Handling the discontinuity in futures prices when time series modeling of commodity cash and futures prices

Futures prices are discontinuous, with each future price series ending at maturity. Differencing before splicing can create a continuous future return series, but still leaves price levels with discrete jumps. When comparing cash and futures prices, there is a need to either make the futures more like the cash price by adding back the changes at rollover or removing the nonstationarity and seasonality from cash prices. In the specific situation of only testing market efficiency of futures prices, we propose using panel unit root tests. Our empirical examples using weekly prices show the null hypothesis of a unit root is not rejected in most cases regardless of the test used.