My question is if I have a spot position of a commodity e.g Naturals Gas I want to hedge, how would I determine, which futures e.g. quarterly, yearly I should pick. Should I just take the one it is the most correlated with? And when I calculate the correlation should I take it over the whole time period i.e 10 years? And lastly should I take daily, weekly or monthly returns as the correlation is going to change depending on the frequency?
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You are referring to the position to be hedged, as "spot position", which in gas markets means next day delivery. Hedging this with a longer-dated futured contract does not make sense, since the correlation will be rather low.
If by spot you mean near-term deliveries, such as e.g. next month, next quarter etc. then a matching traded contract will usually be available in the market, so there is no problem.
Generally, proxy-hedging will be required when long-dated illiquid contracts have to be hedged with shorter-dated contracts. In terms of hedge effectiveness, the correlation will decrease, as the tenor difference between the position and the hedge increases. For most commodities, volatilities are also tenor-dependent. The optimal hedge size $Q_{hedge}$ against a position of size $Q_{pos}$ and volatility $\sigma_{pos}$ is the quantity that results in minimal portfolio variance given hedge volatility $\sigma_{hedge}$ and correlation $\rho_{hedge,pos}$. Besides the variance of the portfolio of position and hegde, the hedging cost (bid-ask) needs to be taken into account. When hedging very long-dated positions, the hedge may have to be rolled over multiple times, i.e. bid-ask will be incurred multiply.
The optimal hedge would then be defined as the hedge with the lowest loss at a defined confidence level. This is defined by the tradeoff between hedge effectiveness and cost of hedging
