Serial Correlation

As I think, this would represent the serial correlation for the process

E.g.

S(t) = ρ S(t – 1) + ε

S(t) – S(t – 1) = ρ S(t – 1) – S(t – 1) + ε

ΔS(t) = (ρ – 1) S(t – 1) + ε


As the sapling interval becomes smaller

ρ ≈ 1 – c Δt (Assuming an exponentially decaying function proportional to the sampling interval)

S(t – 1) -> S(t)

Then,

ΔS(t) = – c S(t) Δt + ε


Similarly,

ΔS(t) = (ρ – 1) S(t – 1) + μ S(t – 1) Δt + ε

Becomes

ΔS(t) = (μ – c) S(t) Δt + ε

Best regards, Suminda Sirinath Salpitikorala Dharmasena

P.S. I am not a mathematician so please help me if there is a problem with my thinking.