Instruction DIFFERENCE and the option FRACTION

[g_defi]

Dear Tom,

I'm interested in the simulation of type I and type II fractional processes (in the terminology of Marinucci & Robinson 1999, Journal of Statistical Planning and Inference) and I look for some details about the instruction "DIFFERENCE" and the option "FRACTION" when d is outside the range (-0.5,0.5). For example, how this instruction operates when d is -0.8 or 0.8?

Thanks for your help.

[TomDoan]

Dear Tom,

I'm interested in the simulation of type I and type II fractional processes (in the terminology of Marinucci & Robinson 1999, Journal of Statistical Planning and Inference) and I look for some details about the instruction "DIFFERENCE" and the option "FRACTION" when d is outside the range (-0.5,0.5). For example, how this instruction operates when d is -0.8 or 0.8?

Thanks for your help.

Values in (0,1) are done in the frequency domain. For d between -1 and 0, the calculation is done as

y(t)=(1-L)^(-1) x (1-L)^(d+1) x(t)

which uses the method for positive values for (1-L)^(d+1)x(t), then accumulates the filtered series to implement the (1-L)^(-1).

The (-.5,+.5) range is important for statistical reasons (it's the range where the process is stationary), but not for computations.