Multivariate Extension
Multi-channel, Multivariate SSA (or M-SSA) is a natural extension of SSA to for analyzing multivariate time series, where the size of different univariate series does not have to be the same. The trajectory matrix of multi-channel time series consists of stacked trajectory matrices of separate times series. The rest of the algorithm is the same as in the univariate case. System of series can be forecasted analogously to SSA recurrent and vector algorithms (Golyandina and Stepanov, 2005). MSSA has many applications. It is especially popular in analyzing and forecasting economic and financial time series with short and long series length (Patterson et al., 2011 and Hassani et al., 2012) Other multivariate extension is 2D-SSA that can be applied to two-dimensional data like digital images (Golyandina and Usevich, 2010). The analogue of trajectory matrix is constructed by moving 2D windows of size .
Read more about this topic: Singular Spectrum Analysis, SSA As A Model-free Tool
Famous quotes containing the word extension:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)