# How to retrieve and format futures data for use in regression/time series models?

I need to form a predictive time series model for monthly Brent crude oil spot price. I am looking to form 1-12 month ahead forecast horizons. There is a bounty of previous literature which uses futures prices in a regression framework for this purpose. See Crude Oil Price Forecasting Techniques: a Comprehensive Review of Literature and the references cited therein in for examples, I can provide more citations if necessary.

In general the models are of the form. $$E[P_{t+h}]=F_{t,t+h}+x_{t,h}'\beta$$

where $E[P_{t+h}]$ is the expected value of Brent crude oil spot price $h$ months in the future at time $t$, $F_{t,t+h}$ is the price of the oil futures contract at time $t$ with maturity $t+h$, and $x_{t,h}$ is a vector of other economic and financial variables (i.e. proxies for business cycles and or risk premia, etc). This would call for a regression model of the form $$P_{t+h}=F_{t,t+h} + x_{t,h}'\beta+\varepsilon_{t,h}$$ Where $\varepsilon_{t,h}$ is the error term.

I understand the basic concept behind futures contracts, but am struggling with how to obtain a monthly time series of future prices which I can use in the above equation to form a regression model. That is to say, futures contracts are brought into creation and traded in irregular time intervals, often with more than one outstanding contracting existing at a time. Unlike spot prices, it would seem that obtaining a monthly time series out of futures data would be an involved process, assuming that such futures data was even available.

## What I have Done So far

1. I have researched some methods to form continuous contract series (eg. http://www.premiumdata.net/support/futurescontinuous.php). There are apparently multiple different ways to do "splicing". I would really like to know what methods are preferable for the purposes of regression and if there already exists freely available continuous contract data. Where do I go to look?

2. I have gone onto Quandl and found some futures data with titles like. ICE Brent Crude Oil Futures #11 (B11) - Unadjusted Prices, Roll on First of Month, Continuous Contract History. This sounds kind of like what I want, but I honestly do not know for sure or if it would be appropriate for my model.

All in all, I am just looking for advise on where to start and how to go about doing this, things to watch out for, if there is any free resources/data already available, exc. Any advise would be greatly appreciated.

You're getting confused because data providers will actually give you "continuous" contracts which are not the ones traded.

When you get in a future contract trade, you buy a future contract which has an expiry date. After that date, the contract does not exist anymore, money is exchanged against underlying for those who still have a position. When you do speculative trading, you just don't want to take delivery of thousand of oil barrels, so you basically sell the front-month contract relatively shortly before expiry and buy the following one.

In your case, $F_{t,t+h}$ is the time series of a continous contract $h$ month ahead. You can probably find this for some values of $h$ is some provider, but not everywhere. So what you have to do is basically find and download the whole history of prices for all future contracts $F_{t,T}$ and then find to which value $T$ the $t+h$ of your model corresponds.

So, you will need to download a time series for each future contract that could be concerned by you analysis. It would be good if you added the regression formula you're trying to get to in the question.

• I think I get it...I just want to make sure. I have access to Quandl right now which gives me a ton of individual futures time series between 1993 and 2021. Though, each series differs in length each time series ends (or is set to end) on a unique month/year. So I assume each of these time series corresponds to a single contract with expiry date on the aforementioned month/year. Furthermore that expiry date is $t+h$? – Zachary Blumenfeld Oct 26 '15 at 6:30
• So in that case all I have to do is line up the spot price at time $t$ with all the futures contract prices (I suppose I will use the settle) existing at time $t$ and which have an expiry date sometime in the next 12 months. Assuming I can get all 12 futures contracts, they will be the $F_{t,t+1},...,F_{t,t+12}$ I was looking for? Thanks for the help. Hopefully I am understanding you correctly – Zachary Blumenfeld Oct 26 '15 at 6:36
• Yeah that's right but you regression formula does not make sense to me, because you do not know $P_{t+h}$ at time $t$. If you're happy with the answer then you can accept it. – SRKX Oct 26 '15 at 7:12
• Yes, the coefficients for the regression are estimated on past historical data where we would know $P_{t+h}$ just like in an ARMA model. In theory, using proper estimation and validation techniques, the right side (the linear combo of the futures prices and other stuff) for this month should provide a good forecast for spot price $h$ months in the future. – Zachary Blumenfeld Oct 26 '15 at 7:23
• If it helps think about it, you can re-parameterise the index so that the regression equation reads $P_t = F_{t-h,t}+x_{t,h}'\beta+\varepsilon_{t,h}$ – Zachary Blumenfeld Oct 28 '15 at 8:58