Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models

The accumulated sum of a stationary series is called integrated. If a linear combination of some of the integrated series is stationary, it is said to be cointegrated. This paper presents empirical results on inventories to consider the possibility of a deeper form of cointegration called multicointegration, which is introduced in Granger and Lee (1989). A vector integrated series is multicointegrated if the accumulated sum of its stationary (cointegrated) linear combination is again cointegrated with itself. Inventory, which is the accumulated sum of production minus sales, is probably cointegrated with production and sales. The empirical results generally support the presence of multicointegration of production and sales in many U.S. industries and industrial aggregates. The results also favour the non-symmetric error correction model, providing evidence that the strength of attraction is different on both sides of the attractor. A modified (S, s) rule for inventory control is investigated in the context of a non-symmetric error correction model, and the results generally do not support the (S, s) rule. Sufficient evidence is found to conclude that multicointegration is a useful concept in the area of inventory determination.