Models

Unrestricted case (φ ≠ 0) or restricted case (φ = 0)

Coefficient Driver of Equation (4)

Coefficient Estimates of γ_0t in Equations (3) and (4)

Coefficient Driver of Equation (5)

Coefficient Estimates of γ_1t in Equations (3) and (5)

Theil Forecasting Values

Conclusion

Z_it

π₀₀

π_0i

Z_jt

π₁₀

π_1j

U Statistic

Accept/Reject

I

φ = 0

CEXPI

159842.90

−512.65

PI

1.985

−0.000018

12.27

REJECT

(10.95)^a

(−4.317)^a

(16.36)^a

(−7.119)^a

II

φ ≠ 0

OMT

55627.70

244.12

PI

2.479

−0.000013

0.65

ACCEPT

(3.307)^a

(1.660)^c

(2.247)^b

(−2.266)^b

III

φ = 0

OMT

9320.21

473.03

PI

9.492

−0.00016

8.91

REJECT

(1.196)

(6.265)^a

(8.089)^a

(−5.081)^a

IV

φ = 0

REEXR

128708.07

−595.29

PI

11.212

−0.0002

10.96

REJECT

(4.656)^a

(−2.566)^a

(7.792)^a

(−4.936)^a

V

φ = 0

CEXPI

33091.90

161.69

GFCF

13.047

−0.00018

11.96

REJECT

(4.417)^a

(3.314)^a

(9.169)^a

(−6.007)^a

VI

φ = 0

OMT

9689.82

468.19

GFCF

9.806

−0.00013

8.71

REJECT

(1.261)

(6.285)^a

(8.277)^a

(−5.291)^a

VII

φ = 0

REEXR

127989.55

−590.57

GFCF

11.577

−0.00016

10.7

REJECT

(4.695)^a

(−2.581)^a

(7.973)^a

(−5.137)^a

VIII

φ ≠ 0

CEXPI

109318.23

−244.65

PC

3.384

−0.0000052

5.91

REJECT

(12.84)^a

(−4.048)^a

(3.534)^a

(−2.430)^b

IX

φ = 0

CEXPI

35287.53

151.79

PC

11.413

−0.00004

18.91

REJECT

(4.379)^a

(2.885)^a

(8.122)^a

(−4.919)^a

X

φ≠0

OMT

76300.71

30.931

PC

3.551

−0.0000054

6.84

REJECT

(4.867)^a

(0.223)

(4.208)^a

(−2.530)^a

XI

φ≠0

OMT

8383.01

486.80

PC

8.581

−0.000029

13.72

REJECT

(1.015)

(6.168)^a

(7.466)^a

(−4.387)^a

XII

φ = 0

REEXR

130223.24

−604.15

PC

10.165

−0.000036

16.89

REJECT

(4.507)^a

(−2.491)^b

(7.213)^a

(−4.287)^a