and the interventions. One way to solve this problem is to choose a tentative model for the time-series structure and estimate the transformation parameter by employing the maximum likelihood method as shown in Ansley et al. (1977). For estimating the transformation parameter 1 the following approach was applied. In case the estimated value of 1 was not significantly different from zero then the natural logarithm was applied to the data. If the estimated I was significantly different from zero and not around the value one then the value of the estimated I would be preserved; if its estimated value is around one we have the original data Z, unchanged.

To estimate 1 in the final model is unnecessary when preliminary estimations have shown that the estimated I is around one. This implies that the model under consideration does not need data transformation. This is illustrated in the example of how the model identification was done. It is worth mentioning that the estimated value of A never exceeded in absolute value the level of one.

A linear stochastic model containing both seasonal and non-seasonal parameters is fitted to the differenced series to determine the estimated SARIMA model. Since the maritime traffic flows at the port of Antwerp do not exhibit strong seasonal effects there was no need for seasonal differencing. This could be roughly explained by the fact that the series under study reflect global traffic at the port of Antwerp (by which we mean most of the countries of the world). So a shortage of a particular traffic of a certain group of commodities will generally be compensated by a similar traffic but from different parts of the world. However, some seasonality was registered, so that the SARIMA model can be considered as the most parsimonious model.

MODELLING AND FORECASTING STUDY

The data in this study comprised 22 monthly maritime traffic time series with length of 135 months. The general procedure was first to truncate the data sets by omitting the last twelve observations. The identification, estimation and forecasting procedures are applied to the first 123 data points. The last twelve observations are used to compare with the forecast values.

Most of the traffic flows under study are general cargo. The average weight considered covers about 60% of Antwerp’s yearly maritime traffic flow.

Some analysts might react against the idea of intervention analysis, using the argument that if economic time series are studied and there are outliers that result from unexpected events, then they, too, participate in the description of the process under consideration. This is indeed an argument that cannot always be rejected if we look at it from a purely economic point of view, e.g. strikes are common events at the port of Rotterdam (but not at the port of Antwerp), so that the effects of the strike should be left unchanged if a time-series study is to be implemented. The irregular events which took place during the period under study for the corresponding maritime traffic flows which resulted in poor forecasting results are described in the next section. Most of the outliers detected at the identification stage are associated with these irregular events. However, taking the methodology into consideration one should be prudent if we think how our forecasts are calculated. The predictors obtained through the Box-Jenkins approach are derived by using the idea of least squares. If no outliers have been detached from a certain time series and the least squares are applied, then it can immediately


be deduced that the accuracy of the forecasts is strongly damaged by the presence of the extreme values in the series. The experiment has definitely shown that abstention of intervention analysis produced forecasts with less accuracy. A partial answer to the question concerning the choice to be made between modelling with interventions or modelling with unadjusted data could be given by a method that would show more robustness. However, the author is aware of the fact that the argument in favor of intervention analysis can also be disputable. As can be seen from Table 11, some SARIMANT (seasonal ARIMA without transformation and interventions) models result in a more accurate forecast than the SARIMA counterparts in a number of cases. But we observe extreme large deviations in forecast accuracy mostly occumng with SARIMANT.

Also from related references (Fox, 1972; Kleiner and Martin and Thompson (1972)), the distinction between ‘innovation outliers’ (the process reacts to usual innovations) and ‘additive outliers’ (the process does not react but effects are added) is crucial. In the first concept, least squares can be super-efficient. In the second concept, the one on which intervention models are built, least squares should be avoided.

However, in this study the full maximum likelihood method is used where the B,“”s, i = 1, . . . , m, are estimated and the t ( j ) ’ s are specified and not estimated (relation (10) and Figure 1). Other related work is by Chen and Tiao (1990) where a random level-shift time-series model that allows the level of the process to change occasionally is introduced.

In Hillmer (1984) it is shown that an additive outlier affects both the accuracy of the forecasts at the time of occurrence and the subsequent forecasts. Tsay (1988) studies the problem of detecting outliers and variance changes in a univariate time series. Appropriate identification, estimation, and diagnostic checking techniques were used. The 22 models were then used to generate 12 one-step-ahead forecasts. Since a one-step-ahead forecast is of no major importance in port traffic, we were inclined to take the sum of the twelve forecasts.

Knowledge of yearly traffic flows is of major importance for short-term planning in port traffic. Therefore the sum of the last 12 predicted values expressed in the original metric were related to the sum of the corresponding 12 actual registrations (that were not involved in the modelling procedure), so the measure of forecasting accuracy is the cumulative relative absolute percentage error (CRAPE):

(Zr+i - 2,+,1,) 1 Z I . i x 100, i = 1, ..., 12; t = 123 [IT I / ; I where 2?,+;, denotes the ith-step-ahead forecast of Z, made from time t and Z,+i the actual value of Z, at time t + i.

Consider as an example the series of 135 monthly observations explaining the unloading of non-ferrous metals at the port of Antwerp. The graphical representation of the original data (Figure 2) shows a need for differencing, the differenced series shows a high autocorrelation at the first lag (Figure 3) whereas the partial autocorrelation shows significant values at the first three lags. By checking both autocorrelation functions we see that there is no direct indication of strong seasonality since we do not notice any significant value at lags 12, 24 and 36. Consequently there is no need for seasonal differencing. We proceed as follows for identifying potential outliers.

The chosen outliers are data points which exhibit a statistically significant increase or decrease with respect to their immediate neighbouring data point. This is represented by the significance level of less than 1% or 1-2% (between 1% and 2%), the level 1-5% (between 1% and 5%)


tm IY 1 9

1I I&

I X

4m

am m

4 10 a t N IN u,

Figure 2. Graphical representation of the incoming maritime traffic flow of non-ferrous metals. The quantities are expressed in tonnes and cover the period January 1971 to March 1982.

. -

Figure 3. Plot of autocorrelations and partial autocorrelations of the differenced series incoming maritime traffic flow of non-ferrous metals

can be considered as more or less acceptable, so it is not seen as an outlier. The outprints of the original data reveal three significant outliers at the 0.2%-1% level, namely August 1971, January 1977 and December 1981. Since we do not use the last 12 observations for estimation and forecasting purposes we will consider the interventions applied to the values of August 1971 and January 1977.


Since p = 3, q = 1 and the order of differencing is d = 1 , the following set of ARIMA( p , d , q ) models are estimated: (0, 1 , l ) , ( 1 , l,O), (2, l,O), (1, 1 , l ) , (3,1,0), (2,1,1) and (3,1,1). For each model the interventions and the Box-Cox transformation parameters A are also included in the estimation procedure. For all the models taken into consideration the estimated A was around one, for example for model (0, 1 , l ) we have with the I intervention type:

[ ;lo8 for c = 71/08 y: = I7701 fort = 77/01

otherwise

(7117.1) (6985.9) (0.036) (0.241) oE = 10,556 I7108 = 35,973 I7701 = 23,114 el = 0.781 A = 1.073

The values in parentheses represent the standard deviations and I7108 denotes the intervention (in this example of the I-type, the D- and a-type interventions are also estimated separately for the same specified months as for the I-type) applied on the eighth month of the year 1971 and the estimated 35,973 tonnes will be added to the corresponding data point. Analogously for 17,701, the corresponding observation will see its original value reduced with the estimated 23,114 tonnes. The third outlier (December 1981) is not estimated. The residual standard deviation is ue. Since the Box-Cox transformation parameter 1 - 1 (and significant at the 95% level) we model the ARIMA schemes without 1. When this has been done for the set of models under study a diagnostic check is applied. The techniques used are: the study of the residual autocorrelation, the Ljung-Box Portmanteau test statistic on residuals, the possible presence of outliers in the residuals and the homogeneity tests. The last tests, (MClard, 1979) are used in order to examine the distributional properties of the residuals (with respect to time).

Eventually the Akaike information criterion (AIC) is applied. The AIC can be written as:

AIC = -2 log 2 + 2 h / ( n - d ) (16) where P is the number of parameters estimated and 2 is the likelihood function. The criterion suggests that from a pool of competing models, the model which minimizes the value of AIC should be chosen. The first term of AIC measures the goodness of fit of the model and the second term expresses the effect of the increase in the number of parameters.

The trade-off between the fit of the model and the number of parameters to be estimated is formulated by the AIC which also formulates the principle of parsimony that advocates the use of the smallest number of parameters in the model. The models studied suggest the following behaviour.

(1) The residual analysis shows no significant outlier. (2) The residual autocorrelations and partial autocorrelations show no immediate need for an

extra coefficient. (3) The Ljung-Box Portmanteau test shows no excess of the critical level of 0.5. (4) The homogeneity tests reveal that the residual variance is not the same in the two halves of

the series.

Based on this, one can conclude that the results cannot be considered as poor but that improvement is desirable, since the homogeneity tests additionally exhibit some seasonal

404 Journal of Forecasting Vol. 15, iss. No. 5

influence in most cases. It is therefore justified to introduce an extra seasonal coefficient and the best resulting models were the seasonal ARIMA ( p , Ps, d , q, Qs) with (O,O, 1 , 1 , l ) and (3,1,1,0,0) for s = 12.

The model chosen as being the most ‘appropriate’ for fitting the data is

(1 - B ) ( z , - y : ) = (1 - elB)(i - elZBIZ)&, e, = 0.78 eI2 = -0.22 17108 = 35,222 17701 = 22,713

(0.06) (0.10) (9782) (9536)

[:lo8 fort = 71/08 for f = 77/01 otherwise

0, = 10,335

y, = I7701

This shows no seasonal influence and has the lowest residual standard deviation and AIC. This is a case where one of the observations to be forecast is also an outlier. The average

CRAPE value (Table 111) is equal to one and for models without transformation and intei vention analysis the CRAPE measure is 15.5. It is worth observing that the timing of outliers of the same commodity for the other direction (in this case, outgoing traffic of non-ferrous metals) is not the same. This holds for all incoming and outgoing maritime traffic flows of the same commodity studied in this paper.

The results for all the sets of data (with standard deviations in parentheses can be summarized in Table I where the ARIMA parameters are given for the final models obtained in a similar way as described above and Table I1 provides the interventions of the I-type. These models are used for forecasting purposes. A similar modelling procedure has been implemented for the D- and a-type of interventions. Table I11 summarizes the forecast results of all three intervention types.

The summary of the forecasting results is displayed in Table 111, where CRAPE values for SARIMA structures with transformation and interventions of type I, D and a are applied and the average of these three values is called AVE. A way to view the effect of the SARIMA model class is by implementing the modelling without data transformation and interventions (called SARIMANT).

It is clear from Table I11 that the SARIMA model performs better than SARIMANT in a sizable majority of cases. A relative forecast error less than 10% for the cumulated twelve-step- ahead forecasts can be considered as ‘satisfactory’. About two-thirds of the SARIMA structures fulfil this requirement and a similar proportion of the models belonging to this category produce a CRAPE value of less than 5%. When no interventions and transformations are applied the proportion of ‘success’ is reversed. Of 22 series under study about three out of four produce more accurate forecasts for SARIMA than with unadjusted data. The largest forecast error for SARIMA is 32.5% whereas for SARIMANT the value of 587% is achieved, but the latter can hardly be considered as reliable.

One can conclude that when the modelling procedure of the SARIMA model class is performed with care, the resulting models forecast better than SARIMANT in a considerable number of cases.

In the next section an attempt is made to explain the large deviations of the forecasts from the actual values for the SARIMA model class. This happens by giving a short description of the economic sector during the period under study and considering its impact on the corresponding Antwerp maritime traffic flow.


4

4 H

0 0 0

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r- d o 0 1 f

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i=' g m 0 I

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i=' 2

g 2

2

0 c? 0 I

h Iz

Iz

I

h 00

\9

I 2 6 9 0, Iz v 0 I

VI

-30333

h 6 2 2 s m 00 m N 0 0

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3

Tabl

e 11

. Es

timat

ed v

alue

s of

y,'

(1)

1 che

mic

al fe

rtiliz

ers

(2)

1 che

mic

al p

rodu

cts

(3)

1 cru

de a

nd m

anuf

actu

red

(4)

1 gla

ss, g

lass

war

e, ce

ram

ics

(5)

1 mac

hine

ry, a

ppar

atus

, mot

ors

(6)

1 mot

or v

ehic

les

(7)

1 non

-fer

rous

met

als

(8)

1 iro

n an

d st

eel

(9)

u fe

edin

g st

uffs

for a

nim

als

(10)

u c

ellu

lose

and

pape

r was

te

(1 1)

u m

achi

nery

, app

arat

us, m

otor

s (1

2) u

che

mic

al fe

rtiliz

ers

(1 3)

u c

hem

ical

pro

duct

s (1

4) u

coa

l and

cok

e (s

olid

fuel

) (1

5) u

cru

de an

d m

anuf

actu

red

min

eral

s, b

uild

ing

mat

eria

ls

(16)

u m

otor

veh

icle

s ( 1

7) u n

atur

al fe

rtiliz

ers

( 18)

u n

on-f

erro

us m

etal

s ( 1

9) u n

on-f

erro

us o

res

(20)

u ir

on a

nd s

teel

(2

1) u w

ood

and

cork

(2

2) u

nat

ural

and

synt

hetic

(min

eral

s, bu

ildin

g m

ater

ials

and

food

stuf

f was

te

(text

ile m

ater

ials

and

was

te

I800

5 =

144

,893

(46,

804)

I7

206

= 1

24,2

20(2

9,59

1)

I761

2 =

103

,951

(22,

059)

I7

109

= 7

314.

5(19

82)

I740

7 =

48,O

l l(3

706)

I1

7105

= 1

9,54

8(49

53)

I781

0 =

24,

968(

5652

) I7

502

= 44

1,50

1 (16

3,63

7)

I761

1 =

98,

869(

8376

) I7

602

= 9

1,16

1 (13

,088

) I7

102

= 2

6,19

9(25

49)

I730

9 =

90,

386(

13,0

65)

I751

0 =

102

,699

(26,

131)

I7

603

= 2

17,9

00(4

6,32

5)

I720

3 =

72,

134(

27,2

81)

I710

7 =

50,

198(

3945

) I7

402

= 1

45,7

70(2

5,27

2)

I710

8 =

35,

222(

9,78

2)

I790

1 =

764

,745

(35,

771)

I7

612

= 1

35,9

23(3

1,86

6)

I740

2 =

44,

977(

9244

)

I710

6 =

13,

029(

3431

)

I791

0 =

109

,994

(31,

306)

1791

0=94

,991

(19,

948)

I7

911

= 1

0,18

8(15

15)

I751

1 =

18,

507(

4689

) I7

212

= 2

5,32

7(55

81)

I760

5 =

-13,

512(

4493

)

I761

2 =

83,

986(

9979

) I7

903

= 5

3,48

2(14

,432

) I7

21 1

= 2

4,79

1 (28

00)

1770

6=71

,193

(15,

631)

I7

612

= 1

06,9

88(2

7,28

1)

1760

4 = 2

36,8

78(4

9,63

1)

I760

3 =

23,

467(

3979

) I7

503

= 7

3,18

9(25

,276

) I7

701

= 2

2,71

3(95

36)

1770

1 = 1

1,84

46(3

2,41

8)

1741

2 = 4

2,92

4(65

98)

I760

6 =

11,

910(

2624

)

I760

6 =

79,

859(

19,5

19)

I800

9 =

10,

056(

1688

) I7

810

= 2

9,31

0(59

10)

I761

2 =

22,

503(

5741

)

I770

1 =

88,

902(

10,5

59)

1800

8 = 4

7,13

8(19

,284

) I7

903

= 1

7,19

4(41

44)

I770

8 =

68,

656(

16,5

98)

I771

0 =

11,

123(

27,9

04)

I800

2 =

282

,853

(74,

960)

I780

1 =

65,

180(

25,2

78)

I770

8 =

205

,841

(29,

976)

I761

2 =

23,

724(

2655

)

b

-. P 3

I800

6 =

653

1.2(

1807

) I7

51 1

= 1

6,57

3(42

63)

I770

2 =

21,2

79 (4

960)

I790

3 =

89,

131(

12,5

26)

(1)

1 che

mic

al fe

rtiliz

ers

(2)

1 che

mic

al p

rodu

cts

(3)

1 cru

de a

nd m

anuf

actu

red

(4)

1 gla

ss, g

lass

war

e, c

eram

ics

(5)

1 mac

hine

ry, a

ppar

atus

, mot

ors

(6)

1 mot

or v

ehic

les

(7)

1 non

-fer

rous

met

als

(8)

1 iro

n an

d st

eel

(9)

u fe

edin

g st

uffs

for a

nim

als

(min

eral

s, b

uild

ing

mat

eria

ls

(and

food

stuf

f was

te

I781

0 =

33,

539(

8041

) 2

(10)

u c

ellu

lose

and

pap

er w

aste

I8

102 =

101

,875

(21,

002)

z 2

(1 1)

u m

achi

nery

, app

arat

us, m

otor

s (1

2) u

che

mic

al fe

rtiliz

ers

I790

1 =

103

,880

(118

,866

) g

(13)

u c

hem

ical

pro

duct

s 17

712 =

133

,080

(27,

988)

00

(1

4) u

coa

l and

cok

e (s

olid

fue

l)

3

( 15)

u c

rude

and

man

ufac

ture

d

(16)

u m

otor

veh

icle

s

(18)

u n

on-f

erro

us m

etal

s (1

9) u n

on-f

erro

us o

res

(21)

u w

ood

and

cork

(2

2) u

nat

ural

and sy

nthe

tic

rl

I800

6 =

16,

027(

5164

)

(D $ 43 rl

(min

eral

s, b

uild

ing

mat

eria

ls

(D a %

( 17)

u n

atur

al fe

rtiliz

ers

I800

9 =

13,

394(

2572

)

(20)

u ir

on a

nd s

teel

I7

712

= 1

41,1

63(3

1,16

2)

3. 5 (te

xtile

mat

eria

ls an

d w

aste

Y

m

1 = lo

adin

g, u

= u

nloa

ding

. %

F

5

408 Journal of Forecasting Val. 15, Iss. No. 5

Table 111. Comparison of one year-forecasts produced by SARIMA and SARIMANT. The results are the CRAPE values which express percentages

~ ~ ~ _ _ _ ~ -

SARIMA SARIMA SARIMA I D S AVE SARIMANT

(1) 1 chemical fertilizers (2) 1 chemical products (3) 1 crude and manufactured

(4) 1 glass, glassware, ceramics (5) 1 machinery, apparatus, motors (6) 1 motor vehicles (7) 1 non-ferrous metals (8) 1 iron and steel (9) u feeding stuffs for animals

(and foodstuff waste (10) u cellulose and paper waste (1 1) u machinery, apparatus, motors (12) u chemical fertilizers (13) u chemical products (14) u coal and coke (solid fuel) (15) u crude and manufactured

(16) u motor vehicles (17) u natural fertilizers (1 8) u non-ferrous metals (19) u non-ferrous ores (20) u iron and steel (21) u wood and cork (22) u natural and synthetic

(minerals, building materials

(minerals, building materials

textile materials and waste

13.5 1 0.78

2.6 3.3 0.5 1 0.4

25.9 0.92 4.2

17.4 14.7 14.9 3.7 3

15.2

5 5.8 1.4 5.2

33 6 0.2

11.9 0.0

2.7 4.1 8 2.2

35.5 0.9 4.5

10.7 10.4 14.8 5 8

12.2

6.6 5.7 0.2 4.2

29.4 4.6 3.5

12.5 12.6 1.2 0.66

0.2 1.8 2.4 3.27 8.4 5.64 0.2 0.93

2.2 1.34 4 4.23

36.1 32.5

14.6 14.23 13.8 13 16.3 15.33 2.1 3.6 0 3.67

13 13.5

15.9 9.16 5.3 5.6 1.4 1 3.9 4.43

23.1 28.5 5.5 5.37 2 1.9

13.4 4.6

25.7 2 2.7

14.9 10 12.6

586.8

5.4 13.2 72.6 22.4 37 14.3

0.1 28.1 15.5 17.1 28.5 6.7

27.6

SOME ECONOMIC CONSIDERATIONS

In this section an attempt is made to explain some forecasting results by refemng to identifiable events. We will not analyze in depth the behaviour of all series but we will concentrate on some that produced less satisfactory forecasts, i.e. CRAPE larger than 10% (see e.g. SEA, 1981). When the interpretation of the forecasting results is carried out the average CRAPE value of the three intervention models will be used. The principal motivation for combining forecasts is to avoid the a priori choice of a single forecasting model. Studies have shown that a combination of forecasts often outperforms the forecasts of a single model (Mahmoud, 1984).

It is also shown in Granger and Ramanathan (1984) that a linear combination of forecasts outperforms individual forecasts. In Hillmer et al. (1983) several model structures are used to forecast three accounting series. The multiple time-series model results in the smallest forecast variance. In a more recent paper, Ledolter and Lee (1993) show that forecast improvement is achieved by shrinkage when applied to credibility models.

As long as each forecasting model provides new information, more reliable forecasts are obtained by combining them. First, attention is paid to the flow of outgoing chemical fertilizers. One should start by making a distinction between elements of the traffic that are determined by different market factors (e.g. the markets of phosphates, potassic fertilizers, nitrogenous

A. Klein Forecasting the Antwerp Maritime Traflc Flows 409

fertilizers and other fertilizers) which are very different. The presence of chemical industries in the direct vicinity of the Antwerp area plays an important role in the outgoing maritime traffic whereby inland navigation also has a considerable share in these transport activities. These production capacities actually have a double function to fulfil. First, the manufactured products are available for export and, second, the factories in the hinterland will make use of the port facilities in order to implement some of their operations. Another quite important factor to be considered is that the European fertilizer industry is very integrated and applies a strongly protectionist policy towards export markets outside Western Europe and America. There they operate as a cartel. Therefore we have to focus on a two-sided problem: (1) when market fluctuations emerge we also experience fluctuations in port activities; (2) what is the position of Antwerp in the Le Havre-Hamburg range of ports (i.e. Le Havre, Dunkirk, Antwerp, Ghent, Zeebrugge, Rotterdam, Amsterdam, Bremen and Hamburg)? These points are of major importance for practically all maritime traffic flows. The average CRAPE value is 12.6%, which is not large and the characteristics of the flow described might contribute to this level of deviation.

Also of importance will be the traffic of outgoing non-ferrous metals. During the period under study two turbulent events happened: the Shaba crisis in Africa, and the military take- over in Allende’s Chile. It is also worth pointing out that the international prices and volumes that are treated are mainly determined by the quotations of the London Metal Exchange. So we are dealing with a commodity that is very sensitive to these quotations and these quotations are in turn very sensitive, which explains the high level (32.5%) for the forecast error. The results obtained reveal that the incoming traffic flow of non-ferrous metals produced a very good forecast performance reaching the level of 1%. It is worth investigating the reasons for the gap in performance between incoming and outgoing traffic flows of the same commodity.

The incoming maritime traffic flow of non-ferrous metals is mainly determined by raw copper. The highly developed copper sector in Belgium does not obtain its supplies in the form of copper ores (Zaire, Chile, Zambia) but in the form of raw metal, which is refined by Belgian industries. This suggests that the import of non-ferrous metals follows a similar path of evolution as the capacity and activity in this Belgian sector. In contrast with the outgoing traffic we are faced with shipments to all parts of the world and they are in turn sensitive to all kinds of fluctuations, as mentioned above. This may conmbute to an explanation of the difference in forecast performance.

The incoming traffic of cellulose and paperwaste is also an interesting matter if we consider that about three quarters of Antwerp’s maritime traffic is bound for other countries. Also worth mentioning is the change in continents of origin, which can be illustrated by the following assessment.

At the beginning of the 1970s about 70% of Antwerp’s traffic was of Scandinavian origin and about 22% came from North America, but at the end of the decade the proportions were reversed. This development can be considered as quite remarkable. A second phenomenon to be considered is that integration is much stronger in the USA. than in Scandinavia, by which is meant that American producers own everything, from the wood to the ships (and most of the intermediate facilities). Scandinavian producers have (during the period considered) switched to secondary ports for their West European market (Temeuzen, Calais, Boulogne-sur-Mer). This short description of this traffic increases our faculty of understanding the result of 14.2% for the average CRAPE value. A clearer picture of the results would be obtained if a distinction could be drawn between the American and the Scandinavian markets by considering two separate time series, but this would be extremely time consuming and would be only worth doing if one wants


to achieve a more consistent analysis of the market of cellulose as a whole, which is not the case in our investigation.

The next traffic flow that will be analysed in both directions is that of crude mineral products. The outgoing traffic of crude mineral products is mainly made up of sand for industrial use (expressed in tonnage) and the shipments originate from a firm that exploits sandpits in Belgium and whose final products are mainly used in the manufacture of glass. This traffic enjoys a quite stable evolution and this may be the reason for 1.8% value of the average CRAPE. However, the incoming traffic of the same commodity has a hybrid range of different components that underwent strong fluctuations during the previous decade. Some examples will illustrate this phenomenon:

(1) The construction of a specialized sulphur terminal in Antwerp at the beginning of the 1970s has led to a fivefold increase in incoming sulphur traffic. Since its inauguration Antwerp has captured about 40% of the incoming (Le Havre-Hamburg) range traffic. It is also worth mentioning that sulphur is very sensitive to business cycles.

(2) The incoming traffic of crushed stone reached between 150,000 and 200,000 tonnes a year at the start of the 1970s but disappeared completely afterwards.

(3) The entry ‘other crude minerals’ attains a deviation on a yearly basis of about 100,000 tonnes. These examples will again partially justify the 13.5% value of the forecast error.

The incoming traffic of machinery comes from other industrialized countries (North America, the United Kingdom and Japan) and its irregular flow is mainly due to transport-economics factors. Ln fact this traffic is strongly linked with containerization. During the 1970s Antwerp was poorly integrated with the container services of the Far East, and this lasted for a few years. This led to a diversion of part of the traffic to Rotterdam, but a change took place in the late 1970s. One can hardly expect the incoming traffic of machinery to follow a smooth path if we know it consists of a whole range of products, from bulldozers to sewing machines and small calculators. Here again the question could be raised as to why the outgoing traffic of the same commodity produced a value of 5.6% for the average CRAPE value whereas the flow in the opposite direction reached 13%. An explanation could be found in the wide spread of countries of destination, whereby much better internal compensation is obtained. Shipments of machinery from the port of Antwerp involve most of the countries of the world as destinations.

The import of fertilizers at the beginning of the 1970s can be related to a temporary unavailability of a certain type of fertilizer, and during this decade an evolution took place from temporary unavailability to fundamentally different market circumstances. We will try to illustrate this.

During the decade under study we saw the establishment of a distribution centre of Russian potassic fertilizers and this introduced a supplementary flow of the commodity. A further increase in the incoming traffic of chemical fertilizers can also be explained by the production increase in nitrogenous fertilizers from countries such as Spain and Portugal, whereby a surplus was created, so that an export increase followed. With US fertilizers (mainly nitrogenous and other fertilizers), the reason for imports must be found in their competitive prices, taking into account that for these respective products the country with the cheapest energy resources (in this case US natural gas) will be able to offer the most attractive prices. An increase in maritime traffic took place because of a drop in the traditional imports from Alsace.

A summary of all these factors could explain the high average CRAPE value obtained.In de Gooijer and Klein (1989), a detailed description of the European steel industry during the 1970s is provided, This enables us to draw relevant conclusions concerning the average CRAPE values of the corresponding maritime traffic flow at the port of Antwerp.

A. Klein Forecasting the Antwerp Maritime Traftc Flows 41 1

CONCLUSIONS

Extremely high forecast errors can be achieved with unadjusted data. This justifies the implementation of data transformations and intervention models when necessary for modelling and forecasting purposes.

APPENDIX: DATA SOURCES

The data used in this article are based on the NSTR (Nomenclature Uniforme des Marchandises pour les Statistiques de Transport Revises) nomenclature. The sample covers 1971: 1 - 1982:3. The data used were obtained from the Belgian National Institute of Statistics. A detailed description of the maritime traffic flow distinguishes between incoming, outgoing and transit traffic flow. In this article incoming and outgoing maritime traffic flows also include the corresponding transit traffic.

ACKNOWLEDGEMENTS

The author would like to thank the Departmental Editor Robert H. Shumway, two anonymous referees and G. MClard for their valuable comments and suggestions.

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Author S biography: Andre Klein is a Lecturer in Statistics in the Faculty of Economics and Econometrics at the University of Amsterdam. He holds an MS degree in Economic Engineering from the University of Antwerp and a Ph.D. in Applied Statistics from the University of Brussels (VUB). He has published articles in the Journal of Computational and Applied Mathematics, Statistics and Probability Letters, Journal of Time Series, IEEE Transactions on Signal Processing, Linear Algebra and its Applications, Journal of Forecasting, International Journal of Forecasting. His research interests are in theory and applications of time series analysis, forecasting and the relation between filtering models and statistics.

Author’s address: Andre Klein, FEE, Department of Economic Statistics, University of Rotterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.

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Forecasting the Antwerp maritime traffic flows using transformations and intervention models