Purpose
An autocorrelation
is the correlation of a series with itself, shifted by a particular lag of k
observations. The plot of autocorrelations for various lags is a crucial tool
for determining an appropriate model for ARIMA analysis.
Preparations
Run
Statistics→Time Series/Forecasting→Autocorrelation
and Partial Autocorrelation....
Results
The computations of the autocorrelation coefficients
r_{k} follow the standard formulas, as
described in most time series references (e.g., Box & Jenkins, see
Bibliography).
Standard error of rk.
Under the assumption that the true moving average process in the series
is of the order k1, then the approximate standard error of rk
is defined as: StdErr(rk)
=
Ö{(1/N) * [1+2*S(ri2
)]} (for i = 1 to k1). Here, N
is the number of observations in the series. However, under the assumption that
the series is a white noise process, that is, that all autocorrelations are
equal to zero, the standard error of rk
is defined as: StdErr(rk)
=
Ö{(1/N) * [(Nk)/(N+2)]}.
Select the White noise standard errors
check box from Advanced Options to compute
the standard errors in this manner.
BoxLjung Q. At a given l ag k the BoxLjung Q statistic is defined by:
Qk
= n*(n+2)*S[ri2
/(ni)] (for i = 1 to k). When the number of observations is large, then
the Q statistic has a ChiSquare distribution with kpq degrees of freedom,
where p and q are the number of autoregressive and moving average parameters,
respectively.
A partial autocorrelation is the correlation of a series
with itself, shifted by a particular lag of k observations, and controlling for
the correlations for all shifts of 1 through k1. The plot of partial
autocorrelations for various lags is a crucial tool for determining an
appropriate model for ARIMA analysis. The computations of the partial
autocorrelation coefficients
fk
follow the standard formulas, as described in most time series references (e.g.,
Box & Jenkins, 1976).
Standard error of
fk.
Under the assumption that the true autoregressive process in the series
is of order p £ k1, then
the approximate standard error of
fk
is defined as: StdErr(fk)
=
Ö(1/N). Here
N is the number of observations in the
series.
