Spurious Regression

Table 4

Orders in probability: variables 𝑦_𝑡 and 𝑥_𝑡 both independently generated by DGP 9. Variables are integrated of different orders 𝑑₁>𝑑₂.

𝛽=𝑂𝑝(𝑇^𝑑1−𝑑2)	𝛼=𝑂𝑝(𝑇^𝑑1−1/2)
𝑡𝛽=𝑂𝑝(𝑇^1/2)	𝑡𝛼=𝑂𝑝(𝑇^1/2)
𝒟𝒲=𝑂𝑝(𝑇^−1) if 𝑑2=1	𝒟𝒲=𝑂𝑝(𝑇^−2) if 𝑑2=2,3,…