Can short-term memory processes be accurately detected? A reexamination of existing definitions

One major inadequacy in using the sample autocorrelation function (ACF) is the results from sample properties. Hassani’s [Formula: see text] theorem demonstrates that the sum of the sample ACF is always [Formula: see text] for any time series with any length. This result has led to doubts about methodologies that sum sample ACFs for diagnostics and analyses. Thus, the current tools and approaches fall short in detecting short-memory processes with due accuracy. Perhaps the larger question that looms here is about whether, with such definitions and methods, short-memory processes can really be picked up? Resolving this issue stands as a basic precursor to strong predictions and to precluding model mis-specification.