Spurious Regression

Table 1

The DGPs for 𝑤_𝑡=𝑥_𝑡,𝑦_𝑡,𝑧_𝑡. Note: 𝑇𝑆,𝑏𝑟 and 𝑑𝑟 stand for trend-stationarity, breaks, and drift, respectively.

#	Name	Model
1	𝑀𝐴(𝑞𝑤) or	𝑤𝑡=∑^𝑞𝑤𝑖=1Θ𝑖𝑤𝜖𝑤𝑡−𝑖 or
	𝐴𝑅(𝑝𝑤)	𝑤𝑡=∑^𝑝𝑤𝑖=1𝜙𝑤𝑖𝑤𝑡−𝑖+𝜖𝑤𝑡 (stationary)
2	𝐼(0)	𝑤𝑡=𝜇𝑤+𝑢𝑤𝑡
3	𝐼(0)+𝑏𝑟	𝑤𝑡=𝜇𝑤+∑^𝑁𝑤𝑖=1𝜃𝑖𝑤𝐷𝑈𝑖𝑤𝑡+𝑢𝑤𝑡
4	𝑇𝑆	𝑤𝑡=𝜇𝑤+𝛽𝑤𝑡+𝑢𝑤𝑡
5	𝑇𝑆+𝑏𝑟	𝑤𝑡=𝜇𝑤+∑^𝑁𝑤𝑖=1𝜃𝑖𝑤𝐷𝑈𝑖𝑤𝑡+𝛽𝑤𝑡+∑^𝑀𝑤𝑖=1𝛾𝑖𝑤𝐷𝑇𝑖𝑤𝑡+𝑢𝑤𝑡
6	𝐼(1)	Δ𝑤𝑡=𝑢𝑤𝑡
7	𝐼(1)+𝑑𝑟	Δ𝑤𝑡=𝜇𝑤+𝑢𝑤𝑡
8	𝐼(1)+𝑑𝑟+𝑏𝑟	Δ𝑤𝑡=𝜇𝑤+∑^𝑁𝑤𝑖=1𝜃𝑖𝑤𝐷𝑈𝑖𝑤𝑡+𝑢𝑤𝑡
9	𝐼(𝑘)	Δ^𝑘𝑤𝑡=𝑢𝑤𝑡 for 𝑘=2,3,…
10	𝐹𝐼(𝑑)	(1−𝐿)^𝑑𝑤𝑡=𝑢𝑤𝑡 for 𝑑∈(0,1/2)
11	𝐹𝐼(1+𝑑)	Δ𝑤𝑡=𝑢𝑤𝑡 with (1−𝐿)^𝑑𝑢𝑤𝑡=𝜖𝑤𝑡 for 𝑑∈(0,3/2)