ImpulseVMA: The Impulse Response Function in the Infinite MA or VMA...

Description Usage Arguments Value Author(s) References See Also Examples

Description

The impulse coefficients are computed.

Usage

1
ImpulseVMA(phi=NULL,theta=NULL,trunc.lag=NULL)

Arguments

phi

a numeric or an array of AR or an array of VAR parameters with order p.

theta

a numeric or an array of MA or an array of VMA parameters with order q.

trunc.lag

truncation lag is used to truncate the infinite MA or VMA Process. IF it is NULL, then the default trunc.lag = p+q.

Value

The impulse response coefficients of order trunc.lag+1 obtained by converting the ARMA(p,q) or VARMA(p,q) process to infinite MA or VMA process, respectively.

Author(s)

Esam Mahdi and A.I. McLeod.

References

Lutkepohl, H. (2005). "New introduction to multiple time series analysis". Springer-Verlag, New York.

Reinsel, G. C. (1997). "Elements of Multivariate Time Series Analysis". Springer-Verlag, 2nd edition.

See Also

ARMAtoMA, varima.sim, vma.sim, InvertQ, InvertibleQ

Examples

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#####################################################################
### Impulse response coefficients from AR(1,1) to infinite MA process. 
### The infinite process is truncated at lag 20
###
k <- 1
trunc.lag <- 20
phi <- 0.7
theta <- array(-0.9,dim=c(k,k,1))
ImpulseVMA(phi,theta,trunc.lag)
#####################################################################
### Impulse response coefficients from VAR(2) to infinite VMA process
### The infinite process is truncated at default lag value = p+q
###
k <- 2
phi <- array(c(0.5,0.4,0.1,0.5,0,0.3,0,0),dim=c(k,k,2))
theta <- NULL
ImpulseVMA(phi,theta)
#####################################################################
### Impulse response coefficients from VARMA(2,1) to infinite VMA process
### The infinite process is truncated at lag 50
###
k <- 2
phi <- array(c(0.5,0.4,0.1,0.5,0,0.25,0,0),dim=c(k,k,2))
theta <- array(c(0.6,0,0.2,0.3),dim=c(k,k,1))
ImpulseVMA(phi,theta,trunc.lag=50)

Example output

Loading required package: parallel
, , 1

     [,1]
[1,]    1

, , 2

     [,1]
[1,]  1.6

, , 3

     [,1]
[1,] 1.12

, , 4

      [,1]
[1,] 0.784

, , 5

       [,1]
[1,] 0.5488

, , 6

        [,1]
[1,] 0.38416

, , 7

         [,1]
[1,] 0.268912

, , 8

          [,1]
[1,] 0.1882384

, , 9

          [,1]
[1,] 0.1317669

, , 10

           [,1]
[1,] 0.09223682

, , 11

           [,1]
[1,] 0.06456577

, , 12

           [,1]
[1,] 0.04519604

, , 13

           [,1]
[1,] 0.03163723

, , 14

           [,1]
[1,] 0.02214606

, , 15

           [,1]
[1,] 0.01550224

, , 16

           [,1]
[1,] 0.01085157

, , 17

            [,1]
[1,] 0.007596098

, , 18

            [,1]
[1,] 0.005317269

, , 19

            [,1]
[1,] 0.003722088

, , 20

            [,1]
[1,] 0.002605462

, , 21

            [,1]
[1,] 0.001823823

, , 1

     [,1] [,2]
[1,]    1    0
[2,]    0    1

, , 2

     [,1] [,2]
[1,]  0.5  0.1
[2,]  0.4  0.5

, , 3

     [,1] [,2]
[1,] 0.29 0.10
[2,] 0.70 0.29

, , 1

     [,1] [,2]
[1,]    1    0
[2,]    0    1

, , 2

     [,1] [,2]
[1,] -0.1 -0.1
[2,]  0.4  0.2

, , 3

      [,1]  [,2]
[1,] -0.01 -0.03
[2,]  0.41  0.06

, , 4

      [,1]   [,2]
[1,] 0.036 -0.009
[2,] 0.176 -0.007

, , 5

       [,1]    [,2]
[1,] 0.0356 -0.0052
[2,] 0.0999 -0.0146

, , 6

        [,1]     [,2]
[1,] 0.02779 -0.00406
[2,] 0.07319 -0.01163

, , 7

         [,1]      [,2]
[1,] 0.021214 -0.003193
[2,] 0.056611 -0.008739

, , 8

          [,1]       [,2]
[1,] 0.0162681 -0.0024704
[2,] 0.0437386 -0.0066617

, , 9

           [,1]        [,2]
[1,] 0.01250791 -0.00190137
[2,] 0.03368004 -0.00511726

, , 10

            [,1]         [,2]
[1,] 0.009621959 -0.001462411
[2,] 0.025910209 -0.003936778

, , 11

           [,1]         [,2]
[1,] 0.00740200 -0.001124883
[2,] 0.01993087 -0.003028696

, , 12

            [,1]          [,2]
[1,] 0.005694087 -0.0008653112
[2,] 0.015331723 -0.0023299040

, , 13

            [,1]         [,2]
[1,] 0.004380216 -0.000665646
[2,] 0.011793996 -0.001792297

, , 14

            [,1]          [,2]
[1,] 0.003369507 -0.0005120527
[2,] 0.009072606 -0.0013787349

, , 15

            [,1]          [,2]
[1,] 0.002592014 -0.0003938999
[2,] 0.006979160 -0.0010606000

, , 16

            [,1]          [,2]
[1,] 0.001993923 -0.0003030099
[2,] 0.005368763 -0.0008158732

, , 17

            [,1]          [,2]
[1,] 0.001533838 -0.0002330923
[2,] 0.004129954 -0.0006276155

, , 18

            [,1]          [,2]
[1,] 0.001179914 -0.0001793077
[2,] 0.003176993 -0.0004827972

, , 19

             [,1]          [,2]
[1,] 0.0009076565 -0.0001379336
[2,] 0.0024439217 -0.0003713947

, , 20

             [,1]          [,2]
[1,] 0.0006982204 -0.0001061063
[2,] 0.0018800020 -0.0002856977

, , 21

             [,1]          [,2]
[1,] 0.0005371104 -0.0000816229
[2,] 0.0014462033 -0.0002197747

, , 22

             [,1]          [,2]
[1,] 0.0004131755 -6.278892e-05
[2,] 0.0011125009 -1.690631e-04

, , 23

             [,1]          [,2]
[1,] 0.0003178379 -4.830077e-05
[2,] 0.0008557983 -1.300528e-04

, , 24

             [,1]          [,2]
[1,] 0.0002444988 -3.715567e-05
[2,] 0.0006583282 -1.000440e-04

, , 25

             [,1]          [,2]
[1,] 0.0001880822 -2.858223e-05
[2,] 0.0005064230 -7.695944e-05

, , 26

             [,1]          [,2]
[1,] 0.0001446834 -2.198706e-05
[2,] 0.0003895691 -5.920153e-05

, , 27

             [,1]          [,2]
[1,] 0.0001112986 -1.691368e-05
[2,] 0.0002996785 -4.554115e-05

, , 28

             [,1]          [,2]
[1,] 8.561715e-05 -1.301096e-05
[2,] 2.305295e-04 -3.503281e-05

, , 29

             [,1]          [,2]
[1,] 6.586153e-05 -1.000876e-05
[2,] 1.773363e-04 -2.694921e-05

, , 30

             [,1]          [,2]
[1,] 5.066439e-05 -7.699300e-06
[2,] 1.364170e-04 -2.073085e-05

, , 31

             [,1]          [,2]
[1,] 0.0000389739 -5.922735e-06
[2,] 0.0001049397 -1.594733e-05

, , 32

             [,1]          [,2]
[1,] 2.998091e-05 -4.556101e-06
[2,] 8.072548e-05 -1.226759e-05

, , 33

             [,1]          [,2]
[1,] 2.306301e-05 -3.504809e-06
[2,] 6.209858e-05 -9.436917e-06

, , 34

             [,1]          [,2]
[1,] 1.774136e-05 -2.696096e-06
[2,] 4.776972e-05 -7.259407e-06

, , 35

             [,1]          [,2]
[1,] 1.364765e-05 -2.073989e-06
[2,] 3.674716e-05 -5.584344e-06

, , 36

             [,1]          [,2]
[1,] 1.049854e-05 -1.595429e-06
[2,] 2.826798e-05 -4.295792e-06

, , 37

             [,1]          [,2]
[1,] 8.076069e-06 -1.227294e-06
[2,] 2.174532e-05 -3.304565e-06

, , 38

             [,1]          [,2]
[1,] 6.212567e-06 -9.441033e-07
[2,] 1.672772e-05 -2.542057e-06

, , 39

             [,1]          [,2]
[1,] 4.779056e-06 -7.262573e-07
[2,] 1.286791e-05 -1.955493e-06

, , 40

             [,1]          [,2]
[1,] 3.676318e-06 -5.586780e-07
[2,] 9.898717e-06 -1.504275e-06

, , 41

             [,1]          [,2]
[1,] 2.828031e-06 -4.297665e-07
[2,] 7.614650e-06 -1.157173e-06

, , 42

             [,1]          [,2]
[1,] 2.175480e-06 -3.306006e-07
[2,] 5.857617e-06 -8.901627e-07

, , 43

             [,1]          [,2]
[1,] 1.673502e-06 -2.543166e-07
[2,] 4.506008e-06 -6.847632e-07

, , 44

             [,1]          [,2]
[1,] 1.287352e-06 -1.956346e-07
[2,] 3.466275e-06 -5.267584e-07

, , 45

             [,1]          [,2]
[1,] 9.903034e-07 -1.504931e-07
[2,] 2.666454e-06 -4.052122e-07

, , 46

             [,1]          [,2]
[1,] 7.617970e-07 -1.157678e-07
[2,] 2.051186e-06 -3.117120e-07

, , 47

             [,1]          [,2]
[1,] 5.860171e-07 -8.905509e-08
[2,] 1.577888e-06 -2.397864e-07

, , 48

             [,1]          [,2]
[1,] 4.507973e-07 -6.850619e-08
[2,] 1.213800e-06 -1.844572e-07

, , 49

             [,1]          [,2]
[1,] 3.467787e-07 -5.269881e-08
[2,] 9.337232e-07 -1.418948e-07

, , 50

             [,1]          [,2]
[1,] 2.667617e-07 -4.053889e-08
[2,] 7.182724e-07 -1.091535e-07

, , 51

             [,1]          [,2]
[1,] 2.052081e-07 -3.118479e-08
[2,] 5.525355e-07 -8.396700e-08

portes documentation built on Jan. 13, 2021, 6:28 p.m.