Package 'decompML'

CEEMDAN Based Auto Regressive Integrated Moving Average Model

Description

The ceemdanARIMA function gives forecasted value of CEEMDAN based Auto Regressive Integrated Moving Average Model with different forecasting evaluation criteria.

Usage

ceemdanARIMA(data, stepahead = 10,
num.IMFs = emd_num_imfs(length(data)),
  s.num = 4L, num.sift = 50L, ensem.size = 250L, noise.st = 0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the ceemdan procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

This function firstly, decompose the nonlinear and nonstationary time series into several independent intrinsic mode functions (IMFs) and one residual component (Huang et al., 1998). Secondly, Auto Regressive Integrated Moving Average is used to forecast these IMFs and residual component individually. Finally, the prediction results of all IMFs including residual are aggregated to form the final forecasted value for given input time series.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinalceemdanARIMA_forecast	Final forecasted value of the ceemdan based ARIMA model. It is obtained by combining the forecasted value of all individual IMF.
MAE_ceemdanARIMA	Mean Absolute Error (MAE) for ceemdan based ARIMA model.
MAPE_ceemdanARIMA	Mean Absolute Percentage Error (MAPE) for ceemdan based ARIMA model.
rmse_ceemdanARIMA	Root Mean Square Error (RMSE) for ceemdan based ARIMA model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble CEEMDAN: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998) The CEEMDAN and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Jha, G.K. and Sinha, K. (2014) Auto Regressive Integrated Moving Averages for time series prediction: An application to the monthly wholesale price of oilseeds in India. Neural Computing and Applications, 24, 563–571.

See Also

eemdARIMA, emdARIMA

Examples

data("Data_Maize")
ceemdanARIMA(Data_Maize)

---

Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise Based ELM Model

Description

The ceemdanELM function computes forecasted value with different forecasting evaluation criteria for Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise based Extreme Learning Machine model.

Usage

ceemdanELM(data, stepahead=10,
num.IMFs=emd_num_imfs(length(data)),
s.num=4L, num.sift=50L, ensem.size=250L, noise.st=0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

Some useless IMFs are generated in EMD and EEMD, which degrades performance of these algorithms. Therefore, reducing the number of these useless IMFs is advantageous for improving the computation efficiency of these techniques, Torres et al.(2011) proposed CEEMDAN. Fewer IMFs may be generated on the premise of successfully separating different components of a series by using this algorithm, which can reduce the computational cost.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set is used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF
FinalceemdanELM_forecast	Final forecasted value of the ceemdanELM model.It is obtained by combining the forecasted value of all individual IMF.
MAE_ceemdanELM	Mean Absolute Error (MAE) for ceemdanELM model.
MAPE_ceemdanELM	Mean Absolute Percentage Error (MAPE) for ceemdanELM model.
rmse_ceemdanELM	Root Mean Square Error (RMSE) for ceemdanELM model.

References

Huang, G.B., Zhu, Q.Y. and Siew, C.K. (2006). Extreme learning machine: theory and applications. Neurocomputing, 70, 489–501.

Torres, M.E., Colominas, M.A., Schlotthauer, G. and Flandrin, P. (2011) A complete ensemble empirical mode decomposition with adaptive noise. In 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 4144–4147). IEEE.

Wu, Z. and Huang, N.E. (2009) Ensemble empirical mode decomposition: a noise assisted data analysis method. Advances in adaptive data analysis, 1(1), 1–41.

See Also

emdELM, eemdELM

Examples

data("Data_Maize")
ceemdanELM(Data_Maize)

---

CEEMDAN Based Time Delay Neural Network Model

Description

The ceemdanTDNN function computes forecasted value for Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise Based Time Delay Neural Network Model with different forecasting evaluation criteria.

Usage

ceemdanTDNN(data, stepahead=10,
num.IMFs=emd_num_imfs(length(data)),
s.num=4L, num.sift=50L, ensem.size=250L, noise.st=0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

Torres et al.(2011) proposed Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). This algorithm generates a Fewer IMFs on the premise of successfully separating different components of a series, which can reduce the computational cost.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF
FinalCEEMDANTDNN_forecast	Final forecasted value of the CEEMDAN based TDNN model. It is obtained by combining the forecasted value of all individual IMF.
MAE_CEEMDANTDNN	Mean Absolute Error (MAE) for CEEMDAN based TDNN model.
MAPE_CEEMDANTDNN	Mean Absolute Percentage Error (MAPE) for CEEMDAN based TDNN model.
rmse_CEEMDANTDNN	Root Mean Square Error (RMSE) for CEEMDAN based TDNN model.

References

Torres, M.E., Colominas, M.A., Schlotthauer, G. and Flandrin, P. (2011) A complete ensemble empirical mode decomposition with adaptive noise. In 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 4144–4147). IEEE.

Wu, Z. and Huang, N.E. (2009) Ensemble empirical mode decomposition: a noise assisted data analysis method. Advances in adaptive data analysis, 1(1), 1–41.

See Also

emdTDNN, eemdTDNN

Examples

data("Data_Maize")
ceemdanTDNN(Data_Maize)

---

Monthly International Maize Price

Description

Monthly international Maize price from Janurary 2001 to December 2021.

Usage

data("Data_Maize")

Format

A time series data with 252 observations.

price

a time series

Details

Dataset contains 252 observations of monthly international Maize price. It is obtained from World Bank "Pink sheet".

Source

https://www.worldbank.org/en/research/commodity-markets

References

https://www.worldbank.org/en/research/commodity-markets

Examples

data(Data_Maize)

---

Ensemble Empirical Mode Decomposition Based Auto Regressive Integrated Moving Average Model

Description

The eemdARIMA function gives forecasted value of Ensemble Empirical Mode Decomposition based Auto Regressive Integrated Moving Average Model with different forecasting evaluation criteria.

Usage

eemdARIMA(data, stepahead = 10,
num.IMFs = emd_num_imfs(length(data)),
s.num = 4L, num.sift = 50L, ensem.size = 250L, noise.st = 0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the eemd procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

This function firstly, decompose the nonlinear and nonstationary time series into several independent intrinsic mode functions (IMFs) and one residual component (Huang et al., 1998). Secondly, Auto Regressive Integrated Moving Average is used to forecast these IMFs and residual component individually. Finally, the prediction results of all IMFs including residual are aggregated to form the final forecasted value for given input time series.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinaleemdARIMA_forecast	Final forecasted value of the eemd based ARIMA model. It is obtained by combining the forecasted value of all individual IMF.
MAE_eemdARIMA	Mean Absolute Error (MAE) for eemd based ARIMA model.
MAPE_eemdARIMA	Mean Absolute Percentage Error (MAPE) for eemd based ARIMA model.
rmse_eemdARIMA	Root Mean Square Error (RMSE) for eemd based ARIMA model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble Ensemble Empirical Mode Decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998) The Ensemble Empirical Mode Decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Jha, G.K. and Sinha, K. (2014) Auto Regressive Integrated Moving Averages for time series prediction: An application to the monthly wholesale price of oilseeds in India. Neural Computing and Applications, 24, 563–571.

See Also

eemdARIMA, ceeemdanARIMA

Examples

data("Data_Maize")
eemdARIMA(Data_Maize)

---

Ensemble Empirical Mode Decomposition Based ELM Model

Description

The eemdELM function computes forecasted value with different forecasting evaluation criteria for Ensemble Empirical Mode Decomposition based Extreme Learning Machine model.

Usage

eemdELM(data, stepahead=10,
num.IMFs=emd_num_imfs(length(data)), s.num=4L,
num.sift=50L, ensem.size=250L, noise.st=0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

To overcome the problem of EMD (i.e. mode mixing), Ensemble Empirical Mode Decomposition (EEMD) method was developed by Wu and Huang (2009), which significantly reduces the chance of mode mixing and represents a substantial improvement over the original EMD.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set is used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinaleemdELM_forecast	Final forecasted value of the eemdELM model. It is obtained by combining the forecasted value of all individual IMF.
MAE_eemdELM	Mean Absolute Error (MAE) for eemdELM model.
MAPE_eemdELM	Mean Absolute Percentage Error (MAPE) for eemdELM model.
rmse_eemdELM	Root Mean Square Error (RMSE) for eemdELM model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Huang, G.B., Zhu, Q.Y. and Siew, C.K. (2006) Extreme learning machine: theory and applications. Neurocomputing, 70, 489–501.

Wu, Z. and Huang, N.E. (2009) Ensemble empirical mode decomposition: a noise assisted data analysis method. Advances in adaptive data analysis, 1(1), 1–41.

See Also

emdELM, ceemdanELM

Examples

data("Data_Maize")
eemdELM(Data_Maize)

---

Ensemble Empirical Mode Decomposition Based Time Delay Neural Network Model

Description

The eemdTDNN function computes forecasted value with different forecasting evaluation criteria for Ensemble Empirical Mode Decomposition based Time Delay Neural Network Model.

Usage

eemdTDNN(data, stepahead=10,
num.IMFs=emd_num_imfs(length(data)), s.num=4L,
num.sift=50L, ensem.size=250L, noise.st=0.2)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.
ensem.size	Number of copies of the input signal to use as the ensemble.
noise.st	Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input series.

Details

To overcome the problem of mode mixing in EMD decomposition technique, Ensemble Empirical Mode Decomposition (EEMD) method was developed by Wu and Huang (2009). EEMD significantly reduces the chance of mode mixing and represents a substantial improvement over the original EMD.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinaleemdTDNN_forecast	Final forecasted value of the EEMD based TDNN model. It is obtained by combining the forecasted value of all individual IMF.
MAE_eemdTDNN	Mean Absolute Error (MAE) for EEMD based TDNN model.
MAPE_eemdTDNN	Mean Absolute Percentage Error (MAPE) for EEMD based TDNN model.
rmse_eemdTDNN	Root Mean Square Error (RMSE) for EEMD based TDNN model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Wu, Z. and Huang, N.E. (2009) Ensemble empirical mode decomposition: a noise assisted data analysis method. Advances in adaptive data analysis, 1(1), 1–41.

See Also

emdTDNN, ceendanTDNN

Examples

data("Data_Maize")
eemdTDNN(Data_Maize)

---

Empirical Mode Decomposition Based Auto Regressive Integrated Moving Average Model

Description

The emdARIMA function gives forecasted value of Empirical Mode Decomposition based Auto Regressive Integrated Moving Average Model with different forecasting evaluation criteria.

Usage

emdARIMA(data, stepahead = 10,
num.IMFs = emd_num_imfs(length(data)),
s.num = 4L, num.sift = 50L)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.

Details

This function firstly, decompose the nonlinear and nonstationary time series into several independent intrinsic mode functions (IMFs) and one residual component (Huang et al., 1998). Secondly, Auto Regressive Integrated Moving Average is used to forecast these IMFs and residual component individually. Finally, the prediction results of all IMFs including residual are aggregated to form the final forecasted value for given input time series.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinalEMDARIMA_forecast	Final forecasted value of the EMD based ARIMA model. It is obtained by combining the forecasted value of all individual IMF.
MAE_EMDARIMA	Mean Absolute Error (MAE) for EMD based ARIMA model.
MAPE_EMDARIMA	Mean Absolute Percentage Error (MAPE) for EMD based ARIMA model.
rmse_EMDARIMA	Root Mean Square Error (RMSE) for EMD based ARIMA model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Jha, G.K. and Sinha, K. (2014) Auto Regressive Integrated Moving Averages for time series prediction: An application to the monthly wholesale price of oilseeds in India. Neural Computing and Applications, 24, 563–571.

See Also

eemdARIMA, ceemdanARIMA

Examples

data("Data_Maize")
emdARIMA(Data_Maize)

---

Empirical Mode Decomposition Based ELM Model

Description

The emdELM function computes forecasted value with different forecasting evaluation criteria for Empirical Mode Decomposition based Extreme Learning Machine model.

Usage

emdELM(xt, stepahead = 10, s.num = 4L, num.sift = 50L)

Arguments

xt	Input univariate time series (ts) data.
stepahead	The forecast horizon.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.

Details

This function decomposes the original time series into several independent intrinsic mode functions (IMFs) and one residual component (Huang et al., 1998). Then extreme learning machine, a class of feedforward neural network is used to forecast these IMFs and residual component individually (Huang et al., 2006). Finally, the prediction results of all IMFs including residual are aggregated to formulate an ensemble output for the original time series.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set is used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinalemdELM_forecast	Final forecasted value of the emdELM model.It is obtained by combining the forecasted value of all individual IMF.
MAE_emdELM	Mean Absolute Error (MAE) for emdELM model.
MAPE_emdELM	Mean Absolute Percentage Error (MAPE) for emdELM model.
rmse_emdELM	Root Mean Square Error (RMSE) for emdELM model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Dong, J., Dai, W., Tang, L. and Yu, L. (2019) Why do EMD based methods improve prediction. A multiscale complexity perspective. Journal of Forecasting, 38(7), 714–731.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Huang, G.B., Zhu, Q.Y. and Siew, C.K. (2006). Extreme learning machine: theory and applications. Neurocomputing, 70, 489–501.

See Also

emdELM, ceemdanelm

Examples

data("Data_Maize")
emdELM(Data_Maize)

---

Empirical Mode Decomposition Based Time Delay Neural Network Model

Description

The emdTDNN function gives forecasted value of Empirical Mode Decomposition based Time Delay Neural Network Model with different forecasting evaluation criteria.

Usage

emdTDNN(data, stepahead=10,
num.IMFs=emd_num_imfs(length(data)),
s.num=4L, num.sift=50L)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
num.IMFs	Number of Intrinsic Mode Function (IMF) for input series.
s.num	Integer. Use the S number stopping criterion for the EMD procedure with the given values of S. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations.
num.sift	Number of siftings to find out IMFs.

Details

This function firstly, decompose the nonlinear and nonstationary time series into several independent intrinsic mode functions (IMFs) and one residual component (Huang et al., 1998). Secondly, time delay neural network is used to forecast these IMFs and residual component individually. Finally, the prediction results of all IMFs including residual are aggregated to form the final forecasted value for given input time series.

Value

TotalIMF	Total number of IMFs.
AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF.
FinalEMDTDNN_forecast	Final forecasted value of the EMD based TDNN model. It is obtained by combining the forecasted value of all individual IMF.
MAE_EMDTDNN	Mean Absolute Error (MAE) for EMD based TDNN model.
MAPE_EMDTDNN	Mean Absolute Percentage Error (MAPE) for EMD based TDNN model.
rmse_EMDTDNN	Root Mean Square Error (RMSE) for EMD based TDNN model.

References

Choudhary, K., Jha, G.K., Kumar, R.R. and Mishra, D.C. (2019) Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian journal of agricultural sciences, 89(5), 882–886.

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q. and Liu, H.H. (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis. In Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. 454, 903–995.

Jha, G.K. and Sinha, K. (2014) Time delay neural networks for time series prediction: An application to the monthly wholesale price of oilseeds in India. Neural Computing and Applications, 24, 563–571.

See Also

eemdTDNN, ceemdanTDNN

Examples

data("Data_Maize")
emdTDNN(Data_Maize)

---

Variational Mode Decomposition Based Autoregressive Integrated Moving Average Model

Description

The vmdARIMA function computes forecasted value with different forecasting evaluation criteria for Variational Mode Decomposition (VMD) Based Autoregressive Integrated Moving Average (ARIMA).

Usage

vmdARIMA (data, stepahead=10, nIMF=4, alpha=2000, tau=0, D=FALSE)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
nIMF	The number of IMFs.
alpha	The balancing parameter.
tau	Time-step of the dual ascent.
D	a boolean.

Details

In this function, the variational mode decomposition (VMD) used for mining the trend features and detailed features contained in a time series. Moreover, the corresponding autoregressive integrated moving average (ARIMA) models were derived to reflect the different features of the IMFs. The final forecasted values obtained for a given time series.

Value

AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF
FinalvmdARIMA_forecast	Final forecasted value of the VMD based ARIMA model. It is obtained by combining the forecasted value of all individual IMF.
MAE_vmdARIMA	Mean Absolute Error (MAE) for vmdARIMA model.
MAPE_vmdARIMA	Mean Absolute Percentage Error (MAPE) for vmdARIMA model.
rmse_vmdARIMA	Root Mean Square Error (RMSE) for vmdARIMA model.

References

Box, G. E., Jenkins, G. M., Reinsel, G. C. and Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley and Sons.

Dragomiretskiy, K.and Zosso, D. (2014). Variational mode decomposition. IEEE transactions on signal processing, 62(3), 531–544.

Wang, H., Huang, J., Zhou, H., Zhao, L. and Yuan, Y. (2019). An integrated variational mode decomposition and arima model to forecast air temperature. Sustainability, 11(15), 4018.

See Also

vmdTDNN,vmdELM

Examples

data("Data_Maize")
vmdARIMA(Data_Maize)

---

Variational Mode Decomposition Based Extreme Learning Machine Model

Description

The vmdELM function computes forecasted value with different forecasting evaluation criteria for Variational Mode Decomposition (VMD) Based Extreme learning machine (ELM).

Usage

vmdELM (data, stepahead=10, nIMF=4, alpha=2000, tau=0, D=FALSE)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
nIMF	The number of IMFs.
alpha	The balancing parameter.
tau	Time-step of the dual ascent.
D	a boolean.

Details

This function decomposes a nonlinear, nonstationary time series into different IMFs using VMD (Qian et al., 2019). Extreme learning machine (ELM) is used to forecast decomposed IMFs individually. Finally, the prediction results of all three components are aggregated to formulate an ensemble output for the input time series.

Value

AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF
FinalvmdELM_forecast	Final forecasted value of the VMD based ELM model. It is obtained by combining the forecasted value of all individual IMF.
MAE_vmdELM	Mean Absolute Error (MAE) for vmdELM model.
MAPE_vmdELM	Mean Absolute Percentage Error (MAPE) for vmdELM model.
rmse_vmdELM	Root Mean Square Error (RMSE) for vmdELM model.

References

Dragomiretskiy, K.and Zosso, D. (2014). Variational mode decomposition. IEEE transactions on signal processing, 62(3), 531–544.

Shao, Z., Chao, F., Yang, S. L., & Zhou, K. L. (2017). A review of the decomposition methodology for extracting and identifying the fluctuation characteristics in electricity demand forecasting. Renewable and Sustainable Energy Reviews, 75, 123–136.

Qian, Z., Pei, Y., Zareipour, H. andChen, N. (2019). A review and discussion of decomposition-based hybrid models for wind energy forecasting applications. Applied energy, 235, 939–953.

See Also

vmdTDNN,vmdARIMA

Examples

data("Data_Maize")
vmdELM(Data_Maize)

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Variational Mode Decomposition Based Time Delay Neural Network Model

Description

The vmdTDNN function computes forecasted value with different forecasting evaluation criteria for Variational Mode Decomposition (VMD) Based Time Delay Neural Network Model (TDNN).

Usage

vmdTDNN (data, stepahead=10, nIMF=4, alpha=2000, tau=0,D=FALSE)

Arguments

data	Input univariate time series (ts) data.
stepahead	The forecast horizon.
nIMF	The number of IMFs.
alpha	The balancing parameter.
tau	Time-step of the dual ascent.
D	a boolean.

Details

The Variational Mode Decomposition method is a novel adaptive, non-recursive signal decomposition technology, which was introduced by Dragomiretskiy and Zosso (2014). VMD method helps to solve current decomposition methods limitation such as lacking mathematical theory, recursive sifting process which not allows for backward error correction, hard-band limits, the requirement to predetermine filter bank boundaries, and sensitivity to noise. It decomposes a series into sets of IMFs. Time-delay neural networks are used to forecast decomposed components individually (Jha and Sinha, 2014). Finally, the prediction results of all components are aggregated to formulate an ensemble output for the input time series.

Value

AllIMF	List of all IMFs with residual for input series.
data_test	Testing set used to measure the out of sample performance.
AllIMF_forecast	Forecasted value of all individual IMF
FinalvmdTDNN_forecast	Final forecasted value of the VMD based TDNN model. It is obtained by combining the forecasted value of all individual IMF.
MAE_vmdTDNN	Mean Absolute Error (MAE) for vmdTDNN model.
MAPE_vmdTDNN	Mean Absolute Percentage Error (MAPE) for vmdTDNN model.
rmse_vmdTDNN	Root Mean Square Error (RMSE) for vmdTDNN model.

References

Choudhury, K., Jha, G. K., Das, P. and Chaturvedi, K. K. (2019). Forecasting potato price using ensemble artificial neural networks. Indian Journal of Extension Education, 55(1), 73–77.

Choudhary, K., Jha, G. K., Kumar, R. R. and Mishra, D. C. (2019). Agricultural commodity price analysis using ensemble empirical mode decomposition: A case study of daily potato price series. Indian Journal of Agricultural Sciences, 89(5), 882–886.

Dragomiretskiy, K.and Zosso, D. (2014). Variational mode decomposition. IEEE transactions on signal processing, 62(3), 531–544.

Jha, G. K. and Sinha, K. (2014). Time-delay neural networks for time series prediction: An application to the monthly wholesale price of oilseeds in India. Neural Computing and Applications, 24(3–4), 563–571.

See Also

vmdARIMA,vmdELM

Examples

data("Data_Maize")
vmdTDNN(Data_Maize)

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