Structural Analysis and Total Coal Demand Forecast in China

Table 2

Formulae for recursive calculations, point forecasts, and parametric estimated value on sector by ETS method.

Variables	Forms	Models and parameters
AFAFW	(M, N, N)	𝑙𝑡=𝛼𝑦𝑡+(1−𝛼)𝑙𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡,; 𝑦𝑡+1=𝑦𝑡+1∣𝑡1+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1,0<𝛽<𝛼,; 𝛼=0.0001,𝑙=1793.7859,𝜎=0.1809
IND	(A, A, N)	𝑙𝑡=𝛼𝑦𝑡+(1−𝛼)𝑙𝑡−1+𝑏𝑡−1, 𝑏𝑡=𝛽𝑙𝑡−𝑙𝑡−1+1−𝛽𝑏𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡+ℎ𝑏𝑡; 𝑦𝑡+1=𝑦𝑡+1∣𝑡+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1, 0<𝛽<𝛼,; 𝛼=0.9999,𝛽=0.2697,; 𝑙=54782.1109,𝑏=9338.5498,𝜎=12910.3600
CON	(A, A, N)	𝑙𝑡=𝛼𝑦𝑡+(1−𝛼)𝑙𝑡−1+𝑏𝑡−1, 𝑏𝑡=𝛽𝑙𝑡−𝑙𝑡−1+1−𝛽𝑏𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡+ℎ𝑏𝑡; 𝑦𝑡+1=𝑦𝑡+1∣𝑡+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1,0<𝛽<𝛼,; 𝛼=0.0009,𝛽=0.0009,𝑙=448.3868,𝑏=8.7382,𝜎=53.6530
TSP	(M, M, N)	𝑙𝑡=𝑎𝑦𝑡+(1−𝑎)𝑙𝑡−1𝑏𝑡−1, 𝑏𝑡=𝛽𝑙𝑡/𝑙𝑡−1+1−𝛽𝑏𝑡−1, 𝑦𝑡+ℎ|𝑡=𝑙𝑡𝑏𝑡^ℎ; 𝑦𝑡+1=𝑦𝑡+1∣𝑡1+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1, 0<𝛽<𝛼,; 𝛼=0.0001,𝛽=0.0001,𝑙=2305.0531,𝑏=0.9371,𝜎=0.1049
WRHC	(M, M, N)	𝑙𝑡=𝑎𝑦𝑡+(1−𝑎)𝑙𝑡−1𝑏𝑡−1, 𝑏𝑡=𝛽𝑙𝑡/𝑙𝑡−1+1−𝛽𝑏𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡𝑏𝑡^ℎ; 𝑦𝑡+1=𝑦𝑡+1∣𝑡1+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1, 0<𝛽<𝛼,; 𝛼=0.0001,𝛽=0.0001,𝑙=765.1436,𝑏=1.0328,𝜎=0.2562
OS	(A, N, N)	𝑙𝑡=𝑎𝑦𝑡+(1−𝑎)𝑙𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡; 𝑦𝑡+1=𝑦𝑡+1∣𝑡+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1, 0<𝛽<𝛼,; 𝛼=0.8917,𝑙=1148.7978,𝜎=497.8256
HC	(M, N, N)	𝑙𝑡=𝑎𝑦𝑡+(1−𝑎)𝑙𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡,; 𝑦𝑡+1=𝑦𝑡+1∣𝑡1+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1,0<𝛽<𝛼,; 𝛼=0.9999,𝑙=11373.6307,𝜎=0.1327
TO	(A, A, N)	𝑙𝑡=𝛼𝑦𝑡+(1−𝛼)𝑙𝑡−1+𝑏𝑡−1, 𝑏𝑡=𝛽𝑙𝑡−𝑙𝑡−1+1−𝛽𝑏𝑡−1, 𝑦𝑡+ℎ∣𝑡=𝑙𝑡+ℎ𝑏𝑡; 𝑦𝑡+1=𝑦𝑡+1∣𝑡+𝜀𝑡, 𝜀𝑡∼𝑁𝐼𝐷0,𝜎^2, 0<𝛼<1, 0<𝛽<𝛼,; 𝛼=0.9999,𝛽=0.1665,𝑙=78421.9911,𝑏=9365.1674,𝜎=14646.2100

In the above formulae for recursive calculations and point forecasts: 𝑙_𝑡 denotes the series level at time 𝑡; 𝑏_𝑡 denotes the slope at time 𝑡; 𝛼 and 𝛽 are smoothness index; ℎ denotes the lag period.