From: Systemic lupus Erythematosus and geomagnetic disturbances: a time series analysis
(a) Estimation of trend parameters. | ||||
Parameter | Estimated Coefficient | Standard Error | t-statistic (value) | t-statistic (p-value) |
\( {\hat{\beta}}_0 \) | 0.715 | 0.009 | 76.663 | 0.000 |
\( {\hat{\beta}}_1 \) | −0.00003 | 0.00005 | −0.607 | 0.544 |
Jarque-Bera (p-value) | 0.041 | Log-Likelihood | 344.97 | |
Durbin-Watson (value) | 0.868 | AIC | − 685.9 | |
R-squared | 0.001 | F-statistic (value) | 0.3682 | |
Adjusted R-squared | −0.002 | F-statistic (p-value) | 0.5440 | |
(b) Estimation of seasonality parameters. | ||||
Parameter | Estimated Coefficient | Standard Error | t-statistic (value) | t-statistic (p-value) |
\( \hat{C} \) | −0.0030 | 0.004 | −0.774 | 0.440 |
\( \hat{A} \) | −0.0732 | 0.005 | −14.163 | 0.000 |
\( \hat{B} \) | 0.0114 | 0.005 | 2.099 | 0.037 |
Jarque-Bera (p-value) | 0.282 | Log-Likelihood | 425.05 | |
Durbin-Watson (value) | 1.417 | AIC | − 844.1 | |
R-squared | 0.387 | F-statistic (value) | 102.4 | |
Adjusted R-squared | 0.383 | F-statistic (p-value) | 0.000 | |
(c) Estimation of ARMA parameters. | ||||
Parameter | Estimated Coefficient | Standard Error | t-statistic (value) | t-statistic (p-value) |
\( {\hat{\psi}}_1 \) | 0.8705 | 0.067 | 13.048 | 0.000 |
\( {\hat{\lambda}}_1 \) | −0.6805 | 0.095 | −7.133 | 0.000 |
Jarque-Bera (p-value) | 0.36 | Log-Likelihood | 447.152 | |
Ljung-Box (p-value) | 0.41 | AIC | − 888.303 |