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Table 1 27-day PGA average time series parameter estimation

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