1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
|
coefficientsP = class=ARMACoefficients, shift=0, value=class=SquareMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[0.2,0.3,0.7,0.4]
coefficientsQ = class=ARMACoefficients, shift=0, value=class=SquareMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[0.1,0,0,0.5]
dist = JointDistribution(Normal(mu = 0, sigma = 0.01), Normal(mu = 0, sigma = 0.02), IndependentCopula(dimension = 2))
Last values of the process = 0 : [ 0.629877 0.135276 ]
Last innovations of the process = 0 : [ 0.882805 0.0325028 ]
process = ARMA(X_{0,t} + 0.2 X_{0,t-1} + 0.7 X_{1,t-1} = E_{0,t} + 0.1 E_{0,t-1}
X_{1,t} + 0.3 X_{0,t-1} + 0.4 X_{1,t-1} = E_{1,t} + 0.5 E_{1,t-1}, E_t ~ JointDistribution(Normal(mu = 0, sigma = 0.01), Normal(mu = 0, sigma = 0.02), IndependentCopula(dimension = 2)))
ARMA process = ARMA(X_{0,t} + 0.2 X_{0,t-1} + 0.7 X_{1,t-1} = E_{0,t} + 0.1 E_{0,t-1}
X_{1,t} + 0.3 X_{0,t-1} + 0.4 X_{1,t-1} = E_{1,t} + 0.5 E_{1,t-1}, E_t ~ JointDistribution(Normal(mu = 0, sigma = 0.01), Normal(mu = 0, sigma = 0.02), IndependentCopula(dimension = 2)))
ARMA process with ARMAstate = ARMA(X_{0,t} + 0.2 X_{0,t-1} + 0.7 X_{1,t-1} = E_{0,t} + 0.1 E_{0,t-1}
X_{1,t} + 0.3 X_{0,t-1} + 0.4 X_{1,t-1} = E_{1,t} + 0.5 E_{1,t-1}, E_t ~ JointDistribution(Normal(mu = 0, sigma = 0.01), Normal(mu = 0, sigma = 0.02), IndependentCopula(dimension = 2)))
One realization= [ t X0 X1 ]
0 : [ 0 0.010204 -0.00744086 ]
1 : [ 0.1 -0.00287281 -0.0293307 ]
2 : [ 0.2 0.0190836 -0.00416576 ]
3 : [ 0.3 0.000428186 -0.0133922 ]
4 : [ 0.4 0.0226688 -0.0154754 ]
5 : [ 0.5 0.0156377 -0.00180096 ]
6 : [ 0.6 -0.00152644 0.0220058 ]
7 : [ 0.7 -0.0290278 -0.000953817 ]
8 : [ 0.8 0.00341936 -0.0137703 ]
9 : [ 0.9 0.00530122 -0.00738418 ]
10 : [ 1 -0.0161936 0.0111398 ]
One future= [ t v0 v1 ]
0 : [ 1.1 -0.00486985 0.0088404 ]
1 : [ 1.2 -0.0213829 0.0140495 ]
2 : [ 1.3 -0.0034992 0.00524708 ]
3 : [ 1.4 0.0067867 -0.00506869 ]
Some futures= [field 0:
[ t v0 v1 ]
0 : [ 1.1 -1.82364e-05 0.0156951 ]
1 : [ 1.2 -0.0150433 -0.0192013 ]
2 : [ 1.3 0.0304955 0.00743803 ]
3 : [ 1.4 -0.00879671 -0.0355234 ]
field 1:
[ t v0 v1 ]
0 : [ 1.1 -0.0129397 -0.00706455 ]
1 : [ 1.2 0.013426 -0.0179524 ]
2 : [ 1.3 -0.00898944 0.00403051 ]
3 : [ 1.4 -0.00677231 0.00868747 ]
field 2:
[ t v0 v1 ]
0 : [ 1.1 -0.00500545 -0.0157516 ]
1 : [ 1.2 0.0236257 0.0301551 ]
2 : [ 1.3 -0.0128599 -0.00625936 ]
3 : [ 1.4 -0.00239186 0.000610274 ]]
|
