Hi Mariusz Buciakowski

The window length is an important parameter in singular spectrum analysis (SSA) because it affects the quality of the signal and noise separation and reconstruction. There are different methods to determine the optimal window length for SSA, depending on the characteristics of the data and the objectives of the analysis. Here are some possible methods:

• One method is based on the concept of separability between the signal and noise components. The idea is to find the window length that maximizes the difference between the eigenvalues corresponding to the signal and noise subspaces1. This method can be applied to a wide class of time series, such as stationary, non-stationary, periodic, chaotic, etc.
• Another method is based on the spectrum characteristics of the circulant matrix and Toeplitz matrix, which are used to construct the trajectory matrix in SSA. The window length is related to the frequency width corresponding to each principal component2. This method can be useful for processing biopotential signals, such as electrocardiogram (ECG) or electroencephalogram (EEG).
• A third method is based on the rule m = βN, where m is the window length, N is the length of the time series, and β is a constant in (0, 0.5). The value of β can be chosen according to the desired level of noise reduction and signal reconstruction3. This method can provide a more objective criterion for assigning window length in SSA.

These are some of the methods that can help you determine the window length for SSA. You may also want to experiment with different values of window length and compare the results using some performance measures, such as signal-to-noise ratio (SNR), mean squared error (MSE), or correlation coefficient (CC).

Learn more:

http://www.numdam.org/item/10.1016/j.crma.2011.07.012.pdf

Article Singular Spectrum Analysis Window Length Selection in Proces...

https://www.academia.edu/47099699/Window_Length_Selection_and_Signal_Noise_Separation_and_Reconstruction_in_Singular_Spectrum_Analysis

Conference Paper Determine a proper window length for singular spectrum analysis

https://ieeexplore.ieee.org/document/6640067/

https://ieeexplore.ieee.org/servlet/opac?punumber=6482821

https://ieeexplore.ieee.org/servlet/opac?punumber=6621666

with Best Regards

Yousef Bahrambeigi Thank you for your detailed answer and tips.!!!

Few methods to determine the window length for SSA:

1. Visual Inspection: Plot your data and visually inspect its patterns and structures. Look for recurring patterns or features that you want to capture with SSA. Based on your observations, estimate the approximate length of the patterns or oscillations. This can provide a rough idea of the window length.

2. Auto-Correlation: Compute the autocorrelation function of your data. The autocorrelation measures the similarity between a signal and a delayed version of itself. Look for significant peaks in the autocorrelation plot, which indicate the presence of repeating patterns. The lag at which the peaks occur can give you an estimate of the period or length of the patterns. Use this information to determine the window length accordingly.

3. Periodogram Analysis: Apply a periodogram analysis to your data using techniques like the Fast Fourier Transform (FFT). The periodogram provides a spectral representation of the data, showing the strength of different frequencies present. Identify dominant frequencies or peaks in the periodogram that correspond to the desired patterns you want to capture. Calculate the corresponding period or cycle length and consider it as a potential window length for SSA.

4. Rule of Thumb: There are some general guidelines or rules of thumb you can use as a starting point. For example, some practitioners suggest choosing a window length that is approximately one-fourth to one-tenth the length of the entire dataset. However, keep in mind that these rules may not always apply, and it's important to consider the specific characteristics of your data.

5. Cross-Validation: Split your data into multiple segments of varying window lengths and perform SSA on each segment. Evaluate the quality of the resulting decompositions using appropriate metrics or criteria, such as the reconstruction error or the ability to capture meaningful patterns. Choose the window length that provides the best decomposition based on your evaluation.

6. Prior Knowledge or Domain Expertise: If you have prior knowledge or domain expertise about the data and the underlying patterns, incorporate that knowledge into your decision-making process. Consider any known periodicities, expected cycle lengths, or relevant time scales in your domain to guide the selection of the window length.

Hope it helps