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Table 8 ARFIMA–FIAPARCH parameter estimation of models

From: Long memory mean and volatility models of platinum and palladium price return series under heavy tailed distributions

Parameters Normal platinum Student GED Skewed student Normal palladium Student GED Skewed student
Cst(M) 0.0001 0.0001 0.0001 0.0003*** 0.0001 0.0001 0.0001 0.0001
\(d_m\) −0.0793*** −0.0556 −0.0410 −0.5176*** −0.1001*** −0.0582*** −0.00968 −0.0587**
AR(1) 0.3920*** 0.4053*** 0.4137*** 0.1308*** 0.3884*** 0.4202*** 0.4516*** 0.4186***
MA(1) −0.9327*** −0.9361*** −0.9381*** 0.0687* −0.9229*** −0.9306*** −0.9382*** −0.9306***
Cst(V) 0.0041 0.0043* 0.0046* 0.0005 0.0106 0.0156* 0.0166* 0.0150*
\(d_v\) 0.6512*** 0.6462*** 0.6378*** 0.6432*** 0.7306*** 0.6980*** 0.6877*** 0.6987***
ARCH(\(\alpha _1\)) 0.3974*** 0.3929*** 0.3919*** 0.2325*** 0.3872*** 0.3703*** 0.3551*** 0.3716***
GARCH(\(\beta _1\)) 0.8743*** 0.8744*** 0.8718*** 0.8607*** 0.9035*** 0.8973*** 0.8900*** 0.8974***
APARCH(\(\gamma _1\)) −0.2928*** −0.3716*** −0.4169* −0.2012* −0.0863* −0.0859 −0.09485 −0.0914
APARCH(\(\delta\)) 1.8067*** 1.7569*** 1.7309*** 2.0904*** 1.9933*** 1.9222*** 1.9228*** 1.9234***
Akaike –2.4773 –2.4783 –2.4781 –2.4030 −1.2420 −1.2532 −1.2589 −1.2533
Schwarz –2.4616 –2.4610 –2.4608 –2.3841 −1.2262 −1.2359 −1.2416 −1.2344
ARCH-LM 2.2572 2.6098* 2.7374* 2.8892* 0.67543 3.8257* 2.6699* 3.5548**
  1. *, ** and *** represent the significant level at 10, 5 and 1% levels respectively