Clustering the observations in a price or returns series [closed]

Given one stock, what value would there be in clustering the individual sample observations within that stock's historical prices series, or its return series? is univariate clustering done in finance?

Clustering would allow the formation of a distance matrix that shows how far pairs of observations within that univariate time series are from one another, grouped together by similarity rather than the chaotic randomness seen in their original form, likely causing similar market regimes within that stock's history to be clumped together (or not). Why would this be useful or not useful?

and which dataset makes more sense, clustering observations of prices or returns?

• Hi @develarist, your question seems quite convoluted. Would you be able to make it a bit more specific? – Kermittfrog Nov 4 '20 at 9:56
• think of a return series vector. all its observations are rather chaotic. if instead we measure how far pairs of observations within that univariate time series are from one another, individual distances of those pairs of observations within the same time series can be assembled into what is commonly referred to as a distance matrix. from there, we cluster the distance matrix according to similarities between groups of observations: high magnitude returns are moved next to other high magnitude returns, and the same with low ones in their own group. this is a clustered distance matrix – develarist Nov 4 '20 at 10:00
• my question is whether assembling that single time series' distance matrix, and furthermore re-organizing it into clusters, has some value, or is already a practice found, within finance for some reason and what that reason is, given that multivariate (as opposed to univariate) clustering is already common – develarist Nov 4 '20 at 10:03

• it's good. based on the graphs in the article, do you know if clustering a time series means re-sorting sample observations next to each other if they belong to similar regimes? i.e. $\{t_1, t_2, \dots, t_T\}$ might be reshuffled to $\{t_5, t_{12}, \dots, t_8, t_{40}, t_T\}$? – develarist Nov 4 '20 at 14:51