| Usage: |
A = arima11(y,d,const{,rcheck{,pcheck{,msc}}})
|
| Input: |
| y | input series of length n
|
| d | integer, order of differences
|
| const | string, a constant is included 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" the model selection criteria
are computed.
|
| Output: |
| A.b | estimated parameters. If const="constant",
the first element represents the estimated mean of a stationary
ARMA(1,1) process. |
| A.bst | asymptotic standard deviations. If const="constant",
the first element is the asymptotic standard deviation
of the mean of a stationary ARMA(1,1) process. |
| 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 statistics with p-values and pacf. The
p-values are computed for M>2, and the first 2
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.checkp | if pcheck="pcheck", list containing the parameter
diagnostics:
1. est = string that informs if the estimated process is
not stationary (|phi|>=1). If the stationarity condition holds
the string est takes value 0.
2. inv = string that informs if the estimated process is
not invertible (|theta|>=1). If the invertibility condition holds
the string inv takes value 0.
3. bt = 2 x 2 or 3 x 2 matrix of t-statistics and p-values
(normal cdf) for testing ARMA parameter significance.
If const = "constant", the first element represents the statistic
for testing zero mean ARMA(1,1) process
4. bvar = covariance matrix of ARMA 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. |