Separability and window length in singular spectrum analysis

Abstract

To find the optimal value of window length in singular spectrum analysis (SSA), we consider the concept of separability between the signal and noise component. The theoretical results confirm that for a wide class of time series, the suitable value of this parameter is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">median</mml:mi> <mml:mo stretchy="false">{</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy="false">}</mml:mo> </mml:math> with the series of length T . The theoretical results obtained here coincide with those obtained previously from the empirical point of view.