Summary of rules for identifying ARIMA
models
Identifying the order of
differencing and the constant:

Rule 1: If the series has positive autocorrelations out to a high
number
of lags, then it probably needs a higher order of differencing.

Rule 2: If the lag1 autocorrelation is zero or negative, or the
autocorrelations
are all small and patternless, then the series does not need a
higher
order of differencing. If the lag1 autocorrelation is 0.5 or more
negative,
the series may be overdifferenced. BEWARE OF OVERDIFFERENCING!!

Rule 3: The optimal order of differencing is often the order of
differencing
at which the standard deviation is lowest.

Rule 4: A model with no orders of differencing assumes that the
original series is stationary (among other things, meanreverting). A
model
with one order of differencing assumes that the original series
has a constant average trend (e.g. a random walk or SEStype model,
with
or without growth). A model with two orders of total
differencing
assumes that the original series has a timevarying trend (e.g. a
random
trend or LEStype model).

Rule 5: A model with no orders of differencing normally
includes
a constant term (which represents the mean of the series). A model with
two orders of total differencing normally does not
include
a constant term. In a model with one order of total
differencing,
a constant term should be included if the series has a nonzero average
trend.
Identifying the numbers of
AR and MA terms:

Rule 6: If the partial autocorrelation function (PACF) of the
differenced
series displays a sharp cutoff and/or the lag1 autocorrelation is positivei.e.,
if the series appears slightly "underdifferenced"then consider adding
one or more AR terms to the model. The lag beyond which the
PACF
cuts off is the indicated number of AR terms.

Rule 7: If the autocorrelation function (ACF) of the
differenced
series displays a sharp cutoff and/or the lag1 autocorrelation is negativei.e.,
if the series appears slightly "overdifferenced"then consider adding
an MA term to the model. The lag beyond which the ACF cuts off
is
the indicated number of MA terms.

Rule 8: It is possible for an AR term and an MA term to cancel each
other's
effects, so if a mixed ARMA model seems to fit the data, also try a
model
with one fewer AR term and one fewer MA termparticularly if the
parameter
estimates in the original model require more than 10 iterations to
converge.

Rule 9: If there is a unit root in the AR part of the modeli.e., if
the
sum of the AR coefficients is almost exactly 1you should reduce the
number
of AR terms by one and increase the order of differencing by
one.

Rule 10: If there is a unit root in the MA part of the modeli.e., if
the sum of the MA coefficients is almost exactly 1you should reduce
the
number of MA terms by one and reduce the order of differencing
by
one.

Rule 11: If the longterm forecasts appear erratic or unstable, there
may
be a unit root in the AR or MA coefficients.
Identifying the seasonal
part of the model:

Rule 12: If the series has a strong and consistent seasonal pattern,
then
you should use an order of seasonal differencingbut never use more
than
one order of seasonal differencing or more than 2 orders of total
differencing
(seasonal+nonseasonal).

Rule 13: If the autocorrelation at the seasonal period is
positive,
consider adding an SAR term to the model. If the
autocorrelation
at the seasonal period is negative, consider adding an SMA
term to the model. Do not mix SAR and SMA terms in the same model, and
avoid using more than one of either kind.