| int __stdcall NDK_INTEG | ( | double * | X, |
| size_t | N, | ||
| size_t | S, | ||
| size_t | D, | ||
| double * | X0, | ||
| size_t | N0 | ||
| ) |
Returns an array of cells for the integrated time series (inverse operator of NDK_DIFF).
- Returns
- status code of the operation
- Return values
-
NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
- Parameters
-
[in,out] X is the univariate time series data (a one dimensional array). [in] N is the number of observations in X. [in] S is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.). [in] D is the number of repeated differencing (e.g. d=0 (none), d=1 (difference once), 2=(difference twice), etc.). [in] X0 is the initial (un-differenced) univariate time series data (a one dimensional array). If missing (i.e. NULL), zeros are assumed. [in] N0 is the number of observations in X0.
- Remarks
-
- The input (differenced) time series (i.e. Y) is defined as follow: \[ Y_t=\left(1-L^k\right)^d X_t\] Where:
- \(\left[Y_t\right]\) is the differenced time series.
- \(\left[X_t\right]\) is the input time series.
- \(L\) is the lag (backward shift or backshift) operator.
- \(k\) is the seasonal difference order.
- \(d\) is the number of repeated differencing.
- The initial values array is assumed to end at the last non-missing value in the difference array start
- If the difference cell range includes missing values at the beginning, the result array will substute the initial values for missing ones; as we assume the initial values cover up to 1st non-missing value.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. NaN) at either end.
- The integral transform operator requires an SxD points in the initial time series (i.e. X0). If X0 is missing or has fewer points, points with zeros values are appended.
- The time order (i.e. ascending or descending) for the initial (un-differenced) time series X0) is assumed the same as the differenced time series (Y).
- Similar to the DIFF operator, INTG can be cascaded (i.e. INTG(INTG(INTG...)))), but care must be taken when you specify the initial time series for each level.
- The lag order (i.e. k) must be non-negative and smaller than the time series size. \[ 0 \leq K \leq T-1 \]
- The input (differenced) time series (i.e. Y) is defined as follow: \[ Y_t=\left(1-L^k\right)^d X_t\] Where:
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
- Examples
-
| Namespace: | NumXLAPI |
| Class: | SFSDK |
| Scope: | Public |
| Lifetime: | Static |
| int NDK_INTEG | ( | double[] | data, |
| UIntPtr | nSize, | ||
| UIntPtr | nLag, | ||
| UIntPtr | nDifference, | ||
| double[] | pX0, | ||
| UIntPtr | nX0Len | ||
| ) |
Returns an array of cells for the integrated time series (inverse operator of NDK_DIFF).
- Returns
- status code of the operation
- Return values
-
NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
- Parameters
-
[in,out] data is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in data. [in] nLag is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.). [in] nDifference is the number of repeated differencing (e.g. d=0 (none), d=1 (difference once), 2=(difference twice), etc.). [in] pX0 is the initial (un-differenced) univariate time series data (a one dimensional array). If missing (i.e. NULL), zeros are assumed. [in] nX0Len is the number of observations in pX0.
- Remarks
-
- The input (differenced) time series (i.e. Y) is defined as follow: \[ Y_t=\left(1-L^k\right)^d X_t\] Where:
- \(\left[Y_t\right]\) is the differenced time series.
- \(\left[X_t\right]\) is the input time series.
- \(L\) is the lag (backward shift or backshift) operator.
- \(k\) is the seasonal difference order.
- \(d\) is the number of repeated differencing.
- The initial values array is assumed to end at the last non-missing value in the difference array start
- If the difference cell range includes missing values at the beginning, the result array will substute the initial values for missing ones; as we assume the initial values cover up to 1st non-missing value.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. NaN) at either end.
- The integral transform operator requires an SxD points in the initial time series (i.e. pX0). If pX0 is missing or has fewer points, points with zeros values are appended.
- The time order (i.e. ascending or descending) for the initial (un-differenced) time series pX0) is assumed the same as the differenced time series (Y).
- Similar to the DIFF operator, INTG can be cascaded (i.e. INTG(INTG(INTG...)))), but care must be taken when you specify the initial time series for each level.
- The lag order (i.e. k) must be non-negative and smaller than the time series size. \[ 0 \leq K \leq T-1 \]
- The input (differenced) time series (i.e. Y) is defined as follow: \[ Y_t=\left(1-L^k\right)^d X_t\] Where:
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.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
