  Autoregressive processes (AR) have typical short-range memory. Detrended
Fluctuation Analysis (DFA) was basically designed to reveal long range
correlation in non stationary processes. However DFA can also be regarded as a
suitable method to investigate both long-range and short range correlation in
non-stationary and stationary systems. Applying DFA to AR processes can help
understanding the non uniform correlation structure of such processes. We
systematically investigated a first order autoregressive model AR(1) by DFA and
established the relationship between the interaction constant of AR(1) and the
DFA correlation exponent. The higher the interaction constant the higher is the
short range correlation exponent. They are exponentially related. The
investigation was extended to AR(2) processes. The presence of a distant
positive interaction in addition to a near by interaction will increase the
correlation exponent and the range of correlation while the effect of a distant
negative interaction will decrease significantly only the range of interaction.
This analysis demonstrate the possibility to identify and AR(1) model in an
unknown DFA plot or to distinguish among AR(1) and AR(2) models. The analysis
was performed on medium long series of 1000 terms.
