Question

Consider a series of values for spot and futures prices of a given commodity. Which of the following statements are TRUE in order to conclude that the series are cointegrated? Justify your answer. (i) Both series are stationary and thus a linear combination of the series will be stationary. (ii) The series follow a common stochastic trend and a linear combination between them also exhibits a stochastic trend. (iii) Although both series have deterministic trends, a linear combination between them is stationary. (iv) The series follow a common stochastic trend and a linear combination between them is l(0)

Answer 1

If we take into consideration spot and futures prices, there is bound to be randomness in the values. Thus to conclude that they are cointegrated, the following must hold true;

(iv) The series follow a common stochastic trend and a linear combination between them is I(0).

Reason:

Spot and futures prices will display stochastic movements, but the movements will have a common trend. If the linear combination exhibits I(0), we can conclude that they are cointegrated.

Why other options are incorrect:

The two series will not be stationary at levels, and neither will they have a deterministic trend. The linear combination must be I(0) to conclude cointegration.