Generative Learning for Financial TS with Irregular and Scale-Invariant PatternsPermalink


ContentsPermalink

  1. Abstract
  2. Introduction
  3. Related Work
  4. Problem Statement
  5. FTS-DIffusion Framwork
    1. Pattern Recognition
    2. Pattern Generation
    3. Pattern Evolution


AbstractPermalink

Limited data in financial applications

Synthesize financial TS !!

  • Challenges: Irregular & Scale-invariant patterns

( Existing approaches: assume regularity & uniformity )


FTS-DiffusionPermalink

To model Irregular & Scale-invariant patterns that consists of 3 modules

  • (1. Patterrn Recognition) Scale-invariant pattern recogntion algorithm
    • to extract recurring patterns that vary in duration & magnitude
  • (2. Pattern Generation) Diffusion-based generative network
    • to synthesize segments of patterns
  • (3. Pattern Evolution)
    • model the temporal transition of patterns


1. IntroductionPermalink

Problem in Finance data

  • (1) dearth of data & low signal-to-noise ratio
  • (2) cannot run experiments to obtain more data


Solution: Data Augmentation, using diffusion model

Still, challenge in “finance TS” … Why??

Two reasons:

  • (1) Lack of regularity
  • (2) Scale-invariance
    • financial TS appear to conatin more subtle patterns that repeat themselves with varyring duration and magnitude


figure2

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SolutionPermalink

Deconstruct financial TS into 3 prong process

  • (1) Pattern Recognition
    • to identify irregular & scale-invariant patterns
  • (2) Generation
    • to synthesize segments of patterns
  • (3) Evolution
    • to connect the generated segments


ContributionPermalink

  1. Identify & Define 2 properties in TS finance

    • Irregularity
    • Scale-invariance

    Propose novel FTS-Diffusion framework

  2. Three modules

    • (1) Pattern Recognition: based on SISC (Scale-Invariant Subsequence Clustering) algorithm
      • incorporate DTW to capture irregular patterns
    • (2) Generation: consists of a diffusion-baseed network
      • conditional on the patterns learned by SISC
    • (3) Evolution: made up of pattern transition network
      • produce temporal evolution of consecutive patterns
  3. Experiments on real world finance TS


2. Related WorkPermalink

DGM (Deep Generative Modeling) in TS

  • TimeVAE (2021): VAE to model trend & seasonality in TS
  • RCGAN (2017) & MV-GAN(2020) : GAN for medical TS
  • TimeGAN (2019): GAN for general TS
  • QuantGAN (2020): GAN for financial TS
  • CSDI (2021): Score-based diffusion … unconditional version can be used as generative model
  • DiffWave (2021) & BinauralGrad (2022): Generate waveform TS with diffusion models

Common Limitation: Model TS with REGULAR patterns


3. Problem StatementPermalink

(1) Unique characteristics of Financial TSPermalink

Propose a novel framework to model (1) irregular & (2) scale-invariant TS


Notation

  • X={x1,,xM} : MTS of m segments

    • xm={xm,1,,xm,tm}.
    • Total Length: T=Mm=1tm.xm
  • Sampled from a conditional distribution f(p,α,β)

    • pattern pP,
    • duration is scaled by α and magnitude scaled by β.

    xm will be statistically similar to its underlying pattern p while allowing for adjustments in duration and magnitude.


To model the dynamics across patterns, we employ a Markov chain

  • Tuple (p,α,β) : State
  • Q(pj,αj,βjpi,αi,βi) : State transition probabilities


(2) Problem StatementPermalink

Seek to operationalize the structure laid out in Sec. 3.1

No knowledge of …

  • the segments {xm}Mm=1
  • the set of scale-invariant patterns P
  • the scaling factors α and β
  • the transition probabilities Q(pj,αj,βjpi,αi,βi).


Goal : develop a data-driven framework to accomplish the following:

  • (Pattern Recognition)
    • identify the patterns P
    • group segments into clusters according to their patterns pP;
  • (Pattern Generation)
    • learn the distribution f(p,α,β),pP;
  • (Pattern Evolution)
    • learn the pattern transition probabilities Q(pj,αj,βjpi,αi,βi).


4. FTS-Diffusion FrameworkPermalink

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(1) Pattern RecognitionPermalink

Goal: Identify Irregular & Scale-invariant patterns

Propose novel Scale-Invariant Subsequence Clusterint (SISC) algorithm

  • To partition entire TS into segments of variable length … itno K clusters

    ( same cluster = similar shape (DTW-based) )

  • Use K-means
  • Greedy segmentation strategy

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Distance metric: d(,)Permalink

  • DTW: Robust to varying lengths & magnitudes
  • DTW(x,y):=minAAA,Δ(x,y).
    • A : Alignment between two sequences in the set of all possible alignments
    • Δ(x,y)=[δ(xi,yj)]ij : Pointwise distance matrix between two sequences x and y.


(2) Pattern GenerationPermalink

Goal: Learn pattern-conditioned temporal dynamices

Propose a pattern generation module θ


[First network] Pattern-conditioned diffusion network

  • Conditional denoising process
    • Forward: xN=x0+N1i=0N(xi+1;1β(xip),βI)
    • Backward: x0=xNN1i=0ϵθ(xi+1,i,p)

[Second network] Scaling AE

  • learn the transformation btw variable length x and fixed length x0


Jointly train two networks

  • L(θ)=Exm[xmˆxm22]+Ex0m,i,ϵ[ϵiϵθ(xi+1m,i,p)22].


(3) Pattern EvolutionPermalink

Pattern evolution network

(ˆpm+1,ˆαm+1,ˆβm+1)=ϕ(pm,αm,βm).

  • where (ˆpm+1,ˆαm+1,ˆβm+1) denotes the next pattern & scales in length and magnitude.


Loss function

  • L(ϕ)=Exm[CE(pm+1,ˆpm+1)+∣∣αm+1ˆαm+122+∣∣βm+1ˆβm+122].

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