# identify

##### Identify a Time Series Model

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
`NULL`

. - q
- the maximum lag order for MA process. The default is
`NULL`

. - nlag
- the lag parameter to calculate the Ljung-Box test statistic.
The default is
`6`

. - intercept
- an intercept to be included in ARIMA model, only valid for
`p`

> 0 or`q`

> 0. The default is`TRUE`

. - stat.test
- the stationary test for time series, see
`stationary.test`

for more details. The default is`FALSE`

. - method
- the method of stationary test, only valid for
`stat.test = TRUE`

. - output
- a logical value indicating to print the results in R console.
The default is
`TRUE`

.

##### 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 = "Ljung-Box"`

.
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 $$AICC = AIC + 2k(k+1)/(n-k-1),$$ 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 `p > 0`

or`q > 0`

.min.p the optimal order `p`

for AR process, only available for`p > 0`

or`q > 0`

.min.q the optimal order `q`

for AR process, only available for`p > 0`

or`q > 0`

.stnt.test a list of stationary test results with three components. See `stationary.test`

for more details.

##### Note

Missing values are removed before the analysis.

##### References

Akaike, H. (1974), "A new look at the statistical model identification", *IEEE
Transactions on Automatic Control*, 19 (6): 716-723.

Box, G. E. P. and Pierce, D. A. (1970), Distribution of residual correlations
in autoregressive-integrated moving average time series models. *Journal
of the American Statistical Association*, 65, 1509-1526.

Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), Springer-Verlag

Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series
models. *Biometrika* 65, 297-303.

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.
```

*Documentation reproduced from package aTSA, version 3.1.2, License: GPL-2 | GPL-3*