# Time scales in stock markets

## TL;DR

This paper analyzes stock market time scales using empirical mode decomposition and Hurst exponent analysis, revealing different market dynamics in short-term (random) and long-term (correlated) investments, aiding strategy design.

## Contribution

It introduces a method to identify market time scales and dynamics using empirical mode decomposition and Hurst exponent analysis, distinguishing short-term randomness from long-term correlation.

## Key findings

- Short-term market series have Hurst exponent ~0.5, indicating randomness.
- Long-term market series have Hurst exponent ≥0.75, indicating correlation.
- Long-term series are correlated with company fundamentals.

## Abstract

Different investment strategies are adopted in short-term and long-term depending on the time scales, even though time scales are adhoc in nature. Empirical mode decomposition based Hurst exponent analysis and variance technique have been applied to identify the time scales for short-term and long-term investment from the decomposed intrinsic mode functions(IMF). Hurst exponent ($H$) is around 0.5 for the IMFs with time scales from few days to 3 months, and $H\geq0.75$ for the IMFs with the time scales $\geq5$ months. Short term time series [$X_{ST}(t)$] with time scales from few days to 3 months and $H~0.5$ and long term time series [$X_{LT}(t)$] with time scales $\geq5$ and $H\geq0.75$, which represent the dynamics of the market, are constructed from the IMFs. The $X_{ST}(t)$ and $X_{LT}(t)$ show that the market is random in short-term and correlated in long term. The study also show that the $X_{LT}(t)$ is correlated with fundamentals of the company. The analysis will be useful for investors to design the investment and trading strategy.