Analysis of the Hankel Matrix in Embedding Using the Singular Spectrum Analysis (SSA) Method

Singular Spectrum Analysis (SSA) is an effective method of decomposition of time series for separating key components in data, such as trends, seasonality, and noise. This study aims to analyze the role of Hankel matrix in the SSA embedding process and how window length (L) selection can affect the effectiveness of component separation in data time series. In this study, the data used includes public data that can be influenced by seasonal factors and unexpected events, such as natural disasters or regulatory changes. The research process begins with the data preprocessing stage, followed by the embedding stage to form a matrix used in decomposition with Singular Value Decomposition (SVD). To evaluate the similarity of separate components, w-correlation is used. The results show that the selection of optimal window lengths, in the range of N/4 < L < N/2 is very important to maintain a balance between temporal information and matrix dimensions. With the right window selection, the embedding process in SSA can be more effective in separating the trending, seasonal, and noise components in the data pattern. By understanding the structure of the Hankel matrix and selecting the right parameters, the embedding process in SSA can be more effective in separating the components of the time series and preserving temporal information.