Singular spectrum analysis based on the minimum variance estimator

Abstract

Abstract-In recent years Singular Spectrum Analysis (SSA), used as a powerful technique in time series analysis, has been developed and applied to many practical problems. In this paper, we introduce the SSA technique based on the minimum variance estimator. We also consider the SSA technique based on the minimum variance and structured total least squares estimators in reconstructing and forecasting time series. A well-known time series data set, namely, monthly accidental deaths in the USA time series, is used in examining the performance of the technique. The results are compared with several classical methods namely, Box-Jenkins SARIMA models, the ARAR algorithm and the Holt-Winter algorithm.

Signal Extraction and Forecasting of the UK Tourism Income Time Series: A Singular Spectrum Analysis Approach

“…Having completed these steps, one may proceed to forecasting. The presentation below follows Golyandina et al (, Chs 1 and 2), Hassani () and Hassani and Zhigljavsky ().…”

Singular spectrum analysis based on the perturbation theory

“…The reconstructed series using LS estimator has the lowest possible (zero) signal distortion and the highest possible noise level. Note that the results of noise reduced series using SSA technique (based on the LS estimate), are better than those obtained by classical methods which use noisy series (for comparison between SSA and classical time series methods see, for example, [1,10,12,19]). But as we mentioned above the reconstructed series still has some part of the initial noise level δY N due to the nature of LS estimate.…”

“…Possible application areas of SSA are diverse: from mathematics and physics to economics and financial mathematics, from metrology and oceanology to social science and market research (see, for example, [7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein). A thorough description of the theoretical and practical foundations of the SSA technique (with several examples) can be found in [3,20].…”

A comprehensive causality test based on the singular spectrum analysis

“…There are many papers where SSA has been applied to real-life time series. In particular, the performance of the SSA technique has been compared with other techniques for forecasting economics time series (Hassani (2007) and Hassani, et al (2009a-d)), and see also Hassani (2009e) for a new SSA-based algorithm and its application for forecasting.…”