Table 1.
Comparison of insurance development levels in major countries worldwide in 2022.
Fig 1.
(a), (b) and (c) present the trends between the macroeconomic variables CCI, EPU, CPI and insurance demand TID, respectively, which basically show the same growth trends.
Fig 2.
Response of TID to CCI, EPU& CPI.
(a) Presents the impulse response of insurance demand TID to the macroeconomic variable CCI. (b) Presents the impulse response of insurance demand TID to the macroeconomic variable EPU. (c) Presents the impulse response of insurance demand TID to the macroeconomic variable CPI. (d) Presents the impulse response of insurance demand TID to the insurance demand TID.
Table 2.
Descriptive statistics.
Fig 3.
Optimal model selection (full sample).
(a1)-(a4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable CCI in the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model. (b1)-(b4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable EPU for the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model. (c1)-(c4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable CPI in the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model.
Fig 4.
Optimal model selection (in-sample).
(a1)-(a4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable CCI in the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model. (b1)-(b4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable EPU for the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model. (c1)-(c4) present the AIC values corresponding to the 1–30 period lag order of the macroeconomic variable CPI in the Almon-MIDAS model, ExpAlmon-MIDAS model, Beta-MIDAS model, and U-MIDAS model.
Table 3.
Optimal in-sample prediction results.
Fig 5.
Comparison of in-sample predictions.
The figure presents the optimal co-frequency model, mixed-frequency model (univariate, multivariate) based forecasts compared to the true values for the period 2019Q3-2022Q1. Following the legend from top to bottom, the true values, AR model forecasts, ARDL model (CCI, EPU and CPI) forecasts, Eep Almon-MIDAS (CCI) model forecasts, U-MIDAS (EPU) model forecasts, Eep Almon-MIDAS (CPI) model forecasts, and M-MIDAS (CCI, EPU and CPI) model forecasts, and M-MIDAS (CCI and CPI) model forecasts. Of course these models are based on the results under the optimal lag order and optimal weight function. From the graphs, it is obvious that the MIDAS model predictions are generally better than the co-frequency model predictions. 4.3 Optimization of MIDAS estimation methods.
Table 4.
RMSE values of in-sample predictions under different prediction windows.
Table 5.
RMSE values for combined forecasting.
Table 6.
Nowcasting and forecasting.