# NDK_ACF

 int __stdcall NDK_ACF ( double * X, size_t N, size_t K, double * retVal )

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
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
....
}

 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_ACF ( double[] pData, UIntPtr nSize, int nLag, out double retVal )

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

Return Value

a value from NDK_RETCODE enumeration for the status of the call.

 NDK_SUCCESS operation successful Error Error Code
Parameters
 [in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in pData. [in] nLag 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 (nLag) 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, $$\hat{\rho}(0) \equiv 1.0$$
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.DLL
Examples

References
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848