**Prepared by:**

**Team Data Insighters**

Balacoumarane Vetrivel – A0178301L

Mohammed Ismail Khan – A0178366N

Meghna Vinay Amin – A0178307Y

Sreekar Bethu – A0178220L

Vaishnavi Renganathan – A0178229U

# Introduction

With each passing year, oil seems to play an even greater role in the world-wide process of people making, selling, and buying things. In the early days, finding oil during a drill was carefully thought believed somewhat of an annoyance as the meant treasures were usually in a common and regular way water or salt. It wasn’t until 1857 that the first commercial oil well was drilled in Romania. The U.S. petroleum industry was born two years later with a drilling in Titusville, Pa.

Oil has replaced coal as the world’s primary fuel source. Oil’s use in fuels continues to be the primary factor in making it a high-demand commodity around the globe.

**The Determinants of Oil Prices:**

With oil’s stature as a high-demand global commodity comes the possibility that major fluctuations in price can have a significant economic impact. The two primary factors that impact the price of oil are:

- Supply and demand
- Market sentiment

**Supply and demand:**

The price of oil as known is actually set in the oil futures market. An oil futures contract is a binding agreement that gives one the right to purchase oil by the barrel at a predefined price on a predefined date in the future. Under a futures contract, both the buyer and the seller are obligated to fulfil their side of the transaction on the specified date.

**Market sentiment:**

The mere belief that oil demand will increase dramatically at some point in the future can result in a dramatic increase in oil prices in the present as speculators and hedgers alike snap up oil futures contracts. The opposite is also true that means prices can hinge on little more than market psychology at times.

**Other variables:**

- News on new supply
- Changes in consumer habits
- Terrorist attacks and disturbance
- Alternative energy sources
- Economic growth

# Crude oil production in US

For seven straight years, the US has pumped more oil and gas out of the ground than any other country and this lead will only widen. Production of crude topped 10.7 million barrels per day with production of natural gas hitting 4 million barrels per day. The surge in U.S. output is due in large part to the wide use of horizontal hydraulic fracturing, or fracking, as new technologies give drillers access to some of the largest oil deposits in the world that were once too tight to exploit.

# Data source and Understanding

**Data source:**

The data is obtained from the link

https://data.oecd.org/energy/crude-oil-production.htm#indicator-chart

**3.1 Crude oil production (input series):**

Crude oil production is defined as the quantities of oil extracted from the ground after the removal of inert matter or impurities. It includes crude oil, natural gas liquids (NGLs) and additives. This indicator is measured in thousand tonne of oil equivalent (toe). The data which has been considered is Total Crude oil production in US.

**3.2 Crude Oil Import price (output series): **

Crude oil import prices come from the IEA’s Crude Oil Import Register. Average prices are obtained by dividing value by volume as recorded by customs administrations for each tariff position. Values are recorded at the time of import and include cost, insurance and freight, but exclude import duties. The price measured in USD per barrel of oil.

Graph:

The graph depicts the time series of both the crude oil production in US and import price rate. To some extent, there is an inverse relationship between these two.

# Hypothesis framework

Total crude oil production is a major factor in determining the price of a barrel is tacit. To challenge this common belief, import price of oil is considered as Input series(X) and oil production is considered to be the Output series(Y).

Hypothesis – “There is an underlying relationship between the total crude oil production in US and crude oil import price.”

Equation – Production(Y(t)) ~ Import Price(X(t)).

# Procedure

The following steps show how various parameters were considered while building the ARIMA model and ultimately the team arrived at the Transfer Function.

** Step 1:** Fit ARIMA model to the input production series X

_{t. }Input data is now loaded and an ARIMA model is tried to fit with different parameters. The model IMA (2,1) shows good overall summary.

ACF and PACF were less than significant level and model coefficient are significant. The below plot shows the ACF and PACF obtained for the IMA model tried above. It concurs what we have observed. The residuals plot is also attached for the model.

**Arima residual check:**

** Step 2:** By fitting a preliminary model, we can get rid of the autocorrelation, if there exists any in the data. This process is called pre-whitening.

Pre-whiten the input production-output price series and check for cross correlation.

The cross-correlation plot between input and output indicate there is significant correlation in lag 3 to 5 and lag 8.

This suggests that our transfer function equation will have terms related to the input series only for lags 3,4,5 and 8.

The model equation:

Y_{t}=V_{t-3}X_{t-3} +V_{t-4} X_{t-4}+V_{t-5}X_{t-5}+V_{t-6} X_{t-6}+V_{t-7}X_{t-7}+V_{t-8}X_{t-8}+n_{t}.

*Step*** 3: **Compute the transfer function.

Parameters identified are: b=3, s=8-3=5, and r=2, these values were identified from the above pre-whitening plot and used to build transfer function.

Model residual diagnostics:

# Transfer Function Output

The residuals plot for the transfer function is obtained through the software. We do a diagnostic check for the fitted transfer function model – noise. The parameter significance is also checked from the plot and it is found that the ACF and PACF value ranges are in the significant range that we are looking for with varied significance.

**6.1 Final Equation:**

Y_{t }– 0.03 Y_{(t-1) }-1.03 Y_{(t-2) }-1.85 Y_{(t-3)} +1.91 Y_{(t-4)} = -290.3574+197.96X _{(t-3)}-249.74X _{(t-4) }+19.84X _{(t-5) }+ 93.04 X _{(t-6)} + 230.5484 X _{(t-7) }-763.4634 X _{(t-8)} + e_{(t)} +2.56 e_{(t-1)} +3.08 e_{(t-2)} +1.14 e_{(t-3)}

# Inference

Form the transfer function it is evident that import price depends on lag variables (3,4,5,8) of the crude oil production. As mentioned in our hypothesis it has been observed and re-iterated that there indeed exists a relationship, inverse in nature, between the two variables considered under our analysis, namely, Crude oil production and the import prices. Rising production in crude oil shall forecast a diminishment in the import prices.