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Market Affine Aggregated ARTCH (Mkt-Aff-Agg-ARTCH) with MA components

The process is identical to Mkt-Aff-Agg-ARCH process, but with a trend term for each volatility component.

The processs contains 5 components, with the corresponding 5 trend terms. The parameters for the simulation are

• σ∞ = 0.11
• w∞ = 0.113
• τ_k = {0.06, 0.7, 3.5, 14, 30} day.
• The lags in the returns for computing the volatilities σ_k are l_k = {1, 40, 80, 480, 480} on the 3’ grid.
• The volatility coefficients are χ_k = {0.50, 0.18, 0.11, 0.07, 0.14}
  
• The order for the moving average is m = 4.
• The lags in the returns for computing the trend terms are l_k = {20, 480, 3360, 14000, 28000} on the 3’ grid.
• The coefficients for the trend terms are θ_k = {0.015, 0.0006, 0.00007, 0.00003, 0.0000015}
  

The innovations have a Student distribution with 3.5 degree of freedom. The simulation time corresponds to 200 years with a time increment δt = 3 minutes.