NAG Library Function Document

nag_tsa_auto_corr (g13abc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}\left[\mathbf{nx}\right]$ – const doubleInput

On entry: the time series, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

2:    $\mathbf{nx}$ – IntegerInput

On entry: the number of values, $n$, in the time series.

Constraint: $\mathbf{nx}>1$.

3:    $\mathbf{nk}$ – IntegerInput

On entry: the number of lags, $K$, for which the autocorrelations are required. The lags range from 1 to $K$ and do not include zero.

Constraint: $0<\mathbf{nk}<\mathbf{nx}$.

4:    $\mathbf{mean}$ – double *Output

On exit: the sample mean of the input time series.

5:    $\mathbf{var}$ – double *Output

On exit: the sample variance of the input time series.

6:    $\mathbf{r}\left[\mathbf{nk}\right]$ – doubleOutput

On exit: the sample autocorrelation coefficient relating to lag $\mathit{k}$, for $\mathit{k}=1,2,\dots ,K$.

7:    $\mathbf{stat}$ – double *Output

On exit: the statistic used to test the hypothesis that the true autocorrelation function of the time series is identically zero.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_LE

On entry, $\mathbf{nx}=〈\mathit{\text{value}}〉$ while $\mathbf{nk}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{nx}>\mathbf{nk}$.

NE_INT_ARG_LE

On entry, $\mathbf{nk}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nk}>0$.

On entry, $\mathbf{nx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nx}>1$.

NE_TIME_SERIES_IDEN

On entry, all values of x are practically identical, giving zero variance. In this case r and stat are undefined on exit.

7

Accuracy

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Parallelism and Performance

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Further Comments

10

Example

10.1

Program Text

Program Text (g13abce.c)

10.2

Program Data

Program Data (g13abce.d)

10.3

Program Results

Program Results (g13abce.r)