Detecting And Predicting Price Jumps With Consecutive Signature Distance

Abstract

In order to estimate the hidden states of dynamical systems, Jump Models cluster financial observations along time series and impose a cost on jumping from one cluster to another. While these models can detect abrupt changes in the underlying time series, they suffer from two major drawbacks when it comes to detecting price jumps: (1) they cannot detect two (or more) consecutive jumps; (2) they cannot dissociate high volatility from jumps. To remedy these drawbacks, Bloch and Liao consider two seemingly unrelated problems: (1) Detecting and predicting price jumps by identifying whether a new observation results in a price jump relative to previous observations; (2) Anomaly detection of segments of a time series, that is, fixed size segments of a time series are treated as a normal corpus, and search for outliers. It is observed that while these problems are clearly different, the former can be reformulated in terms of the latter and they can therefore associate jump indicators to data-driven metrics for anomaly detection. Bloch and Liao propose a three-step process: (1) jump detection: the variance norm is combined with path signatures to come up with a data-driven jump indicator; (2) training: Bloch and Liao use this Variance Norm Jump Indicator as an input feature for Jump Models; (3) prediction: the authors use new incoming data to predict its hidden state. This approach aims at enhancing the model�s accuracy and predictive capabilities by leveraging the strengths of variance norm on detecting data points after the jump as outliers from previous distribution. Bloch and Liao conducted an extensive analysis on simulated data, examining the structure, benefits and limitations of the approach, and found that they could retrieve the true hidden states with high accuracy without using future information.