| Library: | times |
| See also: | armacls armalik ariols arima11 arimaf |
| Quantlet: | arimacls | |
| Description: | Estimation of ARIMA(p,d,q) models by conditional least squares, where residuals diagnostics and model selection criteria are given. Residuals diagnostics include their timeplot with two-standard error bounds, correlograms and the Ljung-Box statistic with p-values. Computed model selection criteria are AIC and BIC. |
| Usage: | A = arimacls(y,p,d,q,const{,rcheck{,msc}}) | |
| Input: | ||
| y | input series length n | |
| p | integer, order of autorregressive process | |
| d | integer, order of differences | |
| q | integer, order of moving average process | |
| const | string, if const = "constant" a constant is estimated | |
| rcheck | optional string, residual diagnostic checking. if rcheck = "rcheck", residual diagnostics are calculated and plots of the residuals and the corresponding correlograms are displayed, if rcheck = "prcheck", the plots are omitted | |
| msc | optional string, if msc = "msc" model selection criteria are computed. | |
| Output: | ||
| A.b | gives the estimated coefficients. If const = "constant", the first element is the estimated constant term | |
| A.wnv | estimated variance of the innovations | |
| A.conver | list containing: 1. the number of iterations, 2. 0-1 scalar indicating convergence | |
| A.checkr | if rcheck = "prcheck", a list is given that contains residuals diagnostics: 1. res = (n-max(p,q)) x 1 vector of residuals (i.e., one step ahead prediction errors computed with estimated parameters), 2. stat = scalar with statistic for testing H0: zero mean innovations (asymptotically normal under H0) and 3. acfQ = 30 x 4 matrix with the residuals acf, Ljung-Box statistic with p-values and pacf. The p-values are computed for M>p+q, and the first p+q values are filled with zeros. if rcheck = "rcheck", the output contains all of the above mentioned residual diagnostics and plots additionally the residuals and their acf and pacf (correlograms) Otherwise, checkr is a list containing the residuals. | |
| A.ic | if msc = "msc", 2 x 1 vector containing two model selection criteria: the Akaike Information Criterion, AIC, and the Schwarz Information Criterion, SIC. Otherwise, ic = 0. | |
; Example 1: nonzero mean process, estimation and residuals diagnostics
library("times") ; loads the times library Qs
ma = #(0.7,-0.2) ; coefficients of the MA(2) process
randomize(33) ; sets the seed
z = genarma(0,ma,normal(300)) + 3
; z is a MA(2) series with mean = 3
; innovations are generated from NID(0,1)
A = arimacls(z,0,0,2,"constant","prcheck")
A.b ; estimated coefficients
A.wnv ; estimated residual variance
A.checkr.stat ; test for zero-mean residuals
A.checkr.acfQ[3:10|25,2:3] ; Ljung-Box statistic with p-values
Contents of b [1,] 2.9423 [2,] 0.71713 [3,] -0.16703 Contents of wnv [1,] 1.0486 Contents of stat [1,] -0.026312 Contents of _tmp [1,] 1.8504 0.17373 [2,] 2.8827 0.23661 [3,] 3.3295 0.34355 [4,] 3.3307 0.50409 [5,] 4.0214 0.54634 [6,] 4.6462 0.58993 [7,] 6.8113 0.44879 [8,] 6.8421 0.55376 [9,] 25.598 0.32019
; Example 2: zero mean process, estimation and model selection criteria
library("times") ; loads the times library Qs
ar = #(0.7,-0.2) ; coefficients of the AR(2) process
randomize(33) ; sets the seed
z = genarma(ar,0,normal(300))
; z is an AR(2) series with mean = 0
; innovations are generated from NID(0,1);
A = arimacls(z,2,0,0,"noconstant","0","msc")
A.checkr.res[1] ; first residual
A.ic ; AIC(first row) and BIC(second row)
Contents of _tmp [1,] -0.071662 Contents of ic [1,] 0.058868 [2,] 0.08368