B.Arlyuk, D.Sc.
Development
of computer system for short term forecast the prices of commodities and its
application for primary aluminium
1. Introduction
There are no publications in
literature on development of stock exchange price forecasting models for
industrial goods including the metals of industrial group and in particular,
for primary aluminium, which world prices are formed at London Metal Exchange.
At the same time price forecast determines significantly commercial activity of
companies and is necessary for investment planning.
Accuracy of the used world
price forecasting systems can be assessed by the regular information of the
leading analytical companies. When forecasting the primary aluminium prices one
quarter ahead for the period from 1990 to 2001, analytical companies had the
average error in the average quarterly price forecasting of about 92$/t, and
they also had an error in the price variation direction in 45-56% cases. Taking
into account that the average quarterly price variation for the said period
amounted to 94$/t, such results practically do not differ from random
forecasting without taking into account available market information. Average
price forecasting errors for the second quarter ahead and further exceed the
average price variation. This proves the fact that there are actually no
correct models for price forecasting even one quarter ahead.
The performed research
resulted in development of the exchange price forecasting systems for
industrial goods, primary aluminium exchange price forecasting models were got,
which found application in commercial activity of industrial companies, funds
and traders.
We made the first attempts to
develop a model and a computer system for primary aluminium world price
forecasting in 1994, and they were published in “Aluminium” journal [1]. The continuation
of work in this field was published in November 1995 in “Journal of Metals” [2], when the world
price reduction by the end of 1996 was forecasted quite accurately.
Analysis of the market regularities
and the market information structure, which can be used for price forecasting,
allowed to make the following conclusion:
1. Aluminium price
forecasting by purely statistic methods (on the basis of empirical regression
models) does not give the acceptable accuracy of results. This is caused by
incomplete available information on the basic market parameters. Aluminium
demand and supply, its stock of manufacturers, traders and consumers are such
parameters determining the market price behavior. Fixed general market and
exchange indicators characterize these parameters only indirectly and with
delay. That is why there are too many empirical coefficients in the price
forecasting model made by the principle of “black box”, and the reliability of
their definition by the mass of actual data turns out to be very low.
2. Price forecasting
accuracy acceptable for commercial purposes can be reached on the basis of the
market regularities analytical model supplemented by the special assessment
model of the basic market parameters by the available current information. The
analytical model connecting the aluminium price with its demand, supply and the
stock of the market participants contains comparatively few unknown
coefficients, and assessment of these parameters by the fixed market indicators
is made on quite simple and obvious relations.
3. Regularities of the
market price forming depending on demand, supply and aluminium stock are
disturbed significantly in the periods of the world economy crises both under
the influence of objective factors and subjective information spread in the
market. It is impossible to model and account these factors at price
forecasting. But the analytical model of the market price forming makes it
possible to detect the deviations from the established market regularities
quite early. Such deviations are detected by comparing the current moment
forecasting error with its average value. That is why when the current error
starts to exceed its average value more than 2.5-3 times, only the near price
forecasts can be trusted (less than one quarter ahead). The price forecasting
distance should be reduced at these cases in commercial application.
2. Alternative approaches to
the aluminium price forecasting
Price, demand/offer balance,
sellers stock and buyers stock are the basic parameters of the current status
of the primary aluminium market (like any other goods market). All market
regularities are inertial and they can be described by a dynamic model, which
connects the market status in the future moments with the current status. Such
model allows to forecast the future status, in particular, aluminium price, if
the status parameters in the present moment are known. Actually only the
current price can be measured (fixed) directly and correctly. The other market
parameters can be assessed only indirectly by a number of recorded general
market and exchange indicators. Thus, the calculating procedure of the price
forecasting can be presented as two successive procedures – assessment of the
current status parameters not recorded directly and forecasting by them the
price for the given future period.
Fixed data on aluminium
production and consumption in the market, current exchange information as well
as the indicators of the world economy development are the data base for
assessment of the market status parameters. The volume of this information is
quite big – besides the exchange price itself this is the open interest at the
exchange, the volume of the deals made, exchange metal stock (LME stock), IAI
data on primary aluminium production in the Western countries, assessments of
primary aluminium supply and consumption in the world market, fixed stock of
manufacturers (by IAI data) and industrial production indices in the Western
countries (IP).
Two approaches are possible
for creating the price forecasting system: empirical (by statistic methods) and
analytical (by the methods of mathematical modeling).
Many attempts are known of
industrial good prices forecasting by purely statistic methods. Such approach
is attractive due to the fact that it does not require knowledge and
mathematical description of market regularities as the forecasting is made by
the purely empirical regression model.
However, in reality such
approach to forecasting very often does not give satisfactory results, which
happens with the aluminium price forecasting problem. The reason for this is
not obvious and it requires explanation. The thing is that the forecasting
system made on the basis of regression model contains comparatively many
empirical coefficients, and a mass of actual data at a long timed interval is
required for their statistic definition. The minimum possible number of
coefficients even for the simplest linear regression model for aluminium price
forecasting 1 step ahead is equal to the minimum number of the market status
parameters (4 basic parameters) multiplied by the number of recorded market and
exchange indicators (6-8 indicators), and it amounts to 24-32 coefficients. But
the market regularities of the price forming do not remain invariable for a
long time. They depend on the status and variation of the entire world economy,
are subject to crises and other calamities, and so they can differ
significantly within various periods. In
terms of random processes it means non-stability of market regularities.
In such situation identification of regression model (aimed at definition of
its coefficients) for a comparatively long time interval leads to the
situation, when the model reflects not the actual market behavior for the
latest time, but the average behavior for a long period, which is a kind of
compromise for all possible disturbances outside the market. Correct
forecasting by such model will be too conservative and with low information
content.
3. Analytical model of
aluminium price forecasting
In order to make the
analytical model of market regularities relations of the basic market
participants – sellers and buyers- were mathematically formalized. For this
purpose the market structure was analyzed, the purposes of its participants
were formulated and their actions were modeled as the reaction to the market
situation and the partners actions.
The chain of cause and effect
relations between the sellers and the buyers is built based on the fact that
the sellers depending the sale volume variation form the market price, and the
buyers depending on the price change the sale volume. Such system of market
relations in the part of price forming is characterized by 3 basic status
parameters – price P, demand/offer balance dV and goods stock (aluminium)
of the buyers Z (stock sum of consumers and traders). It is described
mathematically by the system of 3 differential equations:
(1)..…dP(t)=A1*dP(t-1)+k1*dV(t-1),
(2)…..dV(t)=A2*dV(t-1)-k2*dP(t-1)-k3*dZ(t-1),
(3)…..dZ(t)=dZ(t-1)+dV(t-1),
where dP – price deviation from its
moving-average value, dZ – stock deviation
from its norm, t – current time, A1, A2, k1, k2,
k3 – constant coefficients.
Equation (1) describes
sellers’ reaction to the demand variation, equation (2) – buyers’ reaction to
the price variation, equation (3) – aluminium stock balance.
For compactness
of record and connection with model of estimation the equations (1) - (3) are
used in vector form:
(4)…..X(t)=A*X(t-1) .
Here by X the vector of condition
the market [ δP, δV, δZ], and
by A - matrix of model coefficients are given.
This system is dynamic as the
sellers’ reaction to demand variation and the buyers’ reaction to the price
variation are not instantaneous, but they are distributed in time and depend on
the accumulated aluminium stock (dynamic coefficients A1 and A2).
Mathematical analysis of such system shows, that its own fluctuations of price
and demand/offer balance can arise with definite frequency. The fluctuations
appear when the market participants react sensitively to the actions of each
other. The clearly observed fluctuating character of actual aluminium prices
proves the adequacy of the created market model.
The received analytical model
of price forecasting allows to calculate the aluminium price, the demand/offer
balance and the stock of the buyers one step ahead via their known values at
the given step. However, such forecasts calculating scheme cannot be realized
in practice as in reality neither demand/offer balance nor aluminium stock of the
buyers are recorded directly. So the problem arises, how to assess them
indirectly by the actually measurable (fixed) values. Besides the current price
itself, such values comprise assessment of the market supply with primary
aluminium production volume in the Western countries by IAI data plus export
from the countries of the former Eastern block), assessment of primary
aluminium consumption in the Western Countries, industrial production index in
the Western counties IP as well as exchange stock in LME warehouses, exchange sale volume under all
concluded contracts and open interest. These indicators reflect the current
market status only indirectly and with big delay. For instance, aluminium
supply and consumption balance does not coincide with the market demand/offer
or put/call balance as these finite flows of manufacturers and consumers are
separated by dynamic buffers in the form of aluminium stock of the market
participants. The above balances coincide only on the average for a
comparatively long period (much further than the price forecasting period). In
its turn, the recorded aluminium stock coincides neither with the stock of
sellers nor with the stock of buyers, and it is only their indirect indicator.
The task of the market status
parameters assessment and forecasting by them the aluminium price has been
formulated and solved within the framework of the theory of optimal assessment
and forecasting of discrete random processors [3, 4]. The price forecasting system
represents a dynamic system with feedback as shown in fig.3.1.
Estimation of current
Model
of market ðûíêà Model
of estimation
Initial market condition price data
forecast
Delay
by one step
Previous
price forecast
Fig.3.1. The flow sheet of aluminium price forecasting
The status parameters assessment
model (demand/offer balance and stock of buyers) and the aluminium price
forecasting dynamic model are connected in sequence in the straight chain. The
price forecast one step ahead is calculated in the market model by the status
parameters at the current moment by equation (4). In their turn, assessments of
these status parameters are calculated in the model of their assessment by the
recorded indicators (input information). The received assessments are revised
taking into account the price discrepancy – the difference between the actual
current price and its forecast made at the previous step. The previous
forecasting is received at the system output by the feedback chain, where it is
retained by one step of calculation.
The model of
estimation is constructed by methods of a filtration of casual processes and
represents Kalman`s filter of the forecast [3]. Within the framework of this
methodology the equation is entered of connection fixed variable (price of
aluminium, stocks of aluminium at LME, volume, open interest, supply and
consumption of aluminium in the market, IP index) with parameters of market
condition - vector X. These equations
are the following :
(5)…..Y(t)=C*X(t) ,
where Y (t) -
vector included listed fixed variable, C - matrix of coefficients.
With relation to model of the market (4)
equations of the filter of forecast the parameters of a condition - vectors X
(t) have the following view:
(6)
….. Xˆ(t+1)=A*Xˆ(t)+A*G*(Y(t)-C*Xˆ(t))
.
here Xˆ(t+1) - forecast
of vector the condition of the market X
(t) for the moment of time t + 1, G - matrix factor of amplification the
filter, which is determined at an adjustment of system under actual data.
Thus, the calculation
procedure is got, at the input of which the current information is used – the
fixed general market and exchange data Y(t),
and at the output the forecasted prices (first component of vector Xˆ) are
received by step-by-step calculation for the required time intervals ahead.
This procedure comprises 10-11 adjustment coefficients, which is 2.5 times less
than the number of coefficients of the calculation procedure on the basis of
the regression model (see p.2).
4. Multifrequency system of
quantitative and qualitative price forecasting
It is clear, that the
possibility to forecast aluminium prices is caused by the market processes time
lag, thanks to which the correlation of future prices with the current market
status exists and, so, with the fixed current market information. This
correlation reduces with the time interval increase between the future price
and the current status. Accordingly, the forecasting error grows and, consequently, there is a maximum
possible interval of forecasting with the required accuracy. It is also clear,
that this interval depends on the averaging period of the forecasted price and,
e.g. for the day prices it is much less than for the average quarterly prices.
For preliminary quantitative assessment of these qualitative relations, the
analysis was carried out of the frequency spectrum of correlation relations
between the market status parameters. Then the forecasting systems described
above were investigated (see fig.3.1) for various periods of price avaraging
and input information. Moving-average periods of 3 days, 8 days, 1 month, 1
quarter and 1 year were assumed. First of all, it was found that the
correlation of the average price with the remaining market status parameters
covers only 1-2 quarters and so the price forecasting by the current market
information is possible not further than 1-2 quarters ahead. It is natural to
call such aluminium price forecasting a short-term one.
For the price avaraging
periods of over one quarter (average annual prices) the market model turns into
the static one, and the average price depends on the status parameters of the
current period (year) only. So, for the aluminium average price forecasting
further than one quarter ahead it is necessary preliminary to forecast the
market status parameters for the respective future periods.
Analytical companies give
long-term forecasts (quarterly up to 1 year ahead and annual up to 5 years
ahead) of primary aluminium production, its consumption and industrial
production indices in the Western countries (IP). Within the framework of our
method the market status parameters (demand/offer or put/call balance and stock
of the buyers) are assessed by this data for the respective future periods, and
then the respective future average quarterly and average annual prices are
calculated by the market static model. It is natural to call such aluminium
price forecasting a long-term one. Thus, the long-term aluminium price
forecasting system also corresponds to the scheme of fig.3.1, but here the
forecasts of aluminium market balance indicators and IP indices are the input
information and the feedback is missing. The long-term aluminium price
forecasting system is dwelt upon in more detail in p.7.
Statistic processing of data
in the average period prospect showed, that the price quantitative forecasting
turns out to be reliable not further than 1-2 steps ahead. Thus, it is possible
to forecast the day prices not further than 1-2 days ahead (1 step – a day), the average monthly prices – 1 month
ahead (1 step –a month), the average
quarterly prices – 1 quarter ahead (one step – a quarter). Price forecasting
errors more than 2 steps ahead are already approaching the average price
variation range for these periods. But the same result would be if forecasted
at random, without involving the fixed current information.
At the same time it is clear,
that the average quarterly price 3 months ahead gives an idea of average
monthly prices behavior further than 1 month ahead. Similarly, if the average
monthly price forecast is known for a month ahead, it is possible to give a
quality forecasting of the 8 day average price behavior further than 8 days. In
other words, the price forecasting system with various averaging periods
(multifrequency dynamic system) in total gives the possibility of qualitative
price behavior forecasting far beyond the limits of reliable quantitative one
step forecasting. This property is highly valuable for sale planning and trader
operations with aluminium, when the qualitative behavior of future prices in
the far prospect is more important
than the near quantitative forecast.
As a result, a complex system
was made of aluminium price qualitative-quantitative forecasting up to 1
quarter ahead. The sub-system of the average quarterly price forecasting for 1
quarter is the basic unit of this system, which will be dwelt upon in detail
below.
As it was already mentioned,
the average quarterly price forecasting sub-system consists of two functional
units – the init of the market status parameters assessment (demand/offer
balance and stock of the buyers) and the unit of price forecasting by the
market dynamic model (see fig.3.1). The greater part of empirical coefficients
determined as the result of the model identification by the mass of actual data
is located in the assessment unit, and their number is in proportion with the
number of the input variables. The reliability of the entire price forecasting
model depends on the number of empirical coefficients. So, the optimal choice
of significant input variables – thefixed general market and exchange
indicators – plays an essential role.
The performed statistic factor
analysis showed, that out of the exchange factors the exchange aluminium price,
open interest and exchange stock are sufficiently significant. The recorded
general market balance indicators are also significant. But if the exchange
parameters are fixed accurately and in time (without delay), the current
balance parameters are not accurate, they are delayed and revised several times
afterwards. Out of the balance parameters only primary aluminium production and
stock of manufacturers in the Western countries are quite reliable and issued
by IAI with the delay of about 1.5 months. The amounts of export from Russia,
which is the main aluminium exporter, is promptly published by SCC only in
relation to unwrought aluminium (the total primary aluminium export together
with the primary and secondary alloys), and the annual primary aluminium export
statistic data is published with a quarter delay. In spite of the fact that the
aluminium associations of the USA, Japan and EC countries give statistic data
on the deliveries volume and primary aluminium processing, this data is not
sufficient for accurate definition of primary aluminium consumption in the
Western countries in total.
Delay and gradual refinement
of the balance data by hind sight correction is specific for the input
information, which has to be accounted in the model. Actually, there are
several balance values for every quarter in the past. There are the forecasted
values, when this quarter was the future quarter, then there are the corrected
values, when this quarter became the current one, and once more (or
several times more) revised values,
when this quarter becomes the past one.
Preliminary the general market
balance parameters reliability was assessed separately. The respective data was
taken from the monthly information of CRU and Brook Hunt. Primary aluminium
production in the Western countries, its import from the countries of the
former Eastern block, the market aluminium supply (the sum of production and
import), aluminium consumption in the Western countries and supply/consumption
balance were analyzed. The statistic analysis was carried out within the
interval from the 3rd quarter of 1995 to the 4th quarter
of 2001. The final revised values were assumed as the actual values of the
above parameters, in relation to which the forecasting errors were determined.
The average errors of forecasting for one quarter ahead and the forecasted
parameters variation direction errors are given in table 4.1a according to CRU
data and in table 4.1b according to Brook Hunt data.
Table 4.1a. Average errors in
one quarter forecasts (in kt/quart) and the forecasted parameters variation
direction errors (in %) according to CRU data.
|
Name of the parameter |
Average quarterly variation |
Average forecasting error |
Fisher criterion* |
Direction error |
|
production |
53 |
41 |
1.31 |
22 |
|
import |
47 |
82 |
0.57 |
- |
|
supply |
70 |
106 |
0.66 |
40 |
|
consumption |
142 |
152 |
0.93 |
38 |
|
balance |
172 |
152 |
1.13 |
32 |
* - ratio of the average
quarterly variation to the average forecasting error.
Table 4.1b. Average errors in
one quarter forecasts (in kt/quart) and the forecasted parameters variation
direction errors (in %) according to Brook Hunt data.
|
Name of the parameter |
Average quarterly variation |
Average forecasting error |
Fisher criterion |
Direction error |
|
production |
38 |
37 |
1.03 |
23 |
|
import |
41 |
69 |
0.6 |
- |
|
supply |
56 |
83 |
0.68 |
45 |
|
consumption |
154 |
73 |
2.1 |
18 |
|
balance |
172 |
99 |
1.74 |
18 |
Distribution of the average
forecasting errors and direction errors turned out to be quite instructive.
First, at any correct forecasting, including a random one, the average
forecasting error must not exceed the average forecasted parameter variation,
i.e. the Fisher criterion value must not be less than 1. But as the tables
show, such anomaly takes place for import and, consequently, for supply. This
can be explained only in the case, if the “actual” supply got as a result of
the following forecast revisions, in reality is made up (at the expense of
import) in order to reach the desired balance or prices. In this case the fact
and the forecast are made from different points of view and turn out to be not
related to each other.
Secondly, very high accuracy
of consumption forecasting according to Brook Hunt data (Fisher criterion is
over 2 and only 18% of direction errors) is not probable in comparison with the
production forecasts. It can be explained by the fact, that the consumption
forecast is revised very little afterwards, and so the “actual” consumption
differs a little from its forecast. Such approach is understandable, if to take
into account, that there is no accurate statistic data on the actual primary
aluminium consumption in the Western countries. The indirect confirmation of
this explanation is the fact that despite the seemingly high balance
forecasting accuracy (see table 4.1b), the price forecasts one quarter ahead of
Brook Hunt for the period of 1991-2001 turned out to be correct in direction in
less than half the cases.
As a result, a conclusion can
be made, that out of all balance parameters only aluminium production is
forecasted correctly, but these forecasts even for one quarter ahead cannot be
considered satisfactory for using as the input information in the aluminium
price forecasting system. Analysis showed that only aluminium production
assessment made at the current moment for the last quarter (for the last 3
months) is a statistically significant parameter.
However, it is not sufficient
to know only aluminium production for the demand/offer balance assessment in
the system assessment unit, it is also necessary to have some analog of
aluminium consumption. As the consumption forecasts and assessments given by
analytical companies turn out to be statistically insignificant, we assumed the
industrial production index in the Western countries IP weight averaged by GDP
values, NAPM and Dow Jones indexes at USA.
IP value for the just passed
quarter is the preliminary assessment, and it is usually clarified within half
a year.
Thus, the factor analysis
carried out for the aluminium average quarterly price forecasting system
resulted in the following input information structure: the current price, open
interest and LME stock (exchange information), assessments of aluminium
production and WW IP index, official statistical data of NAPM and Dow Jones
indexes at USA (general market information) for the passed quarter. These
parameters consist vector of measured variables Y at model (6).
It should be noted, that the
industrial production index IP characterizes the market demand directly and is
connected with the aluminium price through it, and this relation is reflected
by the market analytical mode (4). The price forecasting current error analysis
gives a possibility of a regular control over the market macro processes
behavior and a timely detection of sudden disturbances. If the price
forecasting current error suddenly increases and significantly exceeds its
average value (more than 2.5 times within at least 1 month), it means that the
market regularities have been disturbed, and the accepted forecasting model is
no longer adequate. Hence, it can be diagnosed that the market is under the
strong macroeconomic disturbances.
Such situation was noted, for
instance, in 1980, 1996 and 2000 and it is observed in 2001 in connection with
the economic crisis in the USA. During such periods the established market
relations between the price and demand/offer balance are disturbed, and so the
medium-term aluminium price forecasts cannot be trusted. For example, in the
first and in the second quarters of 2001 all analytical companies forecasted
for the second half of 2001 high aluminium prices as it was expected that the
production cut due to the energy crisis in the region of the USA Pacific North
West and Brazil will be the limiting factor. Actually, the consumption drop
turned out to be more significant than production cut, and the average
quarterly prices for the period from March to December 2001 reduced more than
by 200$.
Thus, if the proposed
indicator in the form of price forecasting error works, then only short term
price forecasting should be used for commercial purposes – not further than one
month ahead. This optimal solution for such situations helps to avoid large
commercial losses.
Systems of average price
forecasting for shorter averaging periods (1 month, 8, 3 and 1 day) are made
similarly to the average quarterly price forecasting system. The only
difference is that each of these prices is presented as the sum of two
components – the already calculated average price for the nearest biggest averaging
period and the deviation from this average value. Thus, for finding the
forecast of every average price (except average quarterly) it is suffice to
forecast its deviation from the moving-average value, which is methodically
more precise.
By such computing procedure
the forecasts of all average prices turn out to be interrelated and they are
calculated in sequence starting from the average quarterly MA price. Here the
general market information is used only for the average quarterly price
forecasting, and the forecasts of all the other average prices are based only
on the exchange information.
5. Identification of the price
forecasting system and practical results.
The first version of the
computer system for primary aluminium average price forecasting was created in
1999. Within the framework of this system regular forecasts were made for quarterly moving average, monthly MA, 8 day
MA, 3 day MA and daily primary aluminium prices. The average price forecasting
models were mutually independent, and the respective sub-systems were adjusted
by their identification on the basis of actual exchange and general market
balance data for the period since 1989. By
identification the matrix coefficients of model A, C and G (see (6)) were
found.
In the process of commercial
application of the forecasting results the system was being improved and by the
end of 2001 it has undergone a significant evolution. Initially the
maximum volume of general market
balance information issued regularly by analytical companies was used in the
sub-system of quarterly price forecasting. The analysis of received results
showed gradually that the balance data forecasts of analytical companies are
not acceptable for aluminium price forecasting. Selection of significant
indicators described in p.3 above was made, among those only assessments of
aluminium production, industrial production index WW IP, NAPM and Dow Jones
indexes for the just passed quarter were left.
In order to increase the
forecasting accuracy, the market analytical model was re-formulated in the
price deviation from its moving-average value. As a result, all sub-systems of
price forecasting, as it was noted in p.3, turned out to be interrelated. The
possibility of reliable forecasting of aluminium day prices appeared and it was
realized, which is important for the exchange speculation with forwards for
metal sale and purchase. Identification results of the aluminium price system
functioning at present are given below.
Empirical coefficients of all
sub-systems of average price forecasting were found by identification on the
basis of actual exchange and general market balance data for the period of
1990-2001. The forecasting accuracy characteristics were obtained. LME data on
the high grade (3M-official) primary aluminium price, exchange stock, total LME
sale volume and the LME open interest was used. CRU assessments of primary
aluminium production, industrial production index IP in the Western countries,
statistical data of NAPM and Dow Jones indexes at USA for the passed quarter
were used as the balance data.
Identification results of
sub-systems of average quarterly, average monthly and day price forecasting are
given in table 5.1.
Table 5.1. Average price forecasts accuracy indicators
|
Period of averaging and price
forecasting |
Average price forecasting
error, $/t |
Average price variation
within the forecasting period, $/t |
Forecasted prices deviation
error, % |
|
1 quarter |
42 |
80 |
20 |
|
1 month |
32 |
47 |
26 |
|
8 days |
19 |
26 |
24 |
|
3 days |
11.5 |
15.6 |
26 |
|
1 day |
7.2 |
11 |
25 |
The average quarterly price
forecasting results are influenced by: the current average quarterly price –
20%, open interest –15%, exchange stock – 8%, production – 15%, WW IP – 25%,
NAPM- 12%, Dow Jones – 5%. There are 8 adjustable coefficients in the price
model, the model memory depth (the former data influence) is about 2 quarters.
As the diagrams show, the
forecasted price variation direction error is distributed within the
identification interval irregularly: the increase of its frequency can be seen
within some periods. Obviously these periods respond to strong market
disturbances under the influence of crisis and political factors. It can be
noted, that the price forecasting error increases significantly in the
beginning of these periods, which proves indirectly the possibility of using
this error as the market processes disturbance indicator.
The average monthly price
forecasting results are influenced by: the current average monthly price – 30%,
volume and open interest – 25% each, exchange stock – 20%. The model contains
12 adjustable coefficients, and the memory depth is about 3 months.
LME close price (besides the
official price) is added to the input information composition in the day price
forecasting sub-system, and the exchange stock becomes insignificant and is
excluded. The forecasting results are influenced by: the current official price
– 35%, the close price – 25%, volume and open interest – 20% each. There are 10
coefficients in the model, and the memory depth is about 5 days.
6. Commercial application of
aluminium average price forecasting.
On the basis of the system of
aluminium price forecasting up to one quarter ahead models and computer systems
were developed for issuance of regular recommendations to aluminium
manufacturers [5], traders at the physical metal trade [6] and at aluminium
forwards operations at LME.
It should be emphasized that
the forecasting of possible maximums and minimums of the average price for the
nearest future, and not its own value is more important in such commercial
applications. For optimal choice of moments for metal or forwards sale/purchase
to manufacturers or traders it is necessary to be sure that all future probable
price maximums will be under the current value, or that the future probable
minimums will be over this value.
Complex forecasting of prices
with various averaging periods allows at any current moment to determine
probability of the indicated events for any future time interval (up to one
quarter ahead).
Aluminium price variation in
time under the influence of the entire mass of market factors belongs to the
class of Mark’s random processes, and so for solving the said problem we
implemented the random processes probability apparatus [7]. Probability
distribution of the random value (future price) maximum deviation from its
average value at the given time period can be found for such processes. In the
problem in question this maximum deviation is compared with the known value at
every current moment – deviation of the actual current price from its moving-average
value, and the probability is calculated if the upwards maximum deviation
(price maximum) would be under the given current value. (Probability for the
future price minimum is calculated in a similar way). The function of
distribution of the said price maximums and minimums probabilities depends on
the random process parameters – its dispersion and autocorrelation time, as
well as the duration of the period under consideration. These parameters of the
price variation random process were found by statistic processing of the actual
aluminium prices for the period of 1989-2001. After that probabilities
distribution function for price maximums and minimums was found.
The application mechanism of
the found probabilities distribution for the definition of the optimal moment
for sale/purchase operation is as follows. The maximum profit from commercial
operations is reached, when they are carried out at the price maximums and
minimums. For instance, it is profitable to conclude (open) futures contracts (forwards)
for metal delivery at the price maximums and to realize (close) them at the
price minimums. At the moment of forward opening it is necessary to have a
sufficiently reliable forecast that the current price will be the maximum one
for the entire future contract validity period. Accordingly, this forward
should be closed (ahead of time) at the moment, when a sufficiently reliable
forecast appears that the current price will be the minimum one for the
remaining validity period of the contract. For this purpose at every current
moment the probability of future prices maximum (or minimum) is found for the
actual price and the given future period and it is compared with the selected
threshold value. If the probability exceeds the threshold value, the probability
forecast is considered reliable, and the respective solution is made on the
given commercial operation.
The threshold probability
value influences significantly the profit from the sale/purchase operation and
it can be found only experimentally, by profit maximization for quite a long
period. For doing this, the economic model of commercial operations is needed,
connecting analytically the profit with the prices and the deals volumes.
We have developed such models
and respective control systems for 3 kinds of commercial operations. They are:
additional pricing of contracts for aluminium delivery by manufacturers to
traders [5], operations of physical metal sale/purchase by traders at LME [6]
and aluminium futures operations at LME. The average price spectrum and
probabilities of the future price maximums and minimums are forecasted in each
of these systems on the basis of the input current information (exchange and
general market indicators). Comparison of these probabilities with the
threshold probabilities results in forming daily recommendations concerning
dates and volumes of sale/purchase
deals. The current material resources of the company (metal stock) and its
economic resources (working and free assets) are also taken into account.
The contracts additional
pricing system was identified on the long time interval – from 1989 to 1999,
and from September 1999 to May 2001 it was used for pricing the contracts for
aluminium sale by Nadvoitsky Aluminium Smelter. The actual average profit from
additional pricing using the developed system amounted to 44$/t (the increase
of sale price to LME price at the day of concluding the contract with trader).
In order to bring this absolute value to the comparable relative indicator the
maximum possible profit for the same period was calculated, which would realize
if the future price behavior were known precisely. This profit amounted to
88$/t. Hence, the developed system provides 50% of the maximum possible profit
at additional pricing of contracts for metal sale [5].
The system of metal
sale/purchase by traders includes three adjusting parameters – threshold
probabilities for price maximums and minimums and the empirical coefficient
determining the sale and purchase volume. These adjusting parameters were optimized
by the profitability maximum, for which the ratio of the average annual balance
profit to the average working capital was assumed on the system identification
interval from 1995 to March 2001.
The threshold probability
values for the future price minimums and maximums turned out to be equal and amounted to 0.6, and the empirical
coefficient for determining metal sale and purchase volumes amounted to 0.35.
The profitability of the trader’s commercial activity for the selected period
of 1995-2001 was about 50 % annually [6].
At forward operations the
gambler makes a deposit (the pledge) with the exchange broker for 10% from the
value of purchased forwards and gets the possibility to open positions – to buy
forwards for metal sale (delivery) or purchase . Positions can be closed before
the prompt date of the forward (by purchasing the forwards of the opposite type
for the remaining period) or due to the prompt date coming. The profit
accumulated from forwards realization is partly deducted and the remaining
profit is capitalized (as deposit increase) for expanding the forward
operations capacity.
Such system for operations
with 3 month aluminium forwards was optimized for the profit maximum for the
period of over 5 years (form January 1996 to May 2001). The optimal deposit
share for positions opening amounted to 62%, and the optimal profit deduction
norm was 90%. The developed system was tested within the 1.5 year period (from
July 2000 to January 2002), the deposit amount being $100 k. Within the system
operation period (18.5 months) the deducted profit amounted to $137 k, which is
equal to 90% annually from the amount of the initial deposit, the amount of
closed positions consist 85 lots.
At usage developed system for
hedging metal at its sales from producer
to consumers or traders in quantity 100 kt/ year it will be necessary to
deposit as the pledge to broker $7.2
mln and the annual profit from hedging will consist $ 7.1 mln due to increase
the prices of realized metal by 71 $/t to average LME cash price plus
premium.
Conclusion
1. On the basis of
research of relations among the market participants the analytical model has
been created which connects the exchange good price with the demand/offer
balance and the stock of the sellers and buyers. Also a model was developed for
assessment of these parameters of the market status by the actually fixed
exchange and general market indicators.
The
composition of these models made it possible to create reliable system of
short-term primary aluminium price forecasting at London Metal Exchange up to
one quarter ahead. Impossibility was shown of creation a model for reliable
primary aluminium price forecasting by purely statistic methods (by the “black
box” principle).
2. The system has been
developed for long-term exchange goods average price forecasting up to two
years ahead using the market analytical model and the available forecasts of
supply and consumption.
The performed
analysis showed that the accuracy of assessments of primary aluminium actual
consumption in the Western countries in total, issued by the analytical
companies, is insufficient for long-term forecasting, but they can be replaced
by more reliable forecasts of industrial production index in the Western
countries.
The
developed system of long-term forecasting can be used for assessment of
possible aluminium world price variation at various options of the world
economy development and for definition of efficiency of construction new
aluminium smelters.
3. The developed
systems of short- and long-term forecasting were identified by the primary
aluminium actual prices at London Metal Exchange for the period of 1990-2001.
The short-term forecasts error within the identification interval is: for 1 day
prices – 7.2 $/t, for average monthly prices – 33 $/t, for average quarterly
prices – 42 $/t.
The error
of long-term average annual price forecasting. provided that the forecasting of
the market supply and industrial production index is correct, amounts to
130$/t. The price variation direction is forecasted 75-80% correctly.
4. A model of price
behavior qualitative forecasting one quarter ahead has been developed, which
determines the probability of reaching in future of the given level as well as
of the price maximums and minimums. Optimal values of threshold probability
were determined for forecasting the future price maximums and minimums securing
the maximum profit from the forecasting system application for commercial
activity.
These models can be
used in commercial activity in order to optimize the operations of additional
pricing of contracts for manufacturers at metal deliveries to traders, physical
aluminium sale-purchase for traders, sale-purchase of 3 month forwards at
London Metal Exchange and hedging the sales of metal by producers.
The executed
developments can be applied to any exchange goods, in relation to which there
is the similar fixed exchange and general market information.
References:
[1] B.I. Arlyuk The
world aluminium industry status and assessment of prospect for 1994
« Aluminium», 1994,
¹ 3-4, s.12-17
[2] B.I. Arlyuk The
world aluminium industry: status and prospects for 1996
«Journal of
Metals», 1995, ¹ 11, p.29-30
[3] V.N.Fomin. Recurrent
assessment and adaptive filtration, M., «Nauka» Publishing House, 1984, p.288
[4] M.F.Rosin, V.S.Bulygin.
Statistic dynamics and control system efficiency theory. M., «Mashinostroyenie»
Publishing House, 1981, p.312
[5] B. I. Arlyuk,
M.Ya. Fiterman. A model for short and medium-term aluminium price forecasting and its commercial
application for additional pricing. Aluminium, 2001, v.77, ¹ 9, s. 699-705
[6] B. I. Arlyuk,
M.Ya. Fiterman Optimisation of trader strategy on the basis of primary aluminium price forecasts.
Aluminium, 2002, v.78, ¹ 1/2, s. 8-14
[7] Yu.F.Rozanov. Random
processes. M., «Nauka» Publishing House, 1971, p.288
[8] B. I. Arlyuk,
M.Ya. Fiterman Long term Forecast the World Prices of aluminium. 2-nd
Aluminium and Alumina Summit, 31May-1
June, 2000, Sydney
[9] B. I. Arlyuk,
M.Ya. Fiterman. Development of an Aluminium World price forecast system and its
Application for Commercial Purposes. TMS2001, New Orleans, Light Metals 2001,
p. 405-411
[10] B. I. Arlyuk, M.Ya.
Fiterman Long term model for
forecasting aluminium prices. Aluminium, 2001, v.77, ¹ 5, s. 391-396
Email address b.arlyuk@mail.ru