Forecasting Indian Goods and Services Tax revenue using TBATS, ETS, Neural Networks, and hybrid time series models

Figures & data

Figure 1. Time series forecasting tools used in the study.

Figure 2. Time series plot of log GST data: this time series plot displays the log of the GST in constant prices, also known as the log GST data. Y-axis = the logGST, X-axis= Time.

Table 1. Test for non-linearity and p-value

Non-linearity tests	p-Value
Teraesvirta’s neural network test	0.027
White neural network test	0.012
Keenan’s one-degree test for nonlinearity	0.009
McLeod-Li test	1.20*10^−8
Tsay’s test for nonlinearity	0.009
Likelihood ratio test for threshold nonlinearity	0.018

Figure 3. RMSE plot for all nine models.

Note. X-axis: Forecast Horizon; Y-axis: RMSE Value.

Table 2. Model validation of log GST data of India

Model	RMSE	MAE	MAPE
ANN	0.271	0.237	2.010
NNAR	2.758	2.638	22.314
ETS	0.146	0.124	1.053
TBATS (Proposed Single)	0.145	0.120	1.017
Hybrid ARIMA-NNAR	0.231	0.207	1.754
Hybrid ARIMA-ANN	0.296	0.275	2.32
Hybrid Theta-ANN	0.147	0.125	1.062
Hybrid Theta-NNAR	0.160	0.143	1.20
Hybrid Theta-TBATS (Proposed Hybrid)	0.141	0.114	0.971

RMSE = root mean square Error; MAE = mean absolute Error; MAPE = mean absolute percentage error.

Figure 4. Actual vs 12-month forecasts data points for all nine models.

Note. X-Axis: Year and Y-Axis: LogGST Revenue.

Data availability statement

Data is available upon request.