# identify

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##### 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:
• WNchecka matrix with three columns for results of white noise check for each lag.
• aiccthe minimum AICC value, only available for p > 0 or q > 0.
• min.pthe optimal order p for AR process, only available for p > 0 or q > 0.
• min.qthe optimal order q for AR process, only available for p > 0 or q > 0.
• stnt.testa 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.

• identify
##### 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

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