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Table 5 ETS model information and parameter estimates with their error measures for Brazil

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 = 0.99; β = 0.00

-0.00

0.26

0.21

-0.11

2.58

0.93

0.18

Total Health Expenditure Per Capita ($PPP)

ETS(M,Ad,N)

α = 0.98; β = 0.00

-12.06

83.95

54.32

-0.68

3.33

0.73

-0.03

Government Health Expenditure Per Capita ($PPP)

ETS(A,A,N)

α = 0.87; β = 0.00

0.00

0.05

0.04

-0.11

2.50

0.84

0.00

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

ETS(A,A,N)

α = 0.99; β = 0.00

0.00

0.05

0.03

-0.09

1.46

0.93

0.12

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

ETS(A,A,N)

α = 0.30; β = 0.00

0.00

0.07

0.05

-0.14

2.40

0.79

0.29

Government Health Expenditure (% of CHE)

ETS(A,A,N)

α = 0.66; β = 0.21

-0.01

0.03

0.02

2.26

10.49

0.94

-0.03

Pre-Paid Private Health Expenditure (% of CHE)

ETS(A,A,N)

α = 0.39; β = 0.00

0.00

0.03

0.02

-0.19

2.60

0.82

0.22

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

ETS(A,A,N)

α = 0.00; β = 0.00

-0.00

0.04

0.03

-0.07

4.83

0.89

0.21

  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