Generative Learning for Financial TS with Irregular and Scale-Invariant PatternsPermalink
ContentsPermalink
- Abstract
- Introduction
- Related Work
- Problem Statement
- FTS-DIffusion Framwork
- Pattern Recognition
- Pattern Generation
- 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
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
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Identify & Define 2 properties in TS finance
- Irregularity
- Scale-invariance
Propose novel FTS-Diffusion framework
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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
- (1) Pattern Recognition: based on SISC (Scale-Invariant Subsequence Clustering) algorithm
-
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 p∈P,
- 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,βj∣pi,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,βj∣pi,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 p∈P;
- (Pattern Generation)
- learn the distribution f(⋅∣p,α,β),∀p∈P;
- (Pattern Evolution)
- learn the pattern transition probabilities Q(pj,αj,βj∣pi,αi,βi).
4. FTS-Diffusion FrameworkPermalink
(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
Distance metric: d(⋅,⋅)Permalink
- DTW: Robust to varying lengths & magnitudes
- DTW(x,y):=minA∈A⟨A,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+∑N−1i=0N(xi+1;√1−β(xi−p),βI)
- Backward: x0=xN−∑N−1i=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[∣∣xm−ˆxm∣∣22]+Ex0m,i,ϵ[∣∣ϵi−ϵθ(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[ℓCE(pm+1,ˆpm+1)+∣∣αm+1−ˆαm+1∣∣22+∣∣βm+1−ˆβm+1∣∣22].