Hi Komal,

what do you mean by "ratio scale data"? Anyway, it is common to cluster statistical units (rows) by using the variables contained in the columns. Therefore, you should have companies in the rows and time in the columns. Then, a simple Euclidean distance among volumes' time series can be used. Clearly, in the case of time series data, it would be better to adopt alternative and more sophisticated distances that account for serial correlation as well as other features. However, using the simple Euclidean distance among time points can be enough.

Ratio scale means simple time series data and it is not interval scale like likert scale and all...

@Derek Cheng, actually I want to make portfolio of low volume and high volume companies, so someone suggested me to use cluster analysis... actually I wanna check herd behavior in in each portfolio based on volume

I have a remark about Derek Cheng

Liao, T. W. (2005). Clustering of time series data—a survey. Pattern recognition, 38(11), 1857-1874.

Maharaj, E. A., D'Urso, P., & Caiado, J. (2019). Time series clustering and classification. Chapman and Hall/CRC.

I mean, clustering time series data is really common and there is huge literature. Let's consider the case of financial time series clustering (such as daily volume data, if you refer to daily trading volumes). In this case, you can construct groups of stocks sharing similar time-varying patterns according to a feature (or model-based) related to a specific variable (i.e. returns, volumes, etc). Some examples:

Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193-197.

Otranto, E. (2008). Clustering heteroskedastic time series by model-based procedures. Computational Statistics & Data Analysis, 52(10), 4685-4698.

Caiado, J., & Crato, N. (2010). Identifying common dynamic features in stock returns. Quantitative Finance, 10(7), 797-807.

D’Urso, P., Cappelli, C., Di Lallo, D., & Massari, R. (2013). Clustering of financial time series. Physica A: Statistical Mechanics and its Applications, 392(9), 2114-2129.

Raffinot, T. (2017). Hierarchical clustering-based asset allocation. The Journal of Portfolio Management, 44(2), 89-99.

Iorio, C., Frasso, G., D’Ambrosio, A., & Siciliano, R. (2018). A P-spline based clustering approach for portfolio selection. Expert Systems with Applications, 95, 88-103.

Cerqueti, R., Giacalone, M., & Mattera, R. (2021). Model-based fuzzy time series clustering of conditional higher moments. International Journal of Approximate Reasoning, 134, 34-52.

But one can also use more variables (i.e. with multivariate trajectories, so with panel dataset) or a very simple raw-data based approach! Then, I really do not understand what is the point related to "likert scale" data, but surely it is my fault. However, note that it is possible to cluster discrete time series data as well.

Hi Mam Komal Jindal :

k-means is designed for low-dimensional spaces with a (meaningful) euclidean distance. It is not very robust towards outliers, as it puts squared weight on them. Doesn't sound like a good idea to use k-means on time series data. Try looking into more modern, robust clustering algorithms. The robust clustering algorithm has been designed to take numerous sets of clusters as input and uses these to generate a set of robust clusters. A robust cluster must only consist of objects that appear together in all the input clusters produced from different clustering algorithms. The below mentioned links are useful for you :

• https://www.pnas.org/content/114/37/9814
• https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-019-3089-6

Regards;

Ehtisham

Thanks sir @Ehtisham Lodhi for the valuable answer