Using arc length to cluster financial time series according to risk

ABSTRACT

This article investigates how arc length can be used to partition financial time series according to variability (risk). This technique is predicated on the idea that arc length is an index of volatility, and thus the end result is that safer stocks can be sorted from more risky ones. Performance of arc length is compared with squared returns and absolute returns, two commonly used measures for quantifying the variability of prices. An application involving 30 popular stocks is presented using Maharaj, k-means ++, and correlation-based clustering techniques.

KEYWORDS:

• Arc length
• k-means++
• Maharaj
• volatility

Notes

1. Persistence is sometimes referred to as volatility clustering, which is not to be confused with this article’s goal of clustering via the feature of volatility.

2. Eastman Kodak has since changed its ticker symbol to KODK.

3. If arc length takes the form , then squared and absolute returns take the forms ∑ⁿ_{t = 2}Y_t² and ∑ⁿ_{t = 2}|Y_t|, respectively.