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. |
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. |
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
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