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.

```
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,
trace = FALSE, approximation = (length(x) > 150 | frequency(x) > 12),
truncate = NULL, xreg = NULL, test = c("kpss", "adf", "pp"),
seasonal.test = c("ocsb", "ch"), allowdrift = TRUE, allowmean = TRUE,
lambda = NULL, biasadj = FALSE, parallel = FALSE, num.cores = 2,
x = y, ...)
```

y

a univariate time series

d

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

D

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

trace

If `TRUE`

, the list of ARIMA models considered will be
reported.

approximation

If `TRUE`

, estimation is via conditional sums of
squares andthe 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.

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 vector or matrix of external regressors, which
must have the same number of rows as `y`

.

test

Type of unit root test to use. See `ndiffs`

for
details.

seasonal.test

This determines which seasonal unit root test is used.
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. Ignored if NULL. Otherwise, data transformed before model is estimated.

biasadj

Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.

parallel

If `TRUE`

and `stepwise = FALSE`

, then the
specification search is done in parallel. This can give a significant
speedup on mutlicore 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`

.

Same as for `Arima`

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`

.

The number of seasonal differences is sometimes poorly chosen. If your data shows strong
seasonality, try setting `D=1`

rather than relying on the automatic selection of `D`

.

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

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

```
# NOT RUN {
fit <- auto.arima(WWWusage)
plot(forecast(fit,h=20))
# }
```

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