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Back when Hugo Chavez was still alive (former leader of Venezuela), he said they made "simulations" to predict how much oil prices will increase if they retire the supply of oil they were giving to the world, and that in that time that would cause trouble to US. That made me wonder how oil price could be predicted, since I had classes of computer simulation of different type of systems in the University and I can't even imagine how could it be done to predict oil prices. If I recall correctly, I was also told by a neuronal network professor that a researcher worked in predicting oil prices for years with neuronal networks, and the work became useless when a war triggered oil prices in a completely unexpected way. Knowing how hard making accurate predictions of oil prices could be, is there still an oversimplificated equation or something to predict oil prices in the market?

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The most comprehensive survey of estimating oil prices is here. There you fund from very complicated models to very simple ones. As the article shows, the ultimate answer depends on whether you are estimating nominal or real price, and short-term or long-term prices.

Some simple models to estimate price of oil might be:

  • no-change forecast: if changes in the spot price are unpredictable, the best forecast of the spot price of crude oil is simply the current spot price ($S_t$):

$$ \hat{S}_{t+h|t} = S_t \quad h>0$$

  • futures-based forecast: simply take the market's average expected oil price forecast as your forecast:

$$ \hat{S}_{t+h|t} = F^h_t \quad h>0$$

where $F^h_t$ is the future forecast in the market. There are plenty of sources available online (e.g. here or here).

  • Double-difference forecasting: proposed by Hendry (2006), it assumes past growth rates for future price changes:

$$ \hat{S}_{t+h|t} = S_t \left(1+ \Delta s_t \right)^h \quad h>0 $$

where $\Delta s_t$ is the percent growth rate of $S_t$ between $t-1$ and $t$

  • inflation-based forecast: use forecasts for inflation to predict oil prices (which according to Anderson et. al. 2011, this is how households predict gasoline prices):

$$ \hat{S}_{t+h|t} = S_t \left(1+ \pi^e_{t,h} \right)^h \quad h>0 $$

where $\pi^e_{t,h}$ is the forecast of inflation, for example, from the Survey of Professional Forecasters.

  • AR, ARMA, ARIMA regression models: last but not least, the famous AR-based models are very common. Simply regress the price of oil on its past values, using as many lags as you want (or the information criterion tells you), accounting for MA errors (ARMA) and possible cointegration (ARIMA). For example, the AR model with $p$ lags is:

$$ S_{t} = \beta_0 + \beta_1 S_{t-1} + \cdots + \beta_p S_{t-p} + \mu_t $$

After you have estimated the model and obtained values for $\beta_i$, you can forecast oil prices by simply lagging the last $p$ observations one period and put into the model, from where you get $\hat{S}_{t+1|t}$ (assuming $\mu_{t+1} =0$). Then, iterate forward to get forecast for any other future period.

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