Estimating potential moves in a time series relative to an other Say we have two time series which over time have a strong correlation, say above 0.8, say for example the price of oil and share price of an oil exploration and extraction company. Now say that we have a universe of oil companies exhibiting a strong correlation with oil, but we are interested in obtaining results for one of them say company A. 
What we want is to have this: If the price of oil goes up by 5USD or down by 5USD how can I expect shares of company A to move? Our past data, may or may not have 5 dollar moves in oil prices. 
What are some methods to look into for such a case based on your experience?
Thank you!
 A: So we are given two time series, price of oil (O) and 'share price of an oil exploration and extraction company' that is not company A (let's call it F), whereas company A data is mixed within a group (G) of other oil companies. Do we have data for this group (that has A but not F)? Even though the given firm's data (F) is correlated to price of oil by 0.8 ($\rho_{F,O}=0.8)$, we do not know the exact value of the group (nor A)'s correlation with the commodity ($\rho_{G,O}=$'high' and so probably $\rho_{A,O}=$'high').
If you had information for A's price by itself, you could regress the price of company A's shares onto the price of oil and expect A to move $\beta_1$ dollars for every unit change in $P_{oil}$:
$$P_A = \beta_0 + \beta_{A,O} P_{O} + \epsilon$$
More directly, in terms of correlation $\rho$, 
$$\beta_{A,O}= \frac{\rho_{A,O} \sigma_{A}}{\sigma_{O}}$$
just because the group has correlation $\rho_{G,O}$ with oil though, we can't expect that $\rho_{A,O} = \rho_{G,O}$. I feel that there might be a mix-up in the given data in the question, otherwise, if data for the group is available, it could be replaced as the independent variable in the regression and be used to proxy the relationship of A to oil assuming $\rho_{A,O} \approx \rho_{G,O}$. If unknown A is the firm of interest, there is not much use for the given firm F's data, unless it is also part of the group.
