Table 1. Hyperparameters used in themachine learning models.
| No | Series | Model | Estimated parameter | AICc/Accuracy | Residuals check (Ljung-Box test dat) |
|---|---|---|---|---|---|
| 1 | Training set of TB incidence (150 observations) | ARIMA(1,0,0)(2,1,0) by R, package: forecast, function: auto.arima | Coefficients: ar1 = −0.2399, sar1 = −0.6395, sar2 = −0.2443, drift = −0.0038 s.e. 0.0866 0.0882 0.0907 0.0002 sigma^2 estimated as 0.00475: log likelihood = 172.81 |
AIC = −335.62, AICc = −335.17, BIC = −320.99; RMSE = 0.0652 MAPE = 0.5127 |
Residuals from ARIMA(1,0,0)(2,1,0) with drift, Q* = 62.283, df = 20, p-value = 3.139e−06, Model df: 4. Total lags used: 24 |
| 2 | Simulation set of TB incidence (192 observations) | ARIMA(3,0,0)(2,1,0) by R, package: forecast, function: auto.arima | Coefficients: ar1 = 0.1283, ar2 = 0.1111, ar3 = 0.2527, sar1 = −0.6137, sar2 = −0.3464, drift = −0.0041 sigma^2 estimated as 0.005094: log likelihood = 219.89 |
AIC = −425.79 AICc = −425.14 BIC = −403.44 RMSE = 0.0652, MAPE = 0.5213 |
Residuals from ARIMA(3,0,0)(2,1,0) with drift Q* = 34.641, df = 18, p-value = 0.01048, Model df: 6. Total lags used: 24 |
| 3 | Training set of TB incidence (150 observations) | ETS(A,A,A) | Smoothing parameters: alpha = 0.0102, beta = 0.0101, gamma = 1e−04; |
AIC = −68.44, AICc = −63.81, BIC = −17.26 RMSE = 0.0581, MAPE = 0.4591 |
Residuals from ETS(A,A,A); Q* = 61.132, df = 8, p-value = 2.793e−10; Model df: 16. Total lags used: 24 |
| 4 | Simulation set of TB incidence (192 observations) | ETS(A,A,A), Call: ets (y = M) |
ETS(A,A,A) Call: ets (y = M) Smoothing parameters: alpha = 0.0738, beta = 1e−04, gamma = 1e−04 , |
AIC = −25.56 AICc = −22.04 BIC = 29.82 RMSE = 0.0618, MAPE = 0.4870 |
Residuals from ETS(A,A,A); Q* = 51.531, df = 8, p-value = 2.073e−08; Model df: 16. Total lags used: 24 |
| 5 | Training set of TB incidence (150 observations) | ARIMA-ETS | Hybrid forecast model comprised of the following models: arima with weight 0.5, ETS with weight 0.5 | RMSE = 0.0585 MAPE = 0.4613 |
Could not find appropriate degrees of freedom for this model |
| 6 | Simulation set of TB incidence (192 observations) | ARIMA-ETS | Hybrid forecast model comprised of the following models: arima with weight 0.5, ETS with weight 0.5 | RMSE = 0.0512 MAPE = 0.5058 |
Could not find appropriate degrees of freedom for this model |