NDK_ACF

Calculates the sample autocorrelation function (ACF) of a stationary time series.

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	Operation unsuccessful. See Macros for full list.

Parameters

[in]	X	is the univariate time series data (a one dimensional array).
[in]	N	is the number of observations in X.
[in]	K	is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.).
[out]	retVal	is the calculated sample autocorrelation value.

Remarks

1. The time series is homogeneous or equally spaced.

2. The time series may include missing values (NaN) at either end.

3. The lag order (k) must be less than the time series size or else an error value NDK_FAILED is returned.

4. The ACF values are bound between -1 and 1, inclusive.

5. The sample autocorrelation is computed as:

• \(\hat{\rho}(h)=\frac{\sum_{k=h}^T{(y_{k}-\bar y)(y_{k-h}-\bar y)}}{\sum_{k=h}^T(y_{k}-\bar y)^2} \)
  where:
  • \(y_{t}\)  is the value of the time series at time t.
  • \(h\) is the lag order.
  • \(T\) is the number of non-missing values in the time series data.
  • \(\bar y\) is the sample average/mean of the time series.

6. Special cases: By definition, \(\hat{\rho}(0) \equiv 1.0\)

Requirements

Header	SFSDK.H
Library	SFSDK.LIB
DLL	SFSDK.DLL

Examples

#include "SFMacros.h"
#include "SFSDK.h"

// Input time series: 110 observation 
double data[110]={0.23, 0.24, 0.45, ..., 0.95}

int nRet = NDK_FAILED;
double retVal = -2.0f;
nRet = NDK_ACF(data, 110, 1, &retVal);
if( nRet < NDK_SUCCESS){
    // Error occured
    // Call NDK_MSG to retrieve description of the error, and write it to the log file
    ....
}