Summary of rules for identifying ARIMA
Identifying the order of
differencing and the constant:
Rule 1: If the series has positive autocorrelations out to a high
of lags, then it probably needs a higher order of differencing.
Rule 2: If the lag-1 autocorrelation is zero or negative, or the
are all small and patternless, then the series does not need a
order of differencing. If the lag-1 autocorrelation is -0.5 or more
the series may be overdifferenced. BEWARE OF OVERDIFFERENCING!!
Rule 3: The optimal order of differencing is often the order of
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, mean-reverting). A
with one order of differencing assumes that the original series
has a constant average trend (e.g. a random walk or SES-type model,
or without growth). A model with two orders of total
assumes that the original series has a time-varying trend (e.g. a
trend or LES-type model).
Rule 5: A model with no orders of differencing normally
a constant term (which represents the mean of the series). A model with
two orders of total differencing normally does not
a constant term. In a model with one order of total
a constant term should be included if the series has a non-zero average
Identifying the numbers of
AR and MA terms:
Rule 6: If the partial autocorrelation function (PACF) of the
series displays a sharp cutoff and/or the lag-1 autocorrelation is positive--i.e.,
if the series appears slightly "underdifferenced"--then consider adding
one or more AR terms to the model. The lag beyond which the
cuts off is the indicated number of AR terms.
Rule 7: If the autocorrelation function (ACF) of the
series displays a sharp cutoff and/or the lag-1 autocorrelation is negative--i.e.,
if the series appears slightly "overdifferenced"--then consider adding
an MA term to the model. The lag beyond which the ACF cuts off
the indicated number of MA terms.
Rule 8: It is possible for an AR term and an MA term to cancel each
effects, so if a mixed AR-MA model seems to fit the data, also try a
with one fewer AR term and one fewer MA term--particularly if the
estimates in the original model require more than 10 iterations to
Rule 9: If there is a unit root in the AR part of the model--i.e., if
sum of the AR coefficients is almost exactly 1--you should reduce the
of AR terms by one and increase the order of differencing by
Rule 10: If there is a unit root in the MA part of the model--i.e., if
the sum of the MA coefficients is almost exactly 1--you should reduce
number of MA terms by one and reduce the order of differencing
Rule 11: If the long-term forecasts appear erratic or unstable, there
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,
you should use an order of seasonal differencing--but never use more
one order of seasonal differencing or more than 2 orders of total
Rule 13: If the autocorrelation at the seasonal period is
consider adding an SAR term to the model. If the
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.