View of THE ROLE OF INTEGRATED ISLAMIC COMMERCIAL AND SOCIAL FINANCE FOR CURBING CREDIT CYCLES AND ACHIEVING MACROPRUDENTIAL OBJECTIVE

ā

ā

𝑦

_𝑡

= 𝑔

_𝑡

+ 𝑐

_𝑡

𝑴𝒊𝒏 {∑

^𝑇_𝑡=1

𝑐

_𝑡²

+ 𝜆 ∑

^𝑇_𝑡=1

[(𝑔

_𝑡

− 𝑔

_𝑡−1

) − (𝑔

_𝑡−1

− 𝑔

_𝑡−2

)]

²

} {𝑔

_𝑡

)

_𝑡=−1 ^𝑇

λ

λ λ

(𝑔

_𝑡

= 𝑦

_𝑡

) λ λ →∞

𝑔

_𝑡

= 𝛽 ∗ 𝑡

λ

λ

λ λ

𝑔𝑎𝑝 = 𝑥

𝑖

− 𝑥

_𝑖^𝑡

𝑚𝑜𝑛𝑡ℎ

𝑖

𝑥

_𝑖^𝑡

𝑚𝑜𝑛𝑡ℎ

_𝑖

σ

𝜎 = √

_𝑁−1¹

∑

𝑛

(𝑥

𝑖

− 𝑥

𝑖𝑡

𝑖=1

)

²

𝑥

𝑖𝑡

− 𝑘𝜎

𝑥

_𝑖^𝑡

+ 𝑘𝜎

μ μ

(𝑦

𝑡−

𝜇

𝑠_𝑡

) = 𝜑

1

((𝑦

𝑡−

𝜇

𝑠_𝑡−1

) + 𝜑

2

((𝑦

𝑡−

𝜇

𝑠_𝑡−2

) + 𝜑

3

((𝑦

𝑡−

𝜇

𝑠_𝑡−3

) +

𝜑

₄

((𝑦

_𝑡−

𝜇

_𝑠𝑡−4

) + 𝜀

_𝑡

ε σ

𝑦

𝑡

= 𝜇

𝑠_𝑡

+ 𝜀

𝑡

𝜀

𝑡

~ 𝑁(0, 𝜎

𝑠𝑡2

)

μ μ μ σ σ

σ

𝑝(𝑦

𝑡

|𝑍

𝑡

; 𝜃) =

¹

√2𝜋𝜎_𝑎𝑡

exp {−

^(𝑦𝑡_2𝜎^{−𝜇𝑠𝑡)2}

𝑠𝑡2

}

𝑝(𝑠

_𝑡

= 𝑗|𝑠

_𝑡−1

= 𝑖) = 𝑝

_𝑖𝑗

∑

𝐾

𝑝

𝑖𝑗

𝑗=1

= 1 𝑓𝑜𝑟 𝑖 = 1, … , 𝐾

𝑝(𝑠

_𝑡

= 1|𝑠

_𝑡−1

= 1) = 𝑝

_11,

𝑝(𝑠

𝑡

= 2|𝑠

𝑡−1

= 1) = 𝑝

12,

𝑝(𝑠

_𝑡

= 3|𝑠

_𝑡−1

= 1) = 𝑝

_13,

𝑝(𝑠

_𝑡

= 1|𝑠

_𝑡−1

= 2) = 𝑝

_21,

𝑝(𝑠

𝑡

= 2|𝑠

𝑡−1

= 3) = 𝑝

22,

𝑝(𝑠

_𝑡

= 3|𝑠

_𝑡−1

= 3) = 𝑝

_23,



 







^k

i i t t

t

t

A X

x

1 1





μ ε

t i t k

i i t

t

t

x x

x         



^ _





¹ 1 1

Π Γ Π

λ β Π λβ λ

β

𝜋

[

∆ 𝑙𝑛𝑟𝑡𝑓

𝑡

∆ 𝑙𝑛𝑔

𝑡

∆ 𝑖𝑛𝑓

_𝑡

∆𝑓𝑡𝑣

𝑡

∆ 𝑟𝑟𝑖𝑏

_𝑡

∆ 𝜋

_𝑡

] =

[ 𝛼

10

𝛼

₂₀

𝛼

₃₀

𝛼

40

𝛼

50

𝛼

60

] +

[

𝛼

11

𝛼

12

𝛼

13

𝛼

14

𝛼

15

𝛼

16

𝛼

17

𝛼

₂₁

𝛼

₂₂

𝛼

₂₃

𝛼

₂₄

𝛼

₂₅

𝛼

₂₆

𝛼

₂₇

𝛼

₃₁

𝛼

₃₂

𝛼

₃₃

𝛼

₃₄

𝛼

₃₅

𝛼

₃₆

𝛼

₃₇

𝛼

41

𝛼

42

𝛼

43

𝛼

44

𝛼

45

𝛼

46

𝛼

47

𝛼

51

𝛼

52

𝛼

53

𝛼

54

𝛼

55

𝛼

56

𝛼

57

𝛼

61

𝛼

62

𝛼

63

𝛼

64

𝛼

65

𝛼

66

𝛼

67

] [

∆ 𝑙𝑛𝑟𝑡𝑓

𝑡−𝑖

∆ 𝑙𝑛𝑔

𝑡−𝑖

∆ 𝑖𝑛𝑓

_𝑡−𝑖

∆ 𝑓𝑡𝑣

𝑡−𝑖

∆ 𝑟𝑟𝑖𝑏

_𝑡−𝑖

∆ 𝜋

_𝑡−𝑖

] +

[ 𝜀

1𝑡

𝜀

_2𝑡

𝜀

_3𝑡

𝜀

4𝑡

𝜀

5𝑡

𝜀

6𝑡

]

[

∆ 𝑙𝑛𝑟𝑡𝑓

𝑡

∆ 𝑙𝑛𝑔

𝑡

∆ 𝑙𝑛𝑧

𝑡

∆ 𝑙𝑛𝑠

_𝑡

∆𝑓𝑡𝑣

𝑡

∆ 𝑟𝑟𝑖𝑏

_𝑡

] =

[ 𝛽

10

𝛽

20

𝛽

30

𝛽

₄₀

𝛽

50

𝛽

₆₀

] +

[

𝛽

11

𝛽

12

𝛽

13

𝛽

14

𝛽

15

𝛽

16

𝛽

21

𝛽

22

𝛽

23

𝛽

24

𝛽

25

𝛽

26

𝛽

31

𝛽

32

𝛽

33

𝛽

34

𝛽

35

𝛽

36

𝛽

₄₁

𝛽

₄₂

𝛽

₄₃

𝛽

₄₄

𝛽

₄₅

𝛽

₄₆

𝛽

51

𝛽

52

𝛽

53

𝛽

54

𝛽

55

𝛽

56

𝛽

₆₁

𝛽

₆₂

𝛽

₆₃

𝛽

₆₄

𝛽

₆₅

𝛽

₆₆

] [

∆ 𝑙𝑛𝑟𝑡𝑓

𝑡−𝑖

∆ 𝑙𝑛𝑔

𝑡−𝑖

∆ 𝑖𝑛𝑓

_𝑡−𝑖

∆ 𝑓𝑡𝑣

𝑡−𝑖

∆ 𝑟𝑟𝑖𝑏

_𝑡−𝑖

∆ 𝜋

_𝑡−𝑖

] +

[ 𝜇

1𝑡

𝜇

_2𝑡

𝜇

_3𝑡

𝜇

4𝑡

𝜇

5𝑡

𝜇

6𝑡

]

Δ α β

𝑡

−𝑖

ε μ

𝜋

-.2 -.1 .0 .1 .2 .3

04 05 06 07 08 09 10 11 12 13 14 15 16 17

ACTUAL FITTED

-.3 -.2 -.1 .0 .1 .2 .3

04 05 06 07 08 09 10 11 12 13 14 15 16 17

A CTUA L FILTE RE D

𝜋

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Inverse Roots of AR Characteristic Polynomial

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Inverse Roots of AR Characteristic Polynomial