# NDK_LRVAR

 int __stdcall NDK_LRVAR ( double * X, size_t N, size_t W, double * retVal )

Returns the long-run variance using a Bartlett kernel with window size k.

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 input data sample (a one/two dimensional array). [in] N is the number of observations in X. [in] w is the input Bartlett kernel window size. If omitted, the default value is the cubic root of the sample data size. [out] retVal is the calculated value of this function.
Remarks
1. The input time series data may include missing values (NaN), but they will not be included in the calculations.
2. The long-run variance is computed as follows:
$\sigma^2=\frac{1}{T}\sum_{t=k}^{T-k}\sum_{i=-k}^k w_i(x_t-\bar{x})(x_{t-i}-\bar{x})$
Where:
• $$x_{t} \in X$$  is a value from the input time series data.
• $$\bar{x}$$  is the mean of the input time series data.
• $$w_i$$ is the Bartlett kernel weight, and it is defined as follows:
• $$w_i= 1- \frac{\left | i \right |}{k+1}$$
• $$k$$ is the input window size for the Bartlett kernel.
Requirements
Examples



 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_LRVAR ( double[] pData, UIntPtr nSize, short argMenthod, ref double retVal )

Returns the long-run variance using a Bartlett kernel with window size k.

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 input data sample (a one/two dimensional array). [in] nSize is the number of observations in pData. [in] argMenthod is the input Bartlett kernel window size. If omitted, the default value is the cubic root of the sample data size. [out] retVal is the calculated value of this function.
Remarks
1. The input time series data may include missing values (NaN), but they will not be included in the calculations.
2. The long-run variance is computed as follows:
$\sigma^2=\frac{1}{T}\sum_{t=k}^{T-k}\sum_{i=-k}^k w_i(x_t-\bar{x})(x_{t-i}-\bar{x})$
Where:
• $$x_{t} \in X$$  is a value from the input time series data.
• $$\bar{x}$$  is the mean of the input time series data.
• $$w_i$$ is the Bartlett kernel weight, and it is defined as follows:
• $$w_i= 1- \frac{\left | i \right |}{k+1}$$
• $$k$$ is the input window size for the Bartlett kernel.
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