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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