INTRODUCTION
The leader in rubber production changed over time. Malaysia used to be number
one before but in 2006, Thailand took over from Malaysia to become the largest
producer with an annual production of 2.69 million MT (32% of world ’s
NR production), followed by Indonesia at 2.45 million MT (27%) and Malaysia
at 1.2 million MT (13%). However in 2008, Indonesia became the largest producer
at 2.7 million MT, followed by Thailand at 2.6 million MT and Malaysia at 1.29
million MT. China was the largest consumer at 2.3 million MT, (26% of world
’s NR consumption), followed by USA at 1.89 million MT (11%) and Japan
at 1.0 million MT (9.5%) in 2008. Table 1 also shows the world
NR supplydemand surplus/deficit situation and from 20052008 shows a deficit
situation in the world natural rubber supplies (IRSG, 2009).
Changes to the world stock situation affect the price, supply and demand of
world natural rubber. The stock of natural rubber was 2.3 million MT in 2004
and it declined to 2.0 million MT in 2008 and it was the lowest level since
2004.
Table 1: 
World supplydemand surplus/deficit situation 

^{a}Rounded to nearest 10,000 MT, Source: IRSG
(2009) 
Table 2: 
Malaysia natural rubber production, consumption, export and
import (‘000 MT) 

Note: NR = Natural rubber, SR = Synthetic rubber, Source:
MRB (2009) 
Moreover, the stock of natural rubber shows a decrease situation in yearonyear
terms during this period and a decrease situation of the world natural rubber
stock was 0.038 million MT in 2008 as compared with 2007. An inverse relationship
between NR price and stock levels is implied because prices tend to peak during
low levels of stock and vice versa in 2004 to 2008. As was evident, the decline
in stocks during this period led to a rise in rubber prices (Burger
and Smit, 2000).
The Malaysian rubber industry had produced positive net trade flows; provided
steady employment and consistent earnings for the government. Rubber was also
planted in Sabah and to a limited extent in Sarawak. Production from the estate
sector accounted for only 5.5% (59 thousand MT) of total NR production in 2008
while production from the smallholder sector accounted for 94.5% (1,013 thousand
MT). During these periods, the increased in production had also been due to
some extent by the government assistance programs for smallholders (principally
the Rubber Smallholders Income Supplement Scheme and Assistance for Low Intensity
Tapping Systems Adoption). This scheme had been implemented since in mid2001
which had encouraged tapping and increased both tree and land productivity (MRB,
2009).
Meanwhile, consumption of natural rubber had shown significant increment indicating
an expanding rubber downstream sector. Domestic consumption of Malaysian NR
recorded an increase of 14% from 2004 (403 thousand MT) to 2008 (469 thousand
MT; i.e. 6.6% of world NR consumption) (Table 2). The increase
was particularly significant in the latex products manufacturing industries,
which accounted for 95% of total domestic consumption of NR in 2008. Similarly,
consumption of synthetic rubber had also increased from 84 thousand MT in 2004
to 139 thousand MT (i.e. 1.4% of world synthetic rubber consumption) in 2008
(Table 2). Moreover, the ratio of natural to synthetic rubber
consumption as at end 2008 was 77.1:22.9, reflecting the demand for natural
rubber especially by the latex products manufacturing industries. This scenario
indicates that the current total supply of natural rubber is sufficient for
domestic consumption with surplus for export (MRB, 2009).
Like any other agricultural commodities, natural rubber was subjected to significant
price fluctuations (Fig. 1). The years 1997 to 1999 and as
well as in the year 2000 were turbulent years for the economies in SouthEast
and East Asia (Fig. 2).

Fig. 1: 
SMR20 price (Standard Malaysia Rubber Grade 20) in Malaysia
and RSS1 price (Ribbed Smoke Sheet Rubber Grade 1) in New York in January
1990 to December 2008 in the world NR market, Source: IRSG
(2009) 

Fig. 2: 
Crude Petroleum Oil (COP), natural rubber (SMR 20) and synthetic
rubber prices in January 1990 to December 2008. Source: IRSG
(2009) 
In 2008, the extremely low prices due to the outbreak of the global recession.
It experienced during these years contributed to price volatility and instability
in many countries, especially rubber smallholders in South East Asia (ANRPC,
2009).
Variations in a series can arise from long term trends, short term fluctuations
(instability) or both together. Uncertainty in a market generally originates
from shortterm fluctuations rather than long term trends. Therefore, a meaningful
measure of instability is one representing shortterm fluctuations alone. A
limitation in measuring instability (i.e., market uncertainty) by using Coefficient
of Variation (CV) (price variability) is that it gives the total variation arising
from both longterm trends and shortterm fluctuations. Economists prefer measuring
instability by using the instability index (Ix) which gives a measure of variability
arising from short term fluctuations after eliminating effect of long term fluctuations.
Table 3 gives CVs and calculated instability indices (Ix)
of major traded forms of NR prices in the world market. It reveals a much higher
degree of market uncertainty in 2008 compared to 2007 and 2009.
Table 3: 
Price total variability and instability index of 2007 to
2009 

Source: NR market review of ANRPC, 2010a,b.
I_{x} = CV (1R^{2}),
where R^{2} is the explanatory power of the best fitting trend curve.
If longterm trend is insignificant for a series, R^{2} would be
zero and I_{x} would be equal to CV 
Moreover, if in terms of price variability (CV) and price instability Index
(I_{x}) examined, it had been much higher in 2008 as compared with 2007
and 2009 in all NR prices. Among various NR markets, the highest degree of uncertainty
was for RSS4 in Kottayam (ANRPC, 2010a,b).
The fundamentals influencing NR prices are demand and supply factors, while all other factors have indirect effects through changes in the fundamentals of demand and supply. For example, an improvement in the world economy leads to an increase in rubber demand. A fall in the price of natural rubber relates to synthetic rubber. Moreover, the crude petroleum oil price is an important component of synthetic rubber. A fall in the crude petroleum oil price also relates to synthetic rubber. It influences a declining share of synthetic rubber in total rubber consumption.
Currency exchange rate also affects in the NR producing countries because most commodities are traded in US dollar. It encourages an increase in exports and concomitant output from these producing countries and hence a rise in world natural rubber supply. If the price is expected to have negative relationship with the exchange rate for Malaysia RM per USD (RM/USD), indicating that more Malaysia RM would be paid for 1 USD, then the NR price would be decreased as experienced during the forecasting period. Natural rubber price rose from USD 2314.51 per MT in June 2007 rising to USD 3457.58/MT in June 2008 whilst RM per USD decreased from 3.38 to 3.22 over the same period. Therefore, world NR supply and demand situation, world NR stocks, trend of crude petroleum oil price and currency exchange rate values in NR exporting countries are the various factors generally should be considered as influencing NR price movements in current Malaysia NR industry and for the modeling process to develop the monthly shortterm price forecasting model of natural rubber in this study. Uncertain weather, including haze, has also affected production. Moreover, the objectives of the study are to determine the interrelationships between NR production, consumption and prices, to forecast the price of NR (SMR20) and to determine which model is more efficient in their price forecasting accuracy.
MATERIALS AND METHODS
The study presents shortterm ex post forecasts of econometric models and univariate
model of autoregressiveintegratedmoving average (ARIMA) model of Natural Rubber
(NR) prices SMR20 (Standard Malaysia Rubber Grade 20) in the Malaysia market.
The econometric models include single equation model using Vector Error Correction
Method, (VECM) (Gilbert, 1986; Hendry
and Ericsson, 2001) and multivariate autoregressivemoving average (MARMA)
model. They were developed to determine the interrelationships between NR production,
consumption and prices, to forecast the price of NR (SMR20) and also to determine
which model is more efficient in terms of their comparative price forecasting
accuracy. The study was conducted in 2009 using secondary data from Jan. 1990
to Dec. 2008.
The earlier studies examined and reviewed the supply, demand and price relationship
based on models developed by Shepherd (1963), Meyanathan
(1983), Tan (1984), Arshad and
Zainalabidin (1994), Barlow et al. (1994),
Goodwin (1994), Shamsudin and Arshad
(1998), Ferris (1998), Burger and
Smit (1997, 2000) and Enders (2004).
Model specification
Singleequation econometric models of nr supply, demand and price
NR supply forecasting model: A monthly shortterm model of the Malaysia
natural rubber market is formulated comprising of three behavioral singleequations
and identified the supply of natural rubber (TPNR) as a function of related
factors (in logs) as follow:
Where:
TPNR 
= 
Total production of natural rubber (Total Supply) (000 metric
tonnes) (MT) 
PSMR20 
= 
Real monthly price of SMR20 in Malaysia (USD/MT) deflated by the CPI 
T 
= 
Time trend, Jan. 1990 to Dec. 2008 
t and e_{i} 
= 
Time period and error terms, respectively 
NR demand forecasting model: The demand of natural rubber (TCNR) as
a function of related factors (in logs) can be specified as follow:
Where:
TCNR 
= 
Total consumption of natural rubber and synthetic rubber (Total
Demand) (000 MT) 
PSMR20 
= 
Real monthly price of SMR20 in Malaysia (USD /MT) deflated by the CPI 
RSS1 
= 
Real monthly price of RSS1 in New York (USD /MT) deflated by the CPI 
T 
= 
Time trend, Jan. 1990 to Dec. 2008 
t and e_{i} 
= 
Time period and error terms, respectively 
NR price forecasting model: The NR price (PSMR20) equation, which was
derived based on related factors (in logs) can be stated as follows:
Where:
PSMR20 
= 
Real monthly price of SMR20 in Malaysia (USD/MT) deflated
by the CPI 
TPNR 
= 
Total production of natural rubber (Total Supply) (000MT) 
TCNR 
= 
Total consumption of natural rubber and synthetic rubber (Total Demand)
(000 MT) 
STONR 
= 
Total stock of natural rubber (000 MT) 
COP 
= 
Crude petroleum oil monthly price (USD/barrel) 
EXM 
= 
Real monthly average exchange rate (Malaysia Ringgit (RM) per USD) (RM/USD) 
T 
= 
Time trend, Jan. 1990 to Dec. 2008 
t and e_{i} 
= 
Time period and error terms 
Model estimation
Vector Error Correction Method (VECM):A vector error correction method (VECM
model) is a restricted vector autoregression (VAR) designed for use with nonstationary
series that are known to be cointegrated (Gilbert, 1986;
Hendry and Ericsson, 2001). The VECM model has cointegration
equation built into the specification so that it restricts the longterm behavior
of the endogenous variables to converge to their cointegrating relationship
while allowing for shortterm adjustment dynamics. The cointegration equation
is known as the error correction method (ECM model) since the deviation from
longterm equilibrium is corrected gradually through a series of partial shortterm
adjustments (Engle and Granger, 1991).
The corresponding VECM model is:
where, α_{i} is a vector of intercept terms, β_{i} is the coefficient matrices and ε_{i} is the disturbance terms. Therefore, the VECM model is included a vector of intercept terms (α_{i}) and the disturbance terms (ε_{i}).
In the error correction method (ECM model) (cointegration equation), the only righthand side variable is the error correction term. In longterm equilibrium, this term is zero. Therefore, ECM models have without a vector of intercept terms (α_{i}) and the disturbance terms (ε_{i}). However, if and deviate from the longterm equilibrium, the error correction model will be nonzero and each variable adjusted to partially restore the equilibrium relation. The coefficient α_{i} measures the speed of adjustment of the ith endogenous variable towards the equilibrium.
For this study, the VECM model for NR supply is:
The VECM model for NR demand is:
The VECM model for NR price is:
The VECM models for NR supply, demand and price have described in detail and, however, the VECM model for NR price will be only carried out for in this study.
MARMA model: The multivariate autoregressivemovingaverage (MARMA)
model is well documented in (Makridakis et al., 1998;
Pindyck and Rubinfeld, 1998). A brief description of the
model is discussed below. The multivariate autoregressivemoving average (MARMA)
model was developed to forecast shortrun monthly prices of SMR20 in the Malaysia
market. The model will also be used to generate ex post forecasts for the period
of January 2007 to December 2008 based on data from period January 1990 to December
2008.
Model specification: Suppose that one would like to forecast a variable PSMR20_{t} using an econometric model. Presumably such a model would include explanatory variables which could provide an explanation for movements in PSMR20_{t} but which are not collinear. One effective application of timeseries analysis is to construct an ARIMA model for the residual series ε_{t} of this regression. Then, the ARIMA model for the implicit error term was substituted in the original regression equation. In using the equation to forecast PSMR20_{t}, it is able to make a forecast of the error term ε_{t} using the ARIMA model. The ARIMA model provides some information about what futures of ε_{t} are likely to be the unexplained variance in the regression equation. The combined regressiontime series model is:
where, Δ_{t} is a normally distributed error term which may have
a different variance from residual error ε_{t}. The parameters
α_{0}, α_{1}, α_{2} and ….. of the
structural regression equation and the parameters φ_{1}, …,
φ_{p} and θ_{1},...., θ_{q }of the timeseries
model should be estimated. Then,
PSMR20 
= 
Real monthly price of SMR20 in Malaysia (USD/MT) deflated
by the CPI. 
TPNR 
= 
Total production of natural rubber (Total Supply) (000 metric tonnes)
(MT) 
TCNR 
= 
Total consumption of natural rubber and synthetic rubber (Total Demand)
(000 MT) 
STONR 
= 
Total stock of natural rubber (000 MT) 
COP 
= 
Crude oil monthly price (USD/barrel) 
EXM 
= 
Real monthly average exchange rate (Malaysia Ringgit (RM) per USD) (RM/USD) 
AR(1)(φ_{1}) 
= 
AR parameter of order 1 (The φ_{1} PSMR20_{t1} represented
the fit to the series value PSMR20_{t},) 
MA(1)(θ_{1}) 
= 
MA parameter of order 1 (The term θ_{1} ε_{t1}
and ε_{t} represented the assumed random error in the data
at period t1 and period t) 
T 
= 
Time trend, 1990 Jan: to 2008 Dec: 
t and e_{i} 
= 
Time period and error terms respectively 
Equation 9 is referred to as a transfer function model or,
alternatively, a multivariate autoregressivemovingaverage (MARMA) model. The
MARMA model with the residual correction methods such as ARCH (LM) (Autoregressive
Conditional Heteroskedasticity) test will be developed to forecast shortterm
monthly natural rubber prices in the Malaysia market. This combined use of regression
analysis with a timeseries model of the error term is an approach to forecasting
that in some cases can provide the best of both worlds.
ARIMA model: The autoregressiveintegratedmoving average (ARIMA) model
is discussed in detail in Box et al. (1994), Hoff
(1983), O ’Donovan (1983) and Cheung
et al. (1998). Briefly, this technique is a univariate approach,
which is built on the premise that knowledge of past values of a time series
is sufficient to make forecasts of the variable in question. There are two types
of basic BoxJenkins models: autoregressive (AR) models and movingaverage (MA)
models. In terms of the original series such models are called integrated models
and the AR and MA models may also be combined to form by Auto Regressive, Integrated,
MovingAverage (ARIMA) models.
Model specification: The shortterm price forecasting models based on the BoxJeckins procedure, univariate timeseries model of the autoregressiveintegrated moving average ARIMA (p,d,q) can be specified follows:
where, PSMR20_{t} = Real monthly price of SMR20 in Malaysia (USD/MT) deflated by the CPI and C = intercept terms and ε_{t} = the disturbance terms.
PSMR20_{t} is related to both past series values and past random errors and it was the stationary series. The ARIMA model of order ARIMA (1,1,1) was found to be the most appropriate model and generate the best forecast with minimum error. The numbers inside the parentheses of ARIMA (1,1,1) model of order (p,d,q) refer to the order of the autoregressive process, the degree of differencing required to induce stationary and the order of the moving average process, respectively. It meant that to find out what the autocorrelation and partial autocorrelation pattern was for the series the monthly prices of PSMR20_{t}, we needed to determine the relationship between PSMR20_{t} and PSMR20_{t1} for all t. Thus, PSMR20_{t} was autocorrelated for lag 1; i.e., the autocorrelation for lag 1 was nonzero. Otherwise, the autocorrelation for any lag greater than 1 was zero.
In Eq. 8, ε_{t} is a random disturbance assumed to be distributed as N (0, σ^{2}). The φ_{i} s are called autoregressive (AR) parameters and θ_{i} s are also called movingaverage (MA) parameters. The subscripts on the φ ’s and θ ’s are called the orders of the parameters. In an AR model p is the order of the model and in an MA model q is the order of the model. The order of an ARMA model is expressed in terms of both p and q.
The stationary conditions for this model are:
The φ_{1}PSMR20_{t1} represented the fit to the series
value PSMR20_{t} and φ_{1} was also called an AR parameter
of order 1. The term θ_{1} ε_{t1} and ε_{t}
represented the assumed random error in the data at period t1 and period t
and θ_{1} was also called a MA parameter of order 1. The parameter
diagnostics showed that any given value in price of PSMR20_{t} was directly
proportional to the previous value PSMR20_{t1} plus some random error
ε_{t} and ε_{t1}. That was, what happens this period
was only dependent on what happened last period, plus some current random error.
The term (θ_{1} ε_{t1}) was the use of the minus
sign in front of θ_{1} was conventional only and had no other significance.
The ARIMA model with the residual correction methods such as ARCH (LM) (Autoregressive Conditional Heteroskedasticity) test will also be developed to forecast shortterm monthly natural rubber prices in the Malaysia market. The model will also be used to generate ex post forecasts for the period of January 2007 to December 2008 based on data from period January 1990 to December 2008.
Model simulation: The comparison of the forecast accuracy of the selected natural rubber price forecasting models of the single equation model, MARMA model and ARIMA model were evaluated and generated. Firstly, the data used from January 1990 to December 2006 for estimation, with observations from January 2007 to June 2007 simulated for ex post forecast. It means that the data was in beyond the time period used to estimate the price SMR20 in the next 6 months or so. Similarly, the data was simulated forward in time beyond the estimation period from January 1990 to June 2007 and reserved for ex post forecast with observations from July 2007 to December 2007. The data was subsequently employed for ex post forecast from January 2008 to June 2008 and ex post forecast from July 2008 to December 2008. Only data up from January 1990 to December 2008 was generated for simulation of ex post forecasts.
Model evaluation: Performance of the model is measured by the validity of its estimate on the basis of its forecasting power. The forecasting ability is tested based on the Root Mean Squared Error (RMSE), the Mean Absolute Error (MAE), the Root Mean Percent Error (RMPE) and Theil ’s inequality coefficients (U) criteria. In the historical or ex post simulation, the RMSE of all the endogenous variables are less than one percent and the values of MAE are all small. The values of the Theil ’s inequality coefficient U are all nearly zero which is that the forecasting performance of the estimated model is satisfactory. The MAE and the RMSE can be used together to diagnose the variation in the errors in a set of forecasts. The RMSE will always be larger or equal to the MAE; the greater the difference between them, the greater the variance in the individual errors in the sample. If the RMSE = MAE, then all the errors are of the same magnitude. Both the MAE and RMSE can range from 0 to ∞. They are negativelyoriented scores and lower values are better.
RESULTS
Single equation NR price econometric model: Table 4 shows that single equation of shortterm monthly natural rubber price econometric model with the forecast error reduced methods using Vector Error Correction Method (VECM) with cointegration characteristics and the explanatory variables which accounted for about only 39% of the variation in the monthly natural rubber price. In the cointegration equation of price (PSMR20) forecasting econometric model, the results indicated that the price of natural rubber (PSMR20) is highly and positively dependent on Total Production of Natural Rubber (TPNR).
The results also indicated that the price of natural rubber (PSMR20) is highly and negatively dependent on Total Consumption of Natural Rubber (TCNR). The cointegration approach was used directly to test longterm variables and indirectly to know imbalance in shortterm by using parameter estimate from longterm relationship variables. Estimations reveal that the explanatory variables, namely Total Production of Natural Rubber (TPNR) and the total consumption of natural rubber and synthetic rubber (TCNR), were the most important explanatory variables in the cointegration equation of price (PSMR20) forecasting econometric model with significance at 0.01 level.
Table 4: 
Results of single equation of NR price econometric model
to determine structural equation 

Source: Own Data calculations, Standard errors in ( ) and
tstatistics in [ ]. Note: ***Statistically significant at the 0.01 level,
**at the 0.05 level and *at the 0.10 level 
Therefore, a 1% increase in price of SMR20 in Malaysia (USD/MT), other things
unchanged, increases Total Production of Natural Rubber (TPNR) by 0.16% with
statistically significance at the 0.01 level. Moreover, a 1% increase in price
of SMR20 in Malaysia (USD/MT), on average, has the adverse effect of decreasing
the total consumption of natural rubber and synthetic rubber (TCNR) by 0.71%
with statistically significance at the 0.01 level. Therefore, they are cointegrated
between the Total Production of Natural Rubber (TPNR), total consumption of
natural rubber and synthetic rubber (TCNR) and price of SMR20 in the single
equation of price econometric forecasting model.
Significantly, in the results of the single equation of price forecasting model with the forecast error reduced methods using Vector Error Correction Method (VECM) with cointegration characteristics, estimations revealed that the explanatory variables, namely, the price of SMR20 in the price (PSMR20) equation, total consumption of natural rubber and synthetic rubber (TCNR) in the supply (TPNR) equation and Total Production of Natural Rubber (TPNR) in the demand (TCNR) equation, were the most important explanatory variables with statistically significance at the 0.01 level, respectively.
MARMA model: In the MARMA model price equation, the explanatory variables and AR and MA parameters also explains about 76% of the variation in the monthly natural rubber price model in Table 5. It also shows the results of the ex post forecast of MARMA model of the shortterm monthly prices of PSMR20. The term AR (1) (φ_{1}) (φ_{1}PSMR20_{t1}) (φ_{1} is an AR parameter of order 1) represents the fit to the series value PSMR20_{t} and the coefficient value is 0.607. The term MA(1) (θ_{1}) (θ_{1} ε_{ t1}) (θ_{1} is a MA parameter of order 1) and ε_{ t1} represents the assumed random error in the data at period t1 and ε_{t} represented at period t and the coefficient value is 0.318 and 0.042. The parameter diagnostics of MARMA model shows that any given value in price of PSMR20_{t} was directly proportional to the previous value PSMR20_{t1} plus some random error ε_{t} and ε_{t1} significant that the model have included the correct parameters. The residual diagnostics shows that residuals are significance at the 0.01 level that the model has included the correct parameters.
Furthermore, a 1% increase in price of SMR20 in Malaysia (USD/MT), other things unchanged, increases total production of natural rubber (TPNR) by 0.49% with statistically significance at the 0.01 level. Moreover, a 1% increase in price of SMR20 in Malaysia (USD/MT), on average, has the adverse effect of decreasing the total consumption of NR and SR (TCNR) by 0.79% with statistically significance at the 0.01 level. Besides, a 1% increase in price of SMR20 in Malaysia (USD/MT), on average, has the adverse effect of decreasing the world total stock of natural rubber (STONR) by 0.45% with statistically significance at the 0.01 level.
The result of the model indicated that there is an inverse relationship between the price of natural rubber (SMR20) and world total stock of NR (STONR). It was indicating that prices may tend to peak while the stock was low level during the forecasting period. The slope coefficient of exchange rate measures the proportional change in price of PSMR20 for a given proportional change in exchange rate. Results indicated that the price of natural rubber (PSMR20) is highly and negatively dependent on the exchange rate for Malaysia RM per USD (RM/USD). It indicates that more Malaysia RM would be paid for 1 USD when the NR price would be low again as experienced during the forecasting period.
Besides, the results indicated that the price of natural rubber (PSMR20) is
highly and positively dependent on Crude Oil Price (COP). Therefore, a 1% increase
in crude oil price (USD/barrel), on average and other things unchanged, increases
the price of PSMR20 by 0.43%. Shane (2007) mentioned
that the outlook for sustained high prices of crude oil and petroleum price
has changed the basic environment for global agriculture in a fundamental way.
The price of crude oil had been on an upward move again, rising from its lowest
level in over five years of USD 40 per barrel in December 2008 and also compared
with the lowest level of natural rubber price (SMR20) of USD 1376.57 per MT
in December 2008 (IRSG, 2009).
Table 5: 
Results of MARMA model to determine structural equation 

Source: Own Data Calculations, Standard errors in ( ) and
tstatistics in [ ]. Note: *** Statistically significant at the 0.01 level,
** at the 0.05 level and * at the 0.10 level 
ARIMA model: Table 6 shows that the results of the
ARIMA model of the ex post forecast of shortterm monthly prices of SMR20. Briefly,
the model was a univariate approach which was built on the premise that knowledge
of past values of a time series was sufficient to make forecasts of the variable
in the equation. The term φ_{1}PSMR20_{t1} (φ_{1}
is an AR parameter of order 1) represents the fit to the series value PSMR20_{t}
and the coefficient value is 0.591. The term θ_{1} ε_{t1}
(θ_{1} is a MA parameter of order 1) and ε_{ t1}
represented the assumed random error in the data at period t1 and ε_{t}
represented at period t and the coefficient value is 0.431 and 0.036.
The parameter diagnostics shows that any given value in price of PSMR20_{t}
was directly proportional to the previous value PSMR20_{t1} plus some
random error ε_{t} and ε_{t1}. Meaning that, what
happens this period was only dependent on what happened last period, plus some
current random error.
Table 6: 
Results of AIRMA model to determine structural equation 

Source: Own Data Calculations, Standard errors in ( ) and
tstatistics in [ ]. Note: *** Statistically significant at the 0.01 level,
** at the 0.05 level and * at the 0.10 level 
The term (θ_{1} ε_{ t1}) with the minus sign in
front of θ_{1} was conventional only and had no other significance.
In BoxJenkins models, the random error component plays a dominant role in determining
the structure of the model. The residual diagnostics (ARCH LM test) shows that
residuals are significance at the 0.01 level that the model has included the
correct parameters. Residual diagnostics and parameter diagnostics comprised
the tools available for determining whether a selected model was valid. In the
ARIMA model price equation, the AR and MA parameters explains about 57% of the
variation in the monthly natural rubber price.
DISCUSSION
The results showed that of the explanatory variables identified, total production
of natural rubber (total supply) (000 MT) (TPNR_{t}),total consumption
of natural rubber and synthetic rubber (total demand) (000 MT) (TCNR_{t}),
world total stock of natural rubber (000 MT) (STONR_{t}), crude oil
monthly price (USD/barrel) (COP_{t}), real monthly average exchange
rate (Malaysia Ringgit (RM) per USD) (RM/USD) (EXM_{t}), (φ_{1})
(is an AR parameter of order 1) represents the fit to the series value PSMR20_{t}
(real monthly price of SMR20 in Malaysia (USD/MT) deflated by the CPI) and (θ_{1})
(is a MA parameter of order 1), were the most important explanatory variables
in the NR price forecasting models. The results of the comparison of the forecast
accuracy of the ex post forecast of natural rubber (SMR20) monthly price (US$
per MT) using single equation model, MARMA model and ARIMA model are presented
in Table 7. The forecasting power was compared based on the
RMSE, MAE, RMPE and Theil ’s inequality coefficients (U) criteria. The
values of the RMSE, MAE, RMPE and U of MARMA model were comparatively smaller
than the values generated by single equation and ARIMA models.
Table 7: 
Model Evaluation of Ex post forecast of monthly natural rubber
price SMR20 (USD per MT) of single equation, MARMA and ARIMA models from
July 2008 to December 2008 

Source: Own Data Calculations 
These statistics suggested that the forecasting performance of the MARMA model
was more efficient than single equation and ARIMA models.
World NR prices were used to forecast by using econometric model of the world
natural and synthetic rubbers market (Tan, 1984). The
study was concerned with the specification, estimation and validation of an
econometric model of the world natural and synthetic rubber market. The study
was also concerned the application of the model to forecast natural rubber price
and to analyse the implications of natural rubber price stabilisation along
the lines of the International Natural Rubber Agreement. The results showed
that of the explanatory variables identified, stock of NR in consuming countries
('000 tons) (SCC_{t}), consumption (demand) of NR ('000 tons) (CON_{t})
and price of NR (PNR_{t}) (for the study, SMR20 spot price in sen/kg)
in the previous two periods, were the most important explanatory variables in
the NR price forecasting model.
Barlow et al. (1994) presented a broad economic
framework and the overall rubber industry where the supply of rubber was determined
by the expected price in the market place, together with its production capacity,
input costs and underlying technological progress. It then interacted in a dynamic
and recursive manner with demand. Demand was set by the expected rubber price
as well as by the income level in the overall economy, prices of rubber substitutes
and prices of final goods, technology, consumer preferences, stocks and manufacturing
capacity utilisation. They also explained that the organisational structure
of production, marketing and consumption and government measures towards rubber
were also important but they entered the rubber framework through the mentioned
supply and demand factors.
Multiple forecasts for autoregressiveintegrated movingaverage (ARIMA) models
are useful in many areas such as economics and business forecasting. Shamsudin
and Arshad (1998) provided some short term ex ante forecasts of Malaysian
crude palm oil prices. The forecasts were derived from a multivariate autoregressivemoving
average (MARMA) model which integrates the normal autoregressive integrated
moving average (ARIMA) model for the residuals into an econometric equation
estimated beforehand. They also found that the MARMA model produced a relatively
more efficient forecast than the econometric model. The forecast figures were
discussed in relation to the current and expected fundamentals of the palm oil
market.
Armstrong and Collopy (1998) argued for offers the characteristics
of forecasting methods and their relationships. Forecasting involved methods
that were derived from judgmental sources and from statistical sources. There
was an increasing amount of integration between judgmental and statistical data
and procedures. This integration, which had been studied by researchers in the
last decade, can improve forecast accuracy.
Burger and Smit (2000) also studied the longterm and
shortterm analysis of the natural rubber market. The essential elements of
NR longterm supply model are: planted area, new planting, replanting and uprooting,
the age of the area and the yield profiles, technical progress, other factors
influencing normal production and prices. The variables used for demand model
are the NR share in total world rubber consumption, the ratio of the Singapore
RSS1 price of NR (in US$) and the US export unit value of SBR (StyreneButadiene
Rubber) (in US$) and also the shortterm price model included world natural
rubber average production, world total rubber consumption, exchange rate, private
world stocks, RSS1 price in Singapore (US$/tonne) and a dummy (taking in time
trend). It included the economies of key players in the natural rubber market
both on the demand side, on the supply side and price fluctuations.
The Asian crisis provided strong evidence on how exchange rates affected natural
rubber price of SMR20 (USD) in the world market (Burger et
al., 2002). From this paper, it provided a theoretical basis for establishing
a link between the exchange rates and the NR price for shortterm natural rubber
price forecasting in the paper.
Lim (2002) estimated the shortterm NR prices and evaluated
the relative performance of 19 models based upon three different forecasting
techniques and four information sets. The modified autoregressive moving average
models were generally better than the simple regression models and the results
can potentially be beneficial to participants in the NR futures market.
Hossain et al. (2006) developed and used ARIMA
model of order (3,1,3)x(2,0,2)12 was selected as the best model for both motor
and mash prices and the model (3,1,2)x(3,0,2)12 was selected as the best model
for mung prices in Bangladesh for policy purposes as far as price forecasts
of the commodities were concerned. He also generated forecasts, namely, historical,
ex post and exante, using the familiar BoxJenkins univariate time series models.
The models on the basis of which these forecasts have been computed were selected
by important information criteria such as Root Mean Squared Percent Errors (RMSPE),
Mean Percent Forecast Errors (MPFE) and Theil's inequality coefficients (U).
The smaller these values, the better are the forecasting performance of the
model.
The generated price forecasts from January 2008 to December 2008 generated from single equation, MARMA and ARIMA models are presented in Table 7. The results of the ex post Natural Rubber (SMR20) monthly price forecast (US$ per MT) using MARMA model is estimated to decrease to around US$ 1269.45 per MT in December 2008, a decrease of 65% from July 2008 at US$ 3530.96 per MT.
CONCLUSION
Based on the results of the above analysis, MARMA ’s ex post forecasts were more efficient measured either in terms of its statistical criteria or even by visual proximity with the actual prices. For many years now, MRB (Malaysia Rubber Board) and IRSG (International Rubber Study Group) have forecasted the price of natural rubber which will be beneficial for the industry in their future economic planning.
A forecast of a high price may lead policy makers to alter their budgetary plans to invest for new decisions in the natural rubber market. The result of the study indicates that NR ex post forecast price of SMR20 shows a decreasing trend. This could be due to global financial crisis during the forecasting periods. The global financial crisis and its concomitant shrinking in demand of virtually on all commodities have resulted in perhaps a widespread global recession. It would be interesting to investigate factors and new parameters that influence the reduction in demand for rubber. The factors could be due in part to the global vehicle sales contraction because of lower purchasing power and delayed buying decisions, the appropriate supply responses by the tripartite NR producing countries. and to determine what the new price forecast of NR would be in the interim world market.
Significantly, shortterm ex post forecast of NR price forecasting models developed in this paper, could provide a useful test of the validity of the model and also beneficial to producers and consumers as well as traders and planners for policy analysis in the world NR market. Furthermore, this conceptual economic framework was a good starting point for discussion and perceptive of shortterm ex post forecast of NR price forecasting models developed, with the opportunity of using some of these factors later in the other study for forecasting of rubber prices. Forecasts using other alternative models such as simultaneous supplydemand and price model, ARCH (Autoregressive Conditional Heteroscedasticity), GARCH (Generalized ARCH) and EGARCH (Log Generalized ARCH), not attempted for this study, could also be potentially beneficial for future work.
ACKNOWLEDGMENTS
The authors would like to thanks University Putra Malaysia (UPM) for supporting this project under the Research University Grant (RUG) funding.