Abstract
The impact of long-memory on the Before-After-Control-Impact (BACI) design and a commonly used nonparametric alternative, Randomized Intervention Analysis (RIA), is examined. It is shown the corrections used based on short-memory processes are not adequate. Long-memory series are also known to exhibit spurious structural breaks that can be mistakenly attributed to an intervention. Two examples from the literature are used as illustrations.
Highlights
Ecological studies often involve data collected over time
Researchers have explored the relationships among long-memory, aggregation, and structural breaks in time series [4] [5] [6]
A short-memory time series has an autocorrelation function (ACF) that decays at an exponential rate, i.e., ρX (h) rh approaches a positive constant as h → ∞ for some 0 < r < 1
Summary
Ecological studies often involve data collected over time. Examples are observations of population densities such as the relative abundance of the white sea urchin (Lytechinus anamesus) in an area offshore the San Onofre Nuclear Generating Station (Schroeter et al [1]), or of the difference in chlorophyll concentrations between two lakes (Carpenter et al [2]). A short-memory time series has an ACF that decays at an exponential rate, i.e., ρX (h) rh approaches a positive constant as h → ∞ for some 0 < r < 1. A long-memory time series has an ACF that decays at a hyperbolic rate: ρX (h) rh approaches a positive constant as h → ∞ for some 0 < r < 1. The ACF of the AR(1) is given by ρ= X (h) φ= h , h 0,1, 2, Long-memory processes, as described by fractionally differenced white noise (FD(d)), define the time series {Xt} by (1− B)d X=t Wt , − 0.5 < d < 0.5. Differenced white noise is a classic long-memory time series, having an ACF that decays at a hyperbolic rate: ρ (h) h1−2d approaches a positive constant as h → ∞. AR(1) model is short-memory since its ACF converges to zero at an exponential rate as h → ∞
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