Journal of Probability and Statistics

Review Article

The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

Table 1

Simulation results of the CSS and two-stage method in SARFIMA ( 1 , 𝐷 , 0 ) 4 .
𝐷 Sample size Φ Mean ( 𝐷 ) Mean ( Φ ) Std. dev. ( 𝐷 ) Std. dev. ( Φ ) R M S E ( 𝐷 ) R M S E ( Φ )
CSSTSMCSSTSMCSSTSMCSSTSMCSSTSMCSSTSM
0.11200.30,060,140,280,280,060,090,120,090,080,100,120,09
0.70,080,150,680,480,070,080,090,070,080,090,100,23
−0.30,050,02−0,30−0,260,060,050,110,090,080,090,110,10
−0.70,040,00−0,69−0,460,060,010,080,070,080,100,080,25
2400.30,050,150,290,290,040,070,070,060,070,080,070,06
0.70,060,160,690,480,050,060,050,050,060,080,050,23
−0.30,040,01−0,30−0,260,040,030,070,060,070,090,070,07
−0.70,040,00−0,69−0,470,040,000,050,050,080,100,050,24
3600.30,040,150,300,290,040,060,060,050,070,080,060,05
0.70,050,160,700,480,040,050,040,040,060,080,040,22
−0.30,040,01−0,30−0,260,040,020,050,050,070,100,050,06
−0.70,040,00−0,69−0,460,040,000,040,040,070,100,040,24
0.21200.30,120,210,290,330,080,070,120,090,110,070,120,09
0.70,140,200,690,510,090,060,090,070,110,060,090,21
−0.30,100,07−0,29−0,230,080,070,120,090,130,150,120,11
−0.70,080,00−0,69−0,450,070,020,080,070,140,200,080,26
2400.30,110,210,300,330,060,050,070,060,110,050,070,07
0.70,120,210,700,510,060,040,060,050,100,040,060,19
−0.30,100,06−0,30−0,230,060,060,070,070,120,150,070,09
−0.70,090,00−0,69−0,450,050,000,050,050,120,200,050,25
3600.30,110,220,300,330,050,040,060,050,100,040,060,06
0.70,110,220,700,510,050,030,040,040,100,030,040,19
−0.30,100,06−0,29−0,240,050,050,050,050,110,150,050,08
−0.70,100,00−0,69−0,450,050,000,040,040,110,200,040,25
0.31200.30,210,270,310,420,090,040,110,110,130,050,110,16
0.70,250,260,700,580,090,040,090,090,100,060,090,15
−0.30,200,16−0,28−0,160,090,070,110,100,140,160,120,17
−0.70,180,02−0,68−0,430,090,040,090,080,150,280,090,28
2400.30,220,270,310,430,060,030,070,080,110,040,070,15
0.70,230,270,710,590,070,030,060,060,100,040,060,13
−0.30,210,17−0,29−0,160,060,060,070,080,110,140,070,16
−0.70,200,01−0,69−0,430,060,020,050,050,120,290,050,27
3600.30,210,270,310,430,050,020,060,070,100,040,060,14
0.70,220,270,720,590,050,030,040,050,100,040,050,12
−0.30,210,17−0,29−0,160,050,050,060,060,110,140,060,15
−0.70,200,01−0,69−0,430,050,020,040,040,110,290,040,27