Base information Home Purpose FAQ Notations Formula Figure descriptions Indexes Links to time series Pop-up to time series Two-time series comparison One figure comparison

Long-Memory Affine Aggregated ARTCH (LM-Aff-Agg-ARTCH) with parameter set 1

The similar process but without trend is the LM-Aff-Agg-ARCH process. The overall introduction for the processes with trend is given in the description for the GARTCH(1,1) process, while the multicomponent version is describe in the LM-Aff-Mic-ARTCH( process.

The coefficients follow a power law decay. The parameters for the simulations are

• σ∞ = 0.11
• w∞ = 0.20
• τ₁ = 1h20 min
• ρ =
• ρ^n-1 = 512 (i.e. n = 19)
• λ = 0.10
• θ₁ = 0.35
• λ′ = 1.7
• The cross term returns use the lags given by l_k = ρ^k-1.

The innovations have a Student distribution with 3.3 degree of freedom. The simulation time corresponds to 200 years with a time increment δt = 3 minutes.