naginterfaces.library.tsa.uni_autocorr¶
- naginterfaces.library.tsa.uni_autocorr(x, nk)[source]¶
uni_autocorr
computes the sample autocorrelation function of a time series. It also computes the sample mean, the sample variance and a statistic which may be used to test the hypothesis that the true autocorrelation function is zero.For full information please refer to the NAG Library document for g13ab
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g13/g13abf.html
- Parameters
- xfloat, array-like, shape
The time series, , for .
- nkint
, the number of lags for which the autocorrelations are required. The lags range from to and do not include zero.
- Returns
- xmfloat
The sample mean of the input time series.
- xvfloat
The sample variance of the input time series.
- rfloat, ndarray, shape
The sample autocorrelation coefficient relating to lag , for .
- statfloat
The statistic used to test the hypothesis that the true autocorrelation function of the time series is identically zero.
- Raises
- NagValueError
- (errno )
On entry, and .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Warns
- NagAlgorithmicWarning
- (errno )
On entry, all values of are practically identical.
- Notes
In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.
The data consists of observations , for from a time series.
The quantities calculated are
The sample mean
The sample variance (for )
The sample autocorrelation coefficients of lags , where is a user-specified maximum lag, and , .
The coefficient of lag is defined as
See page 496 of Box and Jenkins (1976) for further details.
A test statistic defined as
which can be used to test the hypothesis that the true autocorrelation function is identically zero.
If is large and is much smaller than , has a distribution under the hypothesis of a zero autocorrelation function. Values of in the upper tail of the distribution provide evidence against the hypothesis;
stat.prob_chisq
can be used to compute the tail probability.Section 8.2.2 of Box and Jenkins (1976) provides further details of the use of .
- References
Box, G E P and Jenkins, G M, 1976, Time Series Analysis: Forecasting and Control, (Revised Edition), Holden–Day