Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: times
See also: msarimacond msarimamodel

Quantlet: msarimaconvert
Description: Expands a multiplicative seasonal ARIMA model with k coefficients---specified with the quantlet msarimamodel---to an ordinary ARMA model.

Reference(s):

Usage: {y,phiconv,thetaconv,k} = msarimaconvert(x,msarimamodelOut)
Input:
x T x 1 vector of the observed time series
msarimamodelOut list that specifies the original multiplicative seasonal ARIMA model. Use the quantlet msarimamodel to specify your original model. That quantlet produces automatically the requested list.
Output:
y (T-s*d_2-d_1) x 1 vector of the differenced time series x
phiconv (s*P+p+1) x 1 vector with the coefficients of the expanded AR part. Some of the expanded coefficients might be 0. The first entry is 1.
thetaconv (s*Q+q+1) x 1 vector with the coefficients of the expanded MA part. Some of the expanded coefficients might be 0. The first entry is 1.
k scalar, number of coefficients of the original specification.

Note:

Example:
library("times")           ; loads the quantlets of library times
dax  = read("dax")         ; monthly DAX 1979:1-2000:10
arma = list(4,1,0.2,0.1)   ; ordinary ARMA(4,1) part, where only the fourth AR lag is different from zero
; with phi_4 = 0.2 and theta_1 = 0.1
season = list(4,(1|2),0,(0.2|0.1))                   ; season is quarterly, seasonal AR lags phi_s,1 = 0.2 and phi_s,2 = 0.1
msarimamodelOut = msarimamodel((1|1),arma,season)    ;sets the model
{y,phiconv,thetaconv}= msarimaconvert(log(dax),msarimamodelOut)
; expands the model into an ordinary AR(13) for the returns of the dax
phiconv                    ; converted AR polynomial
thetaconv                  ; converted MA polynomial

Result:
Converts a SARIMA(4,1,1)x(4,2,0,0) model into  an ordinary AR model.
The coefficients are phi_4 = 0.2, phi_s,1 = 0.2, phi_s,2 = 0.1 and
theta_1 = 0.1. Thus, the original model is:

(1 - 0.2 L^4)(1 - 0.2 L^4 - 0.1 L^8)(1-L)dax  = (1 + 0.1 L) v_t

The expanded model is:

(1 - 0.4 L^4 - 0.06 L^8 + 0.02 L^12)(1-L)dax = (1 + 0.1 L) v_t

phiconv shows the converted AR polynomial and thetaconv the converted MA polynomial.

Contents of phiconv
[ 1,]        1
[ 2,]        0
[ 3,]        0
[ 4,]        0
[ 5,]     -0.4
[ 6,]        0
[ 7,]        0
[ 8,]        0
[ 9,]    -0.06
[10,]        0
[11,]        0
[12,]        0
[13,]     0.02

Contents of thetaconv
[1,]        1
[2,]      0.1



Author: R. Chen, R. Schulz, 20020408
(C) MD*TECH Method and Data Technologies, 05.02.2006