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Table 9 ETS model information and parameter estimates with their error measures for South Africa

From: Future health expenditure in the BRICS countries: a forecasting analysis for 2035

Indicator

Method

ME

RMSE

MAE

MPE

MAPE

MASE

ACF1

Total Health Expenditure (% of GDP)

ETS(A,A,N)

α = 0.94;β = 0.00

0.00

0.24

0.18

-0.07

2.17

0.93

0.00

Total Health Expenditure Per Capita ($PPP)

ETS(A,A,N)

α = 0.58;β = 0.56

-1.45

26.67

20.66

-0.14

2.20

0.73

0.03

Government Health Expenditure Per Capita ($PPP)

ETS(A,A,N)

α = 0.96;β = 0.00

0.00

0.07

0.05

-0.04

1.95

0.89

0.11

Pre-Paid Private Health Expenditure Per Capita ($PPP)

ETS(A,A,N)

α = 0.99;β = 0.26

0.00

0.03

0.02

0.23

0.98

0.82

0.03

Out-of-Pocket Health Expenditure Per Capita ($PPP)

ETS(A,A,N)

α = 0.00;β = 0.00

0.00

0.06

0.05

-0.03

1.11

1.23

0.32

Government Health Expenditure (% of CHE)

ETS(A,Ad,N)

α = 0.03;β = 0.03

0.01

0.05

0.04

-4.16

15.39

0.84

0.05

Pre-Paid Private Health Expenditure (% of CHE)

ETS(A,A,N)

α = 0.23;β = 0.00

0.00

0.05

0.04

18.14

56.39

1.16

0.27

Out-of-Pocket Health Expenditure (% of CHE)

ETS(A,Ad,N)

α = 0.00;β = 0.00

0.00

0.06

0.05

-0.18

1.98

0.84

0.32

  1. ETS Exponential smoothing model; error, trend, and seasonal components are the three major parameters, which can be additive (A), multiplicative (M), or none (N); α = smoothing parameter for the level component; β = smoothing parameter for trend component; ME Mean Error, RMSE Root Mean Squared Error, MAE Mean Absolute Error, MPE Mean Percentage Error, MAPE Mean Absolute Percentage Error, MASE Mean Absolute Scaled Error, ACFI Auto-correlation of Errors at lag 1