CRUDE OIL PRICE FORECASTING WITH ANFIS
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Crude oil pricing is commonly expressed as a formula referenced to Brent or WTI crude oil.
The final price of these two qualities and the spread between WTI and Brent can drive the decision
when the purchase of a crude oil cargo is evaluated. A crude oil price-forecasting model is
presented. It is based on past data, inventory level and volatility index and it is derived with a
neuro fuzzy inference system. The fuzzy model allows the visualization and analysis of the set of
rules that govern the prediction. Results are compared with the prediction based on an econometric
Generally, crude oil is priced in the period around the process of crude oil loading . This
situation could take place two monthes after the evaluation of the crude purchasing. In some
cases the decision can be correct or not depending on how different are these final prices with
respect to the initial guess. In other cases the decision depends on the spread WTI – Brent,
more predictable than the crude oil benchmarks.
It is important to estimate the value of these two price references because they define the
final cost of the cargo. The WTI and Brent benchmarks are published daily by the Platts
services  .
This work refers specifically to the following two benchmarks: first line WTI (West Texas
Intermediate) crude oil spot price and Brent DTD (Brent Dated) crude oil spot price.
THE PROBLEM. THE MODEL
The problem under consideration is the prediction of the value of two benchmarks in the
next period, based on information available for a previous period. Changes in the value of the
benchmarks with time comes as the result of a set of events. The set of events, can be
associated with input variables in a model. The model must be simplified because it is not
possible to follow all the variables involved in the real problem. The model will take into
account only the variables with major impact in the prediction.
The notation assumes the suffix +1 for a variable in the next period, a 0 for the present
period and the suffix –1 for the previous period.
Based on daily data available for the period 1991-2003, a fifteeen days average was
calculated for each benchmark This was the result of a compromise between the error of the
approach and the number of parameters required. In the rest of the text, WTI and Brent refer
to their averages.
The first variable to consider is the period (1-24). This variable can be correlated with a
IMPLEMENTATION AND RESULTS
The problem was implemented in Matlab  . The Cross Validation technique showed
that the number of points in the data series was enough for the training process. Before the
training process, all data was normalized. Cross validation was applied in order to improve
the forecast of the network The data set was divided at random into two subsets, one for
training and another for testing, in a relation of 2 to 1. Subtractive Clustering provided a
reduction in the number of rules .
Regarding the detection of outliers in the Brent and WTI series, three tests were applied,
each of them based on an interval of acceptance: a range of three standard deviations from
the mean or similar expressions. In addition, the Grub test (extreme studentized deviate) did
not detect outliers in the series .
Different combinations of variables were tested on a trial an error basis and the MSE
results were compared. The variables Period(0), Period(+1), Brent(-2) did not contribute
substantially to the reduction of the training error and were rejected. IR(+1) seemed to be
marginally more appropiate than IR(0). R(+1) contributed significantly.
A crude oil price forecasting model has been presented for crudes Brent and WTI. It is
based on a neuro-fuzzy inference system. A model for the spread WTI-Brent has been
obtained based on a similar approach. Four input variables were considered: R(+1), Brent(0),
IR(+1) and Brent(-1). The model takes into account the effect of the inventory level, past and
present values of the price benchmarks and the volatility of the market.
Variables R and IR are discontinuous in order to represent the lack of information during
the forecast. The model ANFIS-WTI has shown a better approach than the model showed in
reference , at least for the period 1992-2000.
The model ANFIS-Diff shows the lower error distribution and corresponds with the
expected evolution of the time series.
These models can be usefull for sensitivity analysis.
In a next step, the model will be extended to consider the period 2004-2007.