# Do stationary prices need to be differenced for VaR?

I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-at-risk, I can just simulate a set of prices based on the distribution that best fits them -- and then report the nth percentile on those simulations? In other words: is essentially a one-step simulation the same thing as an n-step simulation when directly modeling a stationary underlying?

Thank you.

## 1 Answer

I worry that power prices are very unlikely to be stationary.

It is possible the mean does not vary wildly over time, and the price process may not be integrated, i.e. prices may not require differencing. However, prices (or returns) almost surely require correcting for heteroskedasticity.

If you have a powerstack function estimated, perhaps you could use that to predict volatility. Otherwise, you could use an exponential GARCH model (since commodity prices get more volatile as price rises).

Regarding your last question: if you only care about one point in time, then you can just simulate that one point in time. If you care about multiple points in time, however, you cannot pull all of them from the same distribution -- since prices tend to be strongly mean reverting. That would make your $$n$$ samples negatively serially correlated.

• I should emphasize that I’m working with monthly futures contracts — not real time or day ahead prices. Even so, like you said, I was a bit surprised that the data passed the ADF test — I expected volatility to increase with liquidity as the active month approaches and then decrease as the active-month average and such month’s contract prices converge. Otherwise, each contract (eg CAISO NP15 Jan 2021 Off-Peak) has been fitted separately, as no two contracts are iid. – CasusBelli Aug 3 '20 at 13:29