Usage: |
A = ariols(y,p,d,const{,rcheck{,pcheck{,msc}}})
|
Input: |
| y | input series length n
|
| p | integer, order of autorregresive process
|
| d | integer, order of differences
|
| const | string, a constant is calculated if const = "constant"
|
| 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
|
| pcheck | optional string, parameter diagnostic statistics
are computed if pcheck = "pcheck"
|
| msc | optional string, if msc = "msc" model selection criteria
are computed
|
Output: |
| A.b | estimated coefficients. If const = "constant", the
first element represents the constant term. |
| A.bst | asymptotic standard deviations of estimated parameters. |
| A.wnv | estimated variance of the innovations. |
| A.checkr | if rcheck="prcheck", list containing the residual
diagnostics:
1. res = n-p 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, and the first p
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=list containing the residuals. |
| A.checkp | if pcheck="pcheck", list containing the parameter
diagnostics:
1. est = string that informs if the necessary stationary
condition (phi1+phi2+...+phip) holds or not. If the
estimated values are stationary, it takes value 0.
2. bt = p x 2 or 1+p x 2 matrix of t-statistics and p-values
(asymp. normal) for testing parameter significance and
3. bvar = variance covariance matrix of parameter estimates.
Otherwise, checkp=0. |
| 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. |