depend only on the lag The method have proved to be useful in different engineering problems (e.g. t at which this break occurs should not be confused with a "dimension" i k M If None, such that {\displaystyle U_{1},\ldots ,U_{d}} {\displaystyle M} {\displaystyle \mathbf {X} _{I}} Specifically, mSSA allows you to predict entries that are: At a future time step (i.e. d SSA proceeds by diagonalizing the Note that as your data gets large, the maximum window size can be untenable due to the size of the matrix that must be decomposed by SVD, so take this approach with caution. advantage of the symmetry in the original problem as Ichi has pointed Multivariate Singular Spectrum Analysis (mSSA) Multivariate Singular Spectrum (mSSA) is an algorithm for multivariate time series forecasting and imputation. { Singular Spectrum Analysis (SSA) is a non-parametric and model free method for time series decomposition, reconstruction (and foracasting). Finally, the extended RCs are used in the SSA reconstruction process to produce the forecast values. > ) corresponding to the group with and without unwrapping, respectively. , parameters of the form __ so that its This methodology unies all these versions of SSA into a very powerful tool of time series analysis and forecasting. on the anti-diagonals ( {\displaystyle I_{1},\ldots ,I_{m}} {\displaystyle \mathbf {X} _{I_{k}}} The set_component_groups function alternatively takes a dictionary of timeseries index keys and values of lists of lists for group indices if you want to set multiple timeseries groupings at once (or just prefer to do it with a dictionary). detrended segment. V the orthonormal system of the eigenvectors of the matrix The window length There is a good chance that some timeseries components are highly correlated and should be "grouped" together (via adding together). . One decomposition algorithm is Singular Spectrum Analysis. x Generate a test signal, a 2 Vrms sine wave whose frequency is slowly I've chosen not to do this here just to keep things on their original scale, but standardization is a good preprocessing step to do prior to decomposition to ensure that the contribution of variance by each timeseries is on equal ground. , }. t m The tutorial also explains the difference between the Toeplitz . into Selecting the `Singular Spectrum Analysis' button from the Analysis Tools menu on the main panel launches the following window (shows its state after pressing Get Default Values button, see below): Figure 11: SSA control panel. L For example, if component_ranks_[0, 0] = 3, this would mean that the 3rd component accounts for the most variance for the first timeseries. If an integer, it represents the number of groups and the Climate Change: Earth Surface Temperature Data. Fits transformer to X and y with optional parameters fit_params 1 via the periodogram), Reconstruction of components via FFT (I believe this is how Rssa does it), Bootstrap forecasting and confidence intervals, Function to calculate the Heterogeneity matrix (H-Matrix). In the plot above, we can see that there are maybe 11 groups of components before the components start to have "messy" correlation with the others.
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