Returns best ARIMA model according to either AIC, AICc or BIC value. The function conducts a search over possible model within the order constraints provided.

## Usage

```
auto.arima(
y,
d = NA,
D = NA,
max.p = 5,
max.q = 5,
max.P = 2,
max.Q = 2,
max.order = 5,
max.d = 2,
max.D = 1,
start.p = 2,
start.q = 2,
start.P = 1,
start.Q = 1,
stationary = FALSE,
seasonal = TRUE,
ic = c("aicc", "aic", "bic"),
stepwise = TRUE,
nmodels = 94,
trace = FALSE,
approximation = (length(x) > 150 | frequency(x) > 12),
method = NULL,
truncate = NULL,
xreg = NULL,
test = c("kpss", "adf", "pp"),
test.args = list(),
seasonal.test = c("seas", "ocsb", "hegy", "ch"),
seasonal.test.args = list(),
allowdrift = TRUE,
allowmean = TRUE,
lambda = NULL,
biasadj = FALSE,
parallel = FALSE,
num.cores = 2,
x = y,
...
)
```

## Arguments

- y
a univariate time series

- d
Order of first-differencing. If missing, will choose a value based on

`test`

.- D
Order of seasonal-differencing. If missing, will choose a value based on

`season.test`

.- max.p
Maximum value of p

- max.q
Maximum value of q

- max.P
Maximum value of P

- max.Q
Maximum value of Q

- max.order
Maximum value of p+q+P+Q if model selection is not stepwise.

- max.d
Maximum number of non-seasonal differences

- max.D
Maximum number of seasonal differences

- start.p
Starting value of p in stepwise procedure.

- start.q
Starting value of q in stepwise procedure.

- start.P
Starting value of P in stepwise procedure.

- start.Q
Starting value of Q in stepwise procedure.

- stationary
If

`TRUE`

, restricts search to stationary models.- seasonal
If

`FALSE`

, restricts search to non-seasonal models.- ic
Information criterion to be used in model selection.

- stepwise
If

`TRUE`

, will do stepwise selection (faster). Otherwise, it searches over all models. Non-stepwise selection can be very slow, especially for seasonal models.- nmodels
Maximum number of models considered in the stepwise search.

- trace
If

`TRUE`

, the list of ARIMA models considered will be reported.- approximation
If

`TRUE`

, estimation is via conditional sums of squares and the information criteria used for model selection are approximated. The final model is still computed using maximum likelihood estimation. Approximation should be used for long time series or a high seasonal period to avoid excessive computation times.- method
fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood. Can be abbreviated.

- truncate
An integer value indicating how many observations to use in model selection. The last

`truncate`

values of the series are used to select a model when`truncate`

is not`NULL`

and`approximation=TRUE`

. All observations are used if either`truncate=NULL`

or`approximation=FALSE`

.- xreg
Optionally, a numerical vector or matrix of external regressors, which must have the same number of rows as

`y`

. (It should not be a data frame.)- test
Type of unit root test to use. See

`ndiffs`

for details.- test.args
Additional arguments to be passed to the unit root test.

- seasonal.test
This determines which method is used to select the number of seasonal differences. The default method is to use a measure of seasonal strength computed from an STL decomposition. Other possibilities involve seasonal unit root tests.

- seasonal.test.args
Additional arguments to be passed to the seasonal unit root test. See

`nsdiffs`

for details.- allowdrift
If

`TRUE`

, models with drift terms are considered.- allowmean
If

`TRUE`

, models with a non-zero mean are considered.- lambda
Box-Cox transformation parameter. If

`lambda="auto"`

, then a transformation is automatically selected using`BoxCox.lambda`

. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.- biasadj
Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.

- parallel
If

`TRUE`

and`stepwise = FALSE`

, then the specification search is done in parallel. This can give a significant speedup on multicore machines.- num.cores
Allows the user to specify the amount of parallel processes to be used if

`parallel = TRUE`

and`stepwise = FALSE`

. If`NULL`

, then the number of logical cores is automatically detected and all available cores are used.- x
Deprecated. Included for backwards compatibility.

- ...
Additional arguments to be passed to

`arima`

.

## Value

Same as for `Arima`

## Details

The default arguments are designed for rapid estimation of models for many time series.
If you are analysing just one time series, and can afford to take some more time, it
is recommended that you set `stepwise=FALSE`

and `approximation=FALSE`

.

Non-stepwise selection can be slow, especially for seasonal data. The stepwise algorithm outlined in Hyndman & Khandakar (2008) is used except that the default method for selecting seasonal differences is now based on an estimate of seasonal strength (Wang, Smith & Hyndman, 2006) rather than the Canova-Hansen test. There are also some other minor variations to the algorithm described in Hyndman and Khandakar (2008).

## References

Hyndman, RJ and Khandakar, Y (2008) "Automatic time series
forecasting: The forecast package for R", *Journal of Statistical
Software*, **26**(3).

Wang, X, Smith, KA, Hyndman, RJ (2006) "Characteristic-based clustering
for time series data", *Data Mining and Knowledge Discovery*,
**13**(3), 335-364.