identify {aTSA}  R Documentation 
Identify a Time Series Model
Description
Checks the white noise and stationarity of a univariate time series, and also identifies an appropriate ARIMA model using AICC criterion.
Usage
identify(x, p = NULL, q = NULL, nlag = 6, intercept = TRUE,
stat.test = FALSE, method = c("adf", "pp", "kpss"), output = TRUE)
Arguments
x 
a numeric vector or univariate time series. 
p 
the maximum lag order for AR process. The default is 
q 
the maximum lag order for MA process. The default is 
nlag 
the lag parameter to calculate the LjungBox test statistic.
The default is 
intercept 
an intercept to be included in ARIMA model, only valid for

stat.test 
the stationary test for time series, see 
method 
the method of stationary test, only valid for 
output 
a logical value indicating to print the results in R console.
The default is 
Details
This function is similar to IDENTIFY statement in ARIMA procedure of SAS software,
which is to check the white noise and stationarity for a univariate time
series. The white noise check is accomplished by using Box.test
in stats
package, with the default method type = "LjungBox"
.
The stationary check uses the stationary.test
implemented in this package.
The AICC criterion (Burnham and Anderson (2002)) is used to identify an optimal model which has the minimum AICC value. The AICC is defined as
AICC = AIC + 2k(k+1)/(nk1),
where AIC = 2k  2log(Loglik)
which is called Akaike information criterion
(Akaike (1974)). Here,
k,n
are the number of estimated parameters and observations, respectively.
Loglik
is the maximized value of the likelihood function for the model.
Four plots are made: plot of original data, ACF plot, PACF plot and p.value of white noise check.
Value
A list with class "identify
" containing the following components:
WNcheck 
a matrix with three columns for results of white noise check for each lag. 
aicc 
the minimum AICC value, only available for 
min.p 
the optimal order 
min.q 
the optimal order 
stnt.test 
a list of stationary test results with three components. See

Note
Missing values are removed before the analysis.
Author(s)
Debin Qiu
References
Akaike, H. (1974), "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716723.
Box, G. E. P. and Pierce, D. A. (1970), Distribution of residual correlations in autoregressiveintegrated moving average time series models. Journal of the American Statistical Association, 65, 15091526.
Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical InformationTheoretic Approach (2nd ed.), SpringerVerlag
Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika 65, 297303.
Harvey, A. C. (1993) Time Series Models. 2nd Edition, Harvester Wheatsheaf, NY, pp. 44, 45.
Examples
x < arima.sim(list(order = c(2,0,0),ar = c(0.2,0.4)),n = 100)
identify(x) # white noise check
identify(x,stat.test = TRUE) # white noise and stationarity check
identify(x,p = 3,q = 2) # white noise check and optimal model identification.