README.md

Bootstrap Price Time Series

This repo demonstrates a few time series bootstrap methods to synthesize price/return paths for robustness simulation.

Methods to Synthesize Simulation Data

Parametric model

• Requires parsimonious trade-off between fitting error and model complexity.
• Requires assumptions.

Traditional i.i.d. bootstrapping: resampling history with replacement

• Serial correlation bias in momentum: returns are not independently distributed and tend to be persistent for a stretch.
• Underlying: Anchoring effect / cognitive bias / disposition effect
• Volatility clustering

Block bootstrapping: preserve return autocorrelation

• Sampling histories from blocks of time
• Moving Block Bootstrapping (MBB): Beginning and ending points of blocks are underrepresented.
• Circular Block Bootstrapping (CBB)
• Python: arch, recombinator
• Block length as a hyper parameter

Summary Statistics on Original Real Price Data

Comparing ACF and PACF of the Original and Synthesized Data

ACF & PACF of Real Return Data

ACF & PACF by CBB	ACF & PACF by i.i.d. Bootstrap

Price Paths from Synthesized Data

Synthesized Price Path by CBB	Synthesized Price Path by i.i.d. Bootstrap

Future research:

• Block bootstrap across correlated assets or asset classes.
• Mixture models for generating paths.