| int __stdcall NDK_TESMTH | ( | double * | pData, |
| size_t | nSize, | ||
| BOOL | bAscending, | ||
| double * | alpha, | ||
| double * | beta, | ||
| double * | gamma, | ||
| int | L, | ||
| int | nHorizon, | ||
| BOOL | bOptimize, | ||
| double * | retVal | ||
| ) |
Returns the (Winters's) triple exponential smoothing estimate of the value X at time T+m.
- Returns
- status code of the operation
- Return values
-
NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
- Parameters
-
[in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of elements in pData. [in] bAscending is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)). [in] alpha is the data smoothing factor (alpha should be between zero and one (exclusive)). [in] beta is the trend smoothing factor (beta should be between zero and one (exclusive)). [in] gamma is the seasonal change smoothing factor (Gamma should be between zero and one (exclusive)). [in] L is the season length. [in] nHorizon is the forecast time horizon beyond the end of pData. If missing, a default value of 0 (latest or end of pData) is assumed. [in] bOptimize is a flag (True/False) for searching and using optimal value of the smoothing factor. If missing or omitted, optimize is assumed false. [out] retVal is the calculated value of this function.
- Remarks
-
- The triple exponential smoothing function \(F_{T+m}\) is defined as follows: \[S_1=x_1\] \[b_1=\frac{1}{L}(\frac{x_{L+1}-x_1}{L}+\frac{x_{L+2}-x_2}{L}+\frac{x_{L+3}-x_3}{L}+...+\frac{x_{L+L}-x_L}{L})\] \[S_{t>1}=\alpha \times \frac{x_t}{c_{t-L}}+(1-\alpha)(S_{t-1}+b_{t-1})\] \[b_{t>1}=\beta\times (s_t-s_{t-1})+(1-\beta)b_{t-1}\] \[c_{t>1}= \gamma \times \frac{x_t}{c_t}+(1-\gamma)c_{t-L}\] \[F_{t+m}=(s_t+m\times b_t)c_{t-L + (m-1)\pmod L} \] Where:
- \(X_t\) is the value of the time series at time t
- \(T\) is the time of the latest observation in the sample data
- \(\alpha\) is the smoothing factor
- \(\beta\) is the trend smoothing factor
- \(\gamma\) is the seasonal change smoothing factor
- \(F_{T+m}\) is the output of the algorithm at m steps past the end of the sample
- To search for the optimal values of the smoothing factors (alpha, beta and gamma), the number of non-missing observations should be greater than on seasonal length (L).
- The time series is homogeneous or equally spaced.
- The time series may include missing values (NaN) at either end.
- The triple exponential smoothing function \(F_{T+m}\) is defined as follows: \[S_1=x_1\] \[b_1=\frac{1}{L}(\frac{x_{L+1}-x_1}{L}+\frac{x_{L+2}-x_2}{L}+\frac{x_{L+3}-x_3}{L}+...+\frac{x_{L+L}-x_L}{L})\] \[S_{t>1}=\alpha \times \frac{x_t}{c_{t-L}}+(1-\alpha)(S_{t-1}+b_{t-1})\] \[b_{t>1}=\beta\times (s_t-s_{t-1})+(1-\beta)b_{t-1}\] \[c_{t>1}= \gamma \times \frac{x_t}{c_t}+(1-\gamma)c_{t-L}\] \[F_{t+m}=(s_t+m\times b_t)c_{t-L + (m-1)\pmod L} \] Where:
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
- Examples
-
| Namespace: | NumXLAPI |
| Class: | SFSDK |
| Scope: | Public |
| Lifetime: | Static |
| int NDK_TESMTH | ( | double[] | pData, |
| int | nSize, | ||
| BOOL | bAscending, | ||
| ref double | alpha, | ||
| ref double | beta, | ||
| ref double | gamma, | ||
| int | seasonLength, | ||
| int | nHorizon, | ||
| BOOL | bOptimize, | ||
| ref double | retVal | ||
| ) |
Returns the (Winters's) triple exponential smoothing estimate of the value of X at time T+m.
- Returns
- status code of the operation
- Return values
-
NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
- Parameters
-
[in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of elements in pData. [in] bAscending is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)). [in] alpha is the data smoothing factor (alpha should be between zero and one (exclusive)). [in] beta is the trend smoothing factor (beta should be between zero and one (exclusive)). [in] gamma is the seasonal change smoothing factor (Gamma should be between zero and one (exclusive)). [in] seasonLength is the season length. [in] nHorizon is the forecast time horizon beyond the end of pData. If missing, a default value of 0 (latest or end of pData) is assumed. [in] bOptimize is a flag (True/False) for searching and using optimal value of the smoothing factor. If missing or omitted, optimize is assumed false. [out] retVal is the calculated value of this function.
- Remarks
-
- The triple exponential smoothing function \(F_{T+m}\) is defined as follows: \[S_1=x_1\] \[b_1=\frac{1}{L}(\frac{x_{L+1}-x_1}{L}+\frac{x_{L+2}-x_2}{L}+\frac{x_{L+3}-x_3}{L}+...+\frac{x_{L+L}-x_L}{L})\] \[S_{t>1}=\alpha \times \frac{x_t}{c_{t-L}}+(1-\alpha)(S_{t-1}+b_{t-1})\] \[b_{t>1}=\beta\times (s_t-s_{t-1})+(1-\beta)b_{t-1}\] \[c_{t>1}= \gamma \times \frac{x_t}{c_t}+(1-\gamma)c_{t-L}\] \[F_{t+m}=(s_t+m\times b_t)c_{t-L + (m-1)\pmod L} \] Where:
- \(X_t\) is the value of the time series at time t
- \(T\) is the time of the latest observation in the sample data
- \(\alpha\) is the smoothing factor
- \(\beta\) is the trend smoothing factor
- \(\gamma\) is the seasonal change smoothing factor
- \(F_{T+m}\) is the output of the algorithm at m steps past the end of the sample
- To search for the optimal values of the smoothing factors (alpha, beta and gamma), the number of non-missing observations should be greater than on seasonal length (L).
- The time series is homogeneous or equally spaced.
- The time series may include missing values (NaN) at either end.
- The triple exponential smoothing function \(F_{T+m}\) is defined as follows: \[S_1=x_1\] \[b_1=\frac{1}{L}(\frac{x_{L+1}-x_1}{L}+\frac{x_{L+2}-x_2}{L}+\frac{x_{L+3}-x_3}{L}+...+\frac{x_{L+L}-x_L}{L})\] \[S_{t>1}=\alpha \times \frac{x_t}{c_{t-L}}+(1-\alpha)(S_{t-1}+b_{t-1})\] \[b_{t>1}=\beta\times (s_t-s_{t-1})+(1-\beta)b_{t-1}\] \[c_{t>1}= \gamma \times \frac{x_t}{c_t}+(1-\gamma)c_{t-L}\] \[F_{t+m}=(s_t+m\times b_t)c_{t-L + (m-1)\pmod L} \] Where:
- Exceptions
-
Exception Type Condition None N/A
- Requirements
-
Namespace NumXLAPI Class SFSDK Scope Public Lifetime Static Package 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
