ajdmom.itos_mom.moment_IEI_IEII

ajdmom.itos_mom.moment_IEI_IEII(n4, n5, n6, n7, n8, return_all=False)[source]

Moment of \(\mathbb{E}[m_4m_5m_6m_7m_8]\)

Moment of the combination of Ito processes, conditioning on the previous volatility components, i.e.,

\[\mathbb{E}[I\!E_{1,n-1,t}^{m_4} I_{1,n-1,t}^{m_5} I\!E_{2,n-1,t}^{m_6} I_{2,n-1,t}^{m_7}I_{n-1,t}^{*m_8}|v_{1,n-1},v_{2,n-1}]\]
Parameters:
  • n4 (int) – \(m_4\) in \(I\!E_{1,n-1,t}^{m_4}\).

  • n5 (int) – \(m_5\) in \(I_{1,n-1,t}^{m_5}\).

  • n6 (int) – \(m_6\) in \(I\!E_{2,n-1,t}^{m_6}\).

  • n7 (int) – \(m_7\) in \(I_{2,n-1,t}^{m_7}\).

  • n8 (int) – \(m_8\) in \(I_{1,n-1,t}^{*m_8}\).

  • return_all (bool) – whether or not return lower order moments simultaneously, defaults to False.

Returns:

poly if return_all=False else IEI_IEII

Return type:

Poly or dict of Poly