WATTNet: Learning to Trade FX via Hierarchical Spatio-TemporalRepresentation of Highly Multivariate Time Series

Michael Poli1,2, Jinkyoo Park2, Ilija Ilievski1

1Neuri Pte Ltd, Singapore, Singapore2Department of Industrial & Systems Engineering, KAIST, Daejeon, South Korea

michael.poli@neuri.ai, jinkyoo.park@kaist.ac.kr, ilija139@neuri.ai

Abstract

Finance is a particularly challenging application area fordeep learning models due to low noise-to-signal ratio,non-stationarity, and partial observability. Non-deliverable-forwards (NDF), a derivatives contract used in foreign ex-change (FX) trading, presents additional difficulty in the formof long-term planning required for an effective selection ofstart and end date of the contract. In this work, we focuson tackling the problem of NDF tenor selection by leverag-ing high-dimensional sequential data consisting of spot rates,technical indicators and expert tenor patterns. To this end,we construct a dataset from the Depository Trust & Clear-ing Corporation (DTCC) NDF data that includes a compre-hensive list of NDF volumes and daily spot rates for 64 FXpairs. We introduce WaveATTentionNet (WATTNet), a noveltemporal convolution (TCN) model for spatio-temporal mod-eling of highly multivariate time series, and validate it acrossNDF markets with varying degrees of dissimilarity betweenthe training and test periods in terms of volatility and generalmarket regimes. The proposed method achieves a significantpositive return on investment (ROI) in all NDF markets un-der analysis, outperforming recurrent and classical baselinesby a wide margin. Finally, we propose two orthogonal inter-pretability approaches to verify noise stability and detect thedriving factors of the learned tenor selection strategy.

1 IntroductionFollowing recent trends of successful AI adoption, the finan-cial world has seen a significant surge of attempts at lever-aging deep learning and reinforcement learning techniquesacross various application areas. Slowing down progress inthis field are the particular properties of financial data: lowsignal-to-noise ratio (Guhr and Kalber 2003), partial ob-servability, and irregular sampling. Furthermore, AI break-throughs in finance often go unpublished due to monetaryincentives. Additional challenges are caused by the scarcityof datasets available, which are often limited in scope, dif-ficult to acquire or for some application areas missing alto-gether.

As an attempt to alleviate some of these concerns, we re-lease both a curated dataset and a novel model for foreign

Copyright c© 2020, Association for the Advancement of ArtificialIntelligence (www.aaai.org). All rights reserved.

exchange (FX) futures trading. We focus our attention ona particular class of FX trading methods, non-deliverable-forward (NDF) contracts, which constitute an importantopen problem in finance and can serve as a challengingbenchmark for supervised or reinforcement learning mod-els. We formulate the learning problem as an optimal selec-tion problem in which the model is tasked with selecting theend date of the forward contract (tenor) from a rich inputcontaining past human trade patterns as well as spot ratesand technical indicators. In particular, tenor selection is castinto a direct imitation learning (Judah, Fern, and Dietterich2012) framework, where the model learns policy π directlyfrom a set of execution trajectories of a demonstration pol-icy π∗ without receiving a reward signal from the environ-ment. The demonstrations are derived in a greedy fashionfrom spot rate data and the resulting input-output tuple isutilized to perform standard supervised learning.

A key difference of our approach compared to existingFX trading algorithms lies in the type of data relied uponfor learning, which includes expert tenor patterns in additionto standard technical indicators. Such patterns are extractedfrom a large dataset containing trades from competitive mar-ket players assumed to be informed about market state andto act rationally in order to achieve higher returns. Leverag-ing this additional information allows the models to differ-entiate between profitable and non-profitable market condi-tions with improved accuracy, ultimately leading to higherreturns.

Fundamentally important for finance are models capableof capturing inter and intra-dependencies in highly multi-variate time series. Many, if not most, of such interactionterms are nonlinear and thus challenging to analyze withstandard statistical approaches. A direct consequence hasbeen the new-found popularity of data-driven models for fi-nancial forecasting tasks, in particular recurrent neural net-works (RNN) and their variants. Recurrent models, whileoffering an intuitive approach to time series modeling, lackan explicit module to capture inter-dependencies and per-form relational reasoning (Santoro et al. 2018). A differentapproach to time series modeling relies on temporal con-volutions (TCN) as its fundamental computational block.Particularly successful in this area of research is WaveNet

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(van den Oord et al. 2016), originally developed as a gener-ative model for speech data. However, vanilla WaveNet andits derivative models are primarily designed to handle uni-variate time series and thus are ill-suited for highly multi-variate financial time series. To bridge this gap, we introducea new TCN model called WaveATTentionNet (WATTNet)that incorporates computationally efficient dilated convolu-tions for temporal learning of autoregressive effects and self-attention modules to learn spatial, inter-time series interac-tion terms.

We summarize our main contributions as follows:

• We curate, analyze, and release a new dataset containingspot rates for 64 FX currencies, along with technical in-dicators and hourly frequency NDF contract trade dataspanning the period from 2013 to 2019. Several models,including classical baselines (Momentum-1, Momentum-90) and recurrent baselines (GRUs, LSTMs) are evaluatedagainst expert NDF data.

• We introduce WATTNet, a novel temporal convolution(TCN) architecture for spatio-temporal modeling. WAT-TNet is designed to extend WaveNet models to settingswith highly multivariate time series data.

• We provide two orthogonal approaches to evaluate noisestability and explain driving factors of the learned tradingstrategy, along with examples to highlight their efficacy.

2 Related Work and BackgroundDeep Learning for FX trading Earlier attempts at utiliz-ing the expressivity of neural networks in forex (FX) tradinghave been carried out in (Chan and Teong 1995), which pre-dicts technical indicators via shallow fully-connected neuralnetworks. (Yu, Lai, and Wang 2005) designs a hybrid trad-ing system capable of providing suggestions based on qual-itative expert knowledge and price forecasting data obtainedfrom a neural network. More recently (Czekalski, Niez-abitowski, and Styblinski 2015), (Galeshchuk and Mukher-jee 2017) and (Petropoulos et al. 2017) leverage fully-connected neural networks, CNNs and classical autoregres-sive modeling techniques. However, these approaches focuson regular forex markets and short-term predictions and relyonly on spot rates and technical indicators as informativefeatures. Incorporating additional sources of data has beenexplored in (Nassirtoussi et al. 2015), (Vargas, De Lima,and Evsukoff 2017) (Hu et al. 2018), in which additionaltextual information obtained from financial news articles oronline discussion is included in the input features.

While the literature has no shortage of works in whichreinforcement learning is applied to portfolio management(Yu et al. 2019) and optimal trade execution, the FX mar-kets remain comparatively unexplored. (Carapuco, Neves,and Horta 2018) develops a short-term spot trading systembased on reinforcement learning and obtains positive ROI inthe EURUSD market. (Sornmayura 2019) offers an analysisof deep Q-learning (DQN) performance on two FX instru-ments. We are not aware of any published work where deeplearning or reinforcement systems are introduced to tackleFX trading in an NDF setting.

Spatio temporal modeling WaveNet (van den Oord etal. 2016) is an autoregressive model based on dilated tem-poral convolutions (TCN) in which the joint probability ofthe input sequence is modeled as a factorized product ofconditional probabilities. SNAIL (Mishra et al. 2017) ob-tains improvements over vanilla WaveNet by adding a tem-poral attention layer between dilated convolutions. However,both vanilla WaveNet and SNAIL are originally designedto process univariate time series data and are thus unableto learn interaction terms between time series. ConvLSTM(Xingjian et al. 2015) introduce a convolution operation in-side the LSTM cell to capture spatiotemporal information.A weakness of ConvLSTMs is given by the prior assump-tion of structure in the spatial domain where features closertogether are prioritized by the convolution operation, as isthe case for example with video data. In general applica-tions, the time series are arbitrarily concatenated as inputdata and locality assumptions do not hold. Long-Short TermNetwork (LSTNet) (Lai et al. 2018) extracts local featuresin temporal and spatial domain with convolutions and addsa recurrent layer for longer-term dependencies. Similarly toConvLSTM, LSTNet assumes spatial locality. A more re-cent approach to spatio-temporal modeling based on GraphNeural Networks (GNNs) is Spatio-Temporal Graph Convo-lutional Network (STCGN) (Yu, Yin, and Zhu 2018) whichutilizes graph convolution to carry out learning in both spa-tial and temporal dimensions.

2.1 BackgroundWe briefly introduce the necessary background regardingdifferent types of forex trading.

Foreign Exchanges Trading in forex (FX) markets is gen-erally done via spot exchanges or forward exchanges, wherespot rate indicates the present expected buying rate. Thespot market can be volatile and is affected by news cycles,speculation, and underlying market dynamics. On the otherhand, forward exchanges contain a long-term planning com-ponent: two parties fix a binding amount and date of ex-change and the profits are calculated by comparing currencyrates at the start date and fix date. The difference betweenstart date and fix date is commonly referred to as tenor.

Non-Deliverable-Forward An NDF operates similarly toforward exchange contracts and exists as a replacement toforward FX trades in emerging markets. NDF markets areover-the-counter, meaning they operate directly between in-volved parties without supervision, and are generally morevolatile due to limited market-depth. In NDF trades the par-ties agree on notional amounts of primary and secondarycurrency (e.g. dollar USD and korean won KRW) whichdefine the forward rate. The currency amounts are not ex-changed at the end of the contract: instead, NDF tradesare cash-settled in USD, and the cash flow is computed asRt,a = (xt+a − xt)vt where xt is the spot rate at time t, ais the tenor and v is the notional amount. Longer tenors aregenerally more profitable at the expense of a higher volatil-ity, commonly referred to as risk-premia. A successful trad-

NDF contracts 7,580,814Trading hours 35,712Trading days 1,488Number of features per trade hour 1,123Number of FX spot rates 64

Table 1: Summary of dataset statistics. Additional details in-cluded in Appendix A.

ing agent thus has to find a difficult balance between risky,high return and safer, low return actions.

3 NDF DatasetNotation A multivariate time series of length T and di-mension M is indicated as {X}. We use {xi} for individualtime series indexed by i. xi,t selects a scalar element of timeseries i at time index t . In particular, we indicate a sliceacross all time series at time t with {x1,t . . . xM,t}. When-ever the operations on {X} are batched, we add superscript jfor single samples in the batch: {Xj}. With batch sizeN , theresulting tensor {X1} . . . {XN} has dimensionsN×T×M .We refer to tenors as a and to the set of admissible tenorchoices as A.

Expert benchmarks The NDF trade records have beencollected from the The Depository Trust & Clearning Corpo-ration (DTCC) database. These records contain start and enddates of each NDF contract, along with currency amounts.For each trading day t and admissible tenor a ∈ A we ob-tain trading volumes vt,a. We refer to Expert as a tradingagent that chooses tenors corresponding to maximum vol-umes at = arg maxa∈A vt,a. In addition to Expert we obtaina fictitious agent based on NDF records which is assumedto have partial future knowledge of the market dynamics,which we refer to as Expert oracle. Expert oracle is a fil-tered version of Expert: at each trading day t it selects theshortest tenor with positive return:

at = arg mina∈A

{a|(xt+a − xt) > 0} (1)

In particular, Expert oracle is designed to select shortesttenors to avoid a perfect accuracy exploitation of risk-premiawhich would set an unrealistic benchmark for any model.Expert and Expert oracle are used as human trader bench-marks.

Multivariate input data In order to learn how to effec-tively choose NDF tenors, the models have access to time se-ries that can be broadly categorized in three groups: FX spotrates, technical indicators, and NDF tenor volumes. DailyFX spot rates serve as contextual market information andprovide a frame of reference that aids the model in identify-ing profitable states. We include spot rates of 64 major andminor FX currency pairs, with a complete list provided inAppendix A. Raw financial market data is often augmentedwith hand-crafted features to help combat noise and non-stationarity (Ntakaris et al. 2019). To this end, we choose

the following technical indicators and include details in Ap-pendix A:• Simple moving average (SMA)• Exponential moving average (EMA)• Moving Average Convergence Divergence (MACD)• Rolling standard deviation (RSD)• Bollinger Bands (BB)• ARIMA 1-day spot rate forecastThe last category of input features, NDF tenor volumes, isobtained from DTCC NDF records. For each NDF pair un-der consideration and each admissible tenor a ∈ A, we gen-erate a time series of volumes vt,a which includes a summa-tion over all NDF records at a specific day t. In particular,given a choice of maximum tenor of 90 days, each NDF paircontributes with a 90-dimensional multivariate volume timeseries to the input, which further emphasizes the need fora model capable of processing and aggregating informationacross highly multivariate time series. The code for down-loading and preprocessing the data will be released afterpublication.

4 ModelSpatio-temporal modeling with WATTNet WaveATTen-tionNet (WATTNet) is a novel model designed for highlymultivariate time series inputs. WATTNet includes temporalmodules, tasked with independently aggregating informa-tion across time steps of univariate time series {x} ∈ {X}and spatial modules which aggregate features across slicesof all time series at a specific time t {x1,t, . . . xM,t}. Tempo-ral and spatial modules are alternated and allow for learninga hierarchical spatio-temporal representation. An overviewof the model is given in Figure 1.

Temporal learning Temporal learning is achieved by ap-plying temporal dilated convolutions (TCN) to univariatetime series {x} ∈ {X}. In particular, given a convolutionwith kernel size k and dilation coefficient d, we compute theoutput at time t of a dilated convolution of {x} as:

zt =

k∑i=1

wi ∗ xt−i∗d (2)

where wi is the ith weight of the convolutional kernel. Eachunivariate time series has access to its own set of convolu-tional weights w as temporal convolution operations are car-ried on independently. We note that independence betweenconvolutions is necessary to provide the model with enoughflexibility to treat time series with different characteristics.The outputs of the TCN operation are then concatenated asto form a multivariate latent time series {Z}. In particular,WATTNet includes gated convolutions, a standard architec-tural component for sequential data. Two dilated TCNs areapplied to {X} and the results {Z}α, {Z}β are passed tonon-linear activation functions and then multiplied element-wise:

{Z} = σ({Z}α)� tanh({Z}β) (3)

𝑥 𝑥 𝑥 𝑇𝑧 𝑇

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Figure 1: WATTNet overview: dilated TCNs are independently applied to each univariate input time series. A single dot-product attention head subsequently aggregates information across slices {z1,t . . . zM,t} and the result {Z} is passed to the nextWATTBlock or used directly for the task at hand.

where σ indicates a sigmoid activation. The output {Z} isthen fed into a spatial learning module after which the pro-cess repeats for a number of times depending on WATTNet’slayer depth.

Spatial learning A single-head scaled-dot product atten-tion mechanism (Vaswani et al. 2017) is placed betweendilated TCN layers and allows the model to exchange infor-mation across different input time series at a specific timeslice. We compute key K, query Q and value V by consid-ering a slice {z1,t . . . zM,t} ∈ {Z} of latent time series attime t as the input of learnable linear transformation of thetype ψ({z1,t . . . zM,t}) with weights Wk, Wq , Wv . The re-sulting matrices K, Q, and V are then used in the standardscaled-dot product attention to return M weighted averagesof values V:

{z1,t . . . zM,t} = softmax(QKT

√dk

V) (4)

where dk is a scaling factor given by the second dimen-sion of K. The process is repeated for latent feature slices{z1,t . . . zM,t}, t = 1, . . . T and the results are concate-nated into {Z}, a spatio-temporal latent representation ofinput data {X}. Weights Wq,Wk,Wv are shared acrossthe entire sequence length T , allowing the attention headto capture time-invariant features that incorporate informa-tion from multiple time series. Output {Z} can be used di-rectly for different tasks to perform decision making condi-tioned on multivariate time series data; alternatively, if thetask at hand benefits from deeper models, {Z} can instead

be passed to the following TCN layer to perform additionalcycles of temporal and spatial learning.

Hierarchical representation A single temporal and spa-tial module constitute a full WATTNet layer of computa-tion and is referred to as WATTBlock. WATTBlocks can bestacked, in which case output {Z} becomes a hierarchicalspatio-temporal representation of {X}. As is the case withother TCN-based models, the dilation coefficient is doubledeach temporal module as to provide an increasing recep-tive field which allows for a computationally inexpensiveway to model long sequences. An additional benefit of thegradual dilation increase is the slow introduction of inter-action terms between time series which include less laggedvalues for early WATTBlocks and more for later ones. Atlayer i, the dilated TCN for scalar output zt has a receptivefield of 2ik, with k being the size of the convolutional ker-nel. During spatial learning, the information flow across aslice of latent TCN output {Z} at time t {z1,t, . . . zM,t} isthus limited to 2ik lagged values of the raw {X}, given by{x1,[t−2ik:t], . . . xM,[t−2ik:t]}. We observe that gradually in-creasing the size of this interaction window is key in learninga hierarchical representation of the data that strongly inter-twines spatial and temporal causal effects.

Computational requirements WATTNet can be used as ageneral lightweight tool for spatio-temporal modeling. Thetemporal modules are fully parallelizable due to completeindependence of inputs and convolutional weights acrossdifferent univariate time series. To leverage an already ex-

isting fast CUDA implementation of parallel TCNs in Py-Torch, we utilize grouped-convolutions. In particular, the Mdimension of input time series {X} becomes the channeldimension for the TCN, and different convolutional kernelsare applied to each input channel to obtain the correspondingoutput. On the spatial learning front, the attention moduleshave a computational cost of O(TM2), which is compara-ble to the standard quadratic attention cost of O(M2) whenT << M .

5 NDF Tenor SelectionSelecting a profitable tenor is challenging since it burdensthe model with a choice of short tenors with smaller returnsor long, risky tenors with a potentially greater return. Oneapproach to training a tenor selection model is performingimitation learning on Expert or Expert oracle labels. Bothhave advantages and disadvantages; training on Expert al-lows for daily online training and thus reduces the needfor the model to extrapolate to periods further into the fu-ture. This aspect can be particularly beneficial for turbulentmarkets that display frequent regime switches. Expert ora-cle labels, on the other hand, require information from upto N days in the future, with N being the maximum al-lowed tenor, since positive return filtering can only be per-formed by leveraging spot rate data. Expert oracle labelscan be advantageous since they teach the model to be risk-averse; however, both approaches potentially include un-wanted human-bias in the learned strategy. We propose analternative approach in which WATTNet learns from opti-mal greedy tenor labels obtained directly from market data.Given the spot rate value for target FX pair {y}, we extractthe optimal tenor label at at time t as:

at = arg maxa∈A

(yt+a − yt) (5)

Policy divergence (Ross, Gordon, and Bagnell 2011) isa performance degrading issue often present in imitationlearning where the agent accumulates small expert imitationerrors along the rollout and ends up in unexplored regions ofthe state space. To sidestep this issue, we base our strategyon a conditional independence assumption between tenor atand state dynamics st+1: p(st+1|st) = p(st+1|st, at). Thetraining procedure is then carried out as follows. Input timeseries {X} is split into overlapping length T slices which arethen shuffled into a training dataset. At each trading day t,the model φ is trained via standard gradient-descent methodsto minimize the cross-entropy loss of outputs φ({X[t−T :t]})and tenor labels at.

6 Experimental ResultsNDF Markets The experimental evaluation covers the fol-lowing 6 major NDF markets: Chinese Yuan (USDCNY), In-donesian Rupiah (USDIDR), Indian Rupee (USDINR), Ko-rean Won (USDKRW), Philippine Peso (USDPHP), TaiwanDollar (USDTWD). We elaborate on the results for USD-CNY, USDKRW, USDIDR and include discussion of theremaining 3 markets as supplementary material (AppendixC). The selection has been carried out to test the proposed

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Figure 2: Tenor actions across USDKRW test set. Back-ground gradient is used to indicate the ROI of differenttenors. The gradient is slanted since the raw return at dayt with a tenor of 90 days is the same as the return from trad-ing day t + i with tenor of 90 − i days. WATTNet learnsto correctly exploit long periods of positive trend and placesless actions than LSTM-I in negative (red) return regions.

method on markets with different characteristics as shownin Table 3.

Recurrent and classical baselines Two-layer stackedGRU and LSTMs are used as additional baselines for tenorand referred to as GRU-I and LSTM-I. Both recurrent base-lines and WATTnet are connected to a fully-connected headwhich takes as input the latent representation of {X} pro-duced by the model. A probability distribution over tenoractions is then obtained via softmax. Additionally, we in-clude the following classical trading baselines:• Momentum-1: 1-day lag of expert tenor actions. Effective

in markets where monotonic behavior in the spot rate isfrequent and the monotonic sequences span several trad-ing periods.

• Momentum-90: best performing tenor from 90 days prior.Effective in markets with trends whose duration is longercompared to the maximum tenor.

Training setup The models are implemented in PyTorchand trained using Adam (Kingma and Ba 2014) and a learn-ing rate cosine decay schedule from 6e−4 down to 3e−4. Toavoid overfitting uninformative noisy patterns in stale data

USDCNY USDKRW USDIDR

Model ROI opt.acc nn.acc ROI opt.acc. nn.acc. ROI opt.acc. nn.acc.

Optimal 759.8 100 100 844.2 100 100 1260.0 100 100Expert (oracle) 77.6 21.6 100 139.4 13.7 100 152 3.6 100

Expert 0.0 1.4 47.8 12.7 1.9 49.9 230 0.4 67.0Momentum-1 14.6 1.4 48.3 10.7 0.9 49.7 201 0.7 66.5Momentum-90 4.9 6.7 54.1 31.9 2.6 56.2 338 1.9 69.2GRU-I 26.7.± 48.5 4.9± 0.7 54.7± 1.0 −98.7± 35.4 1.5± 0.5 52.1± 1.4 83.5± 33.1 0.6± 0.1 62.9± 2.6LSTM-I 74.3± 37.3 3.7± 0.9 58.7± 2.2 74.6± 30.0 2.6± 0.6 56.0± 2.5 146.4± 40.4 1.1± 0.3 66.5± 1.1WATTNet 219.1 ± 25.5 6.7 ± 0.7 59.5 ± 1.6 142.4 ± 16.9 2.7 ± 0.2 59.5 ± 1.0 280.2± 39.9 1.3± 0.3 69.5 ± 0.9

Table 2: Test results in percentages (average and standard error). Best performance is indicated in bold.

Market µtrain σtrain µval σval

USDCNY 11.33 231.63 -2.96 232.88USDIDR 22.04 506.17 3.48 335.75USDINR 2.88 297.40 8.19 286.79USDKRW 0.50 471.25 -12.75 387.49USDPHP 10.44 271.37 -0.79 240.37USDTWD -3.73 307.28 -2.09 235.29

Table 3: Statistics of 1-step (daily) percent returns. Units re-ported are scaled up by 1e5 for clarity.

input sequence length is set to 30 days. In addition, to enablea fair comparison and avoid additional overfitting we employan early stopping scheme based on training loss that is moti-vated by different convergence times of different models. Weuse a static testing approach with a long period of 446 out-of-sample trading days to test stability of the learned tradingstrategy under turbulent market conditions and a wider dis-tributional shift between in-sample and out-of-sample data.PyTorch code for models and training procedure is includedin the supplementary material.

Metrics The following metrics are used to benchmark theperformance of trading models and baselines:

• Return on investment (ROI): given a tenor action a at timet and spot rate value xt, the percent ROI is calculated asROIt = 100

(xt+a−xt

xt

)• Optimal accuracy: standard supervised learning accuracy

of model outputs yt versus optimal tenor labels yt.

• Non-negative return accuracy: accuracy of model outputsyt compared to tenor actions with positive or zero re-turn. At time t, there are generally multiple tenor actionswith non-negative return, thus rendering non-negative ac-curacy a less strict metric compared to optimal accuracy.It should be noted that it is possible for a high ROI trad-ing model to show poor optimal accuracy but competitivepositive return accuracy since non-negative accuracy alsocaptures positive ROI strategies that differ from optimaltenor labels.

Discussion of results We characterize the 6 NDF marketsunder evaluation based on mean µ and standard deviationσ of their 1-day returns and performance of classical base-lines. Mean-variance statistics given in Table 3 show easiermarkets with similar volatility in training and test periods(e.g. USDINR) as well as markets that appear more erraticand thus challenging to trade profitably in. From Table 2,we determine USDCNY and USDKRW to be challengingfor Momentum and recurrent baselines, in addition to beingbarely profitable for expert traders. GRU-I is unable to con-sistently get positive ROI and we suspect this is caused byits insufficient ability to exchange information between timeseries. LSTM-I, on the other hand, fares better by leveragingits memory module to perform rudimentary spatial learn-ing (Santoro et al. 2018). USDIDR appears to be highlyprofitable for Momentum-90, a phenomenon highlighting alonger positive trend and a higher density of positive returntrades in the test data.

• USDCNY: The results in Table 2 show that all classi-cal baselines, including expert actions, perform poorlyin terms of ROI and optimal tenor accuracy. LSTM andWATTNet, on the other hand, are able to generalize bet-ter, with WATTNet surpassing ROI of oracle trades.

• USDKRW: The USDKRW train-test split presents themost challenging trading period across all 6 NDF mar-kets considered in this work. The return statistics in Table3 show a decrease in mean return as well as a significantchange in volatility. Traditional baselines perform poorlywhereas WATTNet surpasses Expert oracle ROI. Figure 2highlights the ability of WATTNet to adjust its tenor ac-tions depending on trading spot rate trends.

• USDIDR: USDIDR has been chosen to evaluate the base-lines under a profitable trading period. All classical base-lines trade with positive ROI, even surpassing oracle ROIdue to their propensity to trade at longer tenors. WATTNetachieves performance competitive with Momentum base-lines, showing that it is capable of fully exploiting trad-ing periods with long positive trends and a wide shift involatility between training and test data.

6.1 ExplainabilityModel explainability is particularly important in applica-tion areas where the models are tasked with critical decision

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Figure 4: UMAP embedding of model latents. The points arelabeled according to the final tenor output of the model.

making, as is the case for algorithmic trading. Understand-ing driving factors behind a trading decision is necessaryto properly assess the risks involved. We tackle this issueby proposing two orthogonal approaches for evaluating thetenor selection strategy in terms of noise stability and driv-ing factors.

Feature importance by input gradients To pinpoint thedriving factors of trades at different tenors we propose sort-ing the features by their gradient magnitude. In the case oftenor selection, each input feature carries a specific mean-ing which can be leveraged by domain experts to confirmwhether the model outputs actions consistent with marketdynamics.

Given a batch of N multivariate input sequences{X1} . . . {XN} with tenor labels equal to a, we computethe cross-entropy loss of model L and derive the empiricalexpectation for the absolute value of time series {xj} inputgradient as follows:

Gj =1

T

∣∣∣∣∣T∑t=1

∂L∂xjt

∣∣∣∣∣ (6)

To illustrate the effectiveness of this approach we se-lect 6 spot rate features with highest absolute gradientvalues for tenor actions of 90 days in the USDCNYtest data: EURSGD, GBPAUD, USDCHF, EURDKK, US-DSGD, AUDNZD (Figure 3). The Pearson’s correlation co-

efficient ρ between USDCNY and each of the above-listedfeatures is computed with training and test sets. In the back-ground, 20 day rolling standard deviation highlights regionsof low and high volatility. Input sequences {x} ∈ {X}which are mapped by the model to 90 tenor actions are col-ored in red, whereas the actions themselves are indicated asblack dots. The model learns to trade on long tenors whencurrencies that are positively correlated with USDCNY, suchas USDSGD, undergo periods of growth. The degree towhich such trends affect the model is directly reflected in ρ:USDCHF, still positively correlated with USDCNY, shows aless decisive positive trend, with additional ups and downs.Moreover, the model learns to favor trading periods with lowvolatility. This analysis can be extended by domain expertsto additional input features, such as technical indicators orpast tenor actions, and can boost confidence in the decisionsmade by the model.

Latent space representation Desired properties of thelearned trading strategy are input coherence and stability.Input coherence is achieved by a model that outputs sim-ilar tenors for similar states. Stability, on the other hand,is concerned with how much noise perturbation is requiredto cause a tenor switch from a certain state. We performa visual inspection of these properties via a uniform man-ifold approximation and projection (UMAP) which excelsat capturing both local and global structure of the high-dimensional data (McInnes, Healy, and Melville 2018). Foreach model, latent vectors of their last layer are embeddedinto two-dimensional space. UMAP outputs compact clus-ters of labels for input coherent models and more volumet-ric clusters for stable models. From Figure D we observethat WATTNet learns a coherent latent representation thatclusters low and high tenors correctly and covers a largervolume of the embedding space. Instability of GRU-I andLSTM-I observed in the results of Table 2 can in part be ex-plained by noticing that their learned representation lies onthin lower-dimensional manifolds with mixed tenor labels.As a result, small noise perturbations can cause wide jumpsin tenor actions, potentially causing a drop in performance.

7 ConclusionWe introduced a challenging imitation learning problem,tenor selection for non-deliverable-forward (NDF) con-tracts. With the goal of promoting further research in this di-rection, we constructed and released a comprehensive NDFdataset and designed WaveATTentioNet (WATTNet), a novelmodel for spatio-temporal data which outperforms expertbenchmarks and traditional baselines across several NDFmarkets. Finally, we employed two explainability techniquesto determine driving factors and noise stability of the learnedtenor strategy. Future work includes defining and solving or-der sizing of an NDF contract, as well as augmenting thetenor selection model with a reinforcement learning agenthead. Reminiscent of world models (Ha and Schmidhu-ber 2018), such an approach would sacrifice explainabilityfor additional flexibility; the agent could for example beequipped with a memory module consisting of a recurrentnetwork to keep track of its previous trades. A different di-rection would be exploring the use of multi-head attentioninstead of single-head as an effective modification to WAT-TNet in the case of long input sequences or multiple rela-tions between features.

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6 context FX instruments

Currency 1 Currency 2 Name

United States Dollar Chinese Yuan USDCNYUnited States Dollar Indonesian Rupiah USDIDRUnited States Dollar Indian Rupee USDINRUnited States Dollar Korean Won USDKRWUnited States Dollar Philippine Peso USDPHPUnited States Dollar Taiwan Dollar USDTWD

Table 4: NDF FX instruments

A Dataset detailsHere we report more information about the dataset.

• Period: 2013-09-10 to 2019-06-17

• Number of features (M dimension of {X}): 1123. 64 FXpairs, 519 technical indicators, 540 NDF volume features.More specifically, 90 NDF volume features per NDF pair(90 * 6)

The list of context NDF spot rates is given in Table 1, andcontext FX spot rates in Table 2. Context spot rates havebeen obtained via the Oanda Developer API.

Technical Indicators Here we include more details aboutthe technical indicators, including their dimensionality asnumber of features.

• Simple moving average (SMA): SMA is a trend-followingindicators that filters out high frequency oscillations bysmoothing spot rate time series. We use both 7 day and 21day averages (i.eN = 7,N = 21). Included for all 64 FXpairs (total: 64 * 2 = 128 features).

• Exponential moving average (EMA): similarly to SMA,EMA is a lagging indicator. The weight for each valuesexponentially decreases, with bigger weight assigned tomore recent values of the time series. We include 12 dayand 26 day EMAs (total: 128 features).

µt ={xt t = 1αxt + (1− α)µt−1 t > 1

(7)

• Moving Average Convergence Divergence (MACD): Afiltering function with a bigger time constant is subtractedto another with a smaller one in order to estimate thederivative of a time series. In particular, a common choiceof filtering functions are 12 day and 26 day exponentialmoving averages: MACD = EMA12 − EMA26 (total: 64features).

• Rolling standard deviation (RSD): a window of 20 days isused to compute standard deviation at time t = 20 (total:64 features).

• Bollinger Bands (BB): commonly used to characterizevolatility over time. We include both an upper band de-rived and a lower band as features BB = SMA ± RSD(total: 64 * 2 = 128 features)

58 context FX instruments

Currency 1 Currency 2 Name

Euro United States Dollar EURUSDPound Sterling United States Dollar GBPUSDUnited States Dollar Canadian Dollar USDCADUnited States Dollar Swiss Franc USDCHFUnited States Dollar Japanese Yen USDJPYEuro Pound Sterling EURGBPEuro Swiss Franc EURCHFAustrial Dollar United States Dollar AUDUSDAustrial Dollar Canadian Dollar AUDCADEuro Japanese Yen EURJPYPound Sterling Japanese Yen GBPJPYEuro Australian Dollar EURAUDEuro Czech Koruna EURCZKEuro Hungarian Forint EURHUFEuro New Zealand Dollar EURNZDEuro Swedish Krona EURSEKEuro Singapore Dollar EURSGDEuro Canadian Dollar EURCADEuro Danish Krone EURDKKEuro Norwegian Krone EURNOKEuro Polish Zloty EURPLNEuro Turkish Lira EURTRYEuro South African Rand EURZARUnited States Dollar Danish Krone USDDKKUnited States Dollar Hungarian Forint USDHUFUnited States Dollar Mexican Peso USDMXNUnited States Dollar Poland Zloty USDPLNUnited States Dollar Swedish Krona USDSEKUnited States Dollar Thai Baht USDTHBUnited States Dollar South African Rand USDZARUnited States Dollar Czech Koruna USDCZKUnited States Dollar Hong Kong Dollar USDHKDUnited States Dollar Norwegian Krone USDNOKUnited States Dollar Saudi Riyal USDSARUnited States Dollar Singapore Dollar USDSGDUnited States Dollar Turkish Lira USDTRYPound Sterling Australian Dollar GBPAUDPound Sterling Swiss Franc GBPCHFPound Sterling South African Rand GBPZARPound Sterling Singapore Dollar GBPSGDAustralian Dollar Japanese Yen AUDJPYAustralian Dollar Singapore Dollar AUDSGDCanadian Dollar Japanese Yen CADJPYSwiss Franc Japanese Yen CHFJPYNew Zealand Dollar Canadian Dollar NZDCADNew Zealand Dollar United States Dollar NZDUSDSingapore Dollar Japanese Yen SGDJPYSouth African Rand Japanese Yen ZARJPYPound Sterling Canadian Dollar GBPCADPound Sterling New Zealand Dollar GBPNZDPound Sterling Poland Zloty GBPPLNAustralian Dollar New Zealand Dolar AUDNZDCanadian Dollar Swiss Franc CADCHFCanadian Dollar Singapore Dollar CADSGDSwiss Franc South African Rand CHFZARNew Zealand Dollar Japanese Yen NZDJPYNew Zealand Dollar Singapore Dollar NZDSGDTurkish Lira Japanese Yen TRYJPYUnited States Dollar Malaysian Ringgit USDMYR

Table 5: 58 FX instruments used as context in the dataset

Layer Input dim. Output dim.

Recurrent-1 1123 512Recurrent-2 512 512FC-1 512 128FC-1 128 91

Table 6: Layer dimensions for recurrent models GRU-I andLSTM-I

Layer M-in M-out T-in T-out

FC-cmp 1123 90 30 30WATTBlock-1 90 90 30 27WATTBlock-2 90 90 27 23WATTBlock-3 90 90 23 21WATTBlock-4 90 90 21 17WATTBlock-5 90 90 17 15WATTBlock-6 90 90 15 11WATTBlock-7 90 90 11 9WATTBlock-8 90 90 9 5FC-1 5*90 512 1 1FC-2 512 91 1 1

Table 7: Layer dimensions (M and T) for WATTNet

• ARIMA spot rate forecast: an ARIMA model is trainedto perform 1-day forecasts of spot rates using data fromperiods preceding the start of the training set to avoid in-formation leakage. The forecasts are added as time seriesfeatures. Included for NDF pairs and for USDMYR (total:7 features)

Training hyperparameters The data is normalized asxt = xt−µ

σ where µ and σ are 60-day rolling mean andstandard deviation respectively. The dataset is split into ove-lapping sequences of 30 trading days. Batch size is set to32.

B Architectural hyperparametersWe herein provide detailed information about the model de-sign.

Recurrent Models GRU-I and LSTM-I share the samestructure given in Table 6. Layer depth has been chosenas the best performing in the range 1 to 6. Latent spatio-temporal representation {Z} of input time series {X} is ob-tained as the output of Recurrent-2. {Z} is the tensor trans-formed via UMAP and shown in Appendix D.

WATTNet Details about the WATTNet used are foundin Table 7. We employ fully-connected layer (FC-emp)for compression in order to constrain GPU memory us-age to less than 6GB. Improved results can be obtained bylifting this restriction and increasing the WATTBlock M -dimension. {Z} is the output of WATTBlock-8. Due to the

relatively short input sequence length, the dilation is sched-uled for reset every 2 WATTBlocks. More specifically, thedilation coefficients for temporal learning are 2, 4, 8, 16,2, 4, 8, 16 for WATTBlock-1 to 8. As is common in otherdilated TCN models, dilation introduces a reduction of Tdimension for deeper layers. This effect is observable inTable 7. We utilize a residual architecture for the attentionmodule where the output is the summation of pre and postattention tensors, i.e:{Zout} = σ({z1,t . . . zM,t}) + ({x1,t . . . xM,t}) (8)

C Additional resultsWe provide additonal results and discussion of USDINR,USDPHP and USDTWD. Training and test periods for allNDF pairs are visualized in Figures 1-2 for reference. Figure7 shows Expert and Expert oracle tenor action distributions.The results are given in Table 8.

USDINR USDINR shows positive trend in mean returnand its volatility remains constant between training and test.All baselines achieve high ROI in this scenario. Of partic-ular interest is GRU-I, which surpasses LSTM-I likely dueto the relative simplicity of USDINR dynamics. With a sta-ble, positive trend GRU-I is able to focus on the spot ratesdirectly, thus circumventing its inability to perform properspatial learning.

USDPHP USDPHP is slightly more challenging due to itsminimal volatility shift. WATTNet outperforms other mod-els in terms of ROI and optimal accuracy.

USDTWD USDTWD has negative mean return andshows a reduction in volatility in the test set. WATTNet isable to exploit this phenomenon and significantly outper-forms all other baselines.

Rolling testing and online training In general, static test-ing can turn out to be particularly challenging for finan-cial data with longer test sets, since the models are taskedwith extrapolating for long periods, potentially under non-stationary condition of the market. A rolling testing ap-proach can be beneficial; however, the size of window andtest periods require ad-hoc tuning for each FX currency. Akey factor influencing the optimal choice of window size isthe average length of market regimes. We leave the discus-sion on optimal window selection for rolling testing as fu-ture work. Figure 7 shows distributions of tenor labels andhighlights the difference in average tenor length.

D Tenor actions and latent UMAPembeddings

In this section we provide a complete collection of tenor ac-tion plots and UMAP embeddings for all NDF markets un-der consideration. Background gradient is used to indicatethe ROI of different tenors. The gradient is slanted since theraw return at day t with a tenor of 90 days is the same as thereturn from trading day t+ i with tenor of 90− i days.

USDINR USDPHP USDTWD

Model ROI opt.acc nn.acc ROI opt.acc. nn.acc. ROI opt.acc. nn.acc.

Optimal 1288.7 100 100 900.0 100 100 612.0 100 100Expert (oracle) 123.2 6.7 100 114.1 6.7 100 91.4 9.8 100

Expert 216.1 0.7 62.7 117.1 0.2 57.2 43.3 0.9 50.2Momentum-1 218.1 2.6 62.5 110.9 0.7 58.9 44.0 0.5 50.0Momentum-90 300.9 2.2 57.4 134.9 1.2 58.9 10.0 1.4 55.2GRU-I 273.5± 29.0 2.0± 0.5 63.2± 2.3 244.2± 27.5 2.3± 0.1 62.5± 1.4 46.6± 34.9 2.5± 0.3 57.6± 1.2LSTM-I 239.9± 67.3 2.4± 0.5 61.6± 2.0 307.1± 16.8 1.8± 0.2 71.3 ± 1.0 46.8± 27.9 2.8± 0.6 59.6± 1.4WATTNet 313.0 ± 28.1 3.7 ± 0.2 65.9 ± 1.0 329.7 ± 31.2 3.3 ± 0.6 70.0± 0.7 162.9 ± 13.9 2.8 ± 0.3 59.8 ± 1.4

Table 8: Test results in percentages (average and standard error). Best performance is indicated in bold.

2014 2015 2016 2017 2018 2019

6.2

6.4

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7.0USDCNY spot rate

TrainingValidation

2014 2015 2016 2017 2018 2019100001100012000130001400015000

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Figure 5: Training and test periods for NDF pairs

2014 2015 2016 2017 2018 20191000

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1250 USDKRW spot rateTrainingValidation

2014 2015 2016 2017 2018 20194042444648505254

USDPHP spot rateTrainingValidation

2014 2015 2016 2017 2018 201929

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34 USDTWD spot rateTrainingValidation

Figure 6: Training and test periods for NDF pairs

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Figure 7: Distribution of tenor actions for Expert and ExpertOracle.

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Figure 8: USDCNY tenor actions

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Figure 9: USDIDR tenor actions

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Figure 10: USDINR tenor actions

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Figure 11: USDKRW tenor actions

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Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDPHP: Optimal tenors, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Hold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDPHP: Expert (oracle), % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDPHP: GRU, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDPHP: LSTM, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDPHP: WATTNet, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Figure 12: USDPHP tenor actions

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDTWD: Optimal tenors, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Hold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDTWD: Expert (oracle), % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDTWD: GRU, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDTWD: LSTM, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Trading DaysHold

Buy<10d

Buy<20d

Buy<30d

Buy<40d

Buy<50d

Buy<60d

Buy<70d

Buy<80d

Buy<90dUSDTWD: WATTNet, % return gradient

0.08

0.06

0.04

0.02

0.00

0.02

0.04

0.06

0.08

Figure 13: USDTWD tenor actions

Embedding dim: 0

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GRU-I, `USDCNY`, UMAP

0102030405060708090

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LSTM-I, `USDCNY`, UMAP

0102030405060708090

Embedding dim: 2

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0102030405060708090

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Embedding dim: 1

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WATTNet, `USDCNY`, UMAP

0102030405060708090

Embedding dim: 2

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0102030405060708090

Figure 14: UMAP of latent representation - USDCNY

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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GRU-I, `USDIDR`, UMAP

0102030405060708090

Embedding dim: 2

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

LSTM-I, `USDIDR`, UMAP

0102030405060708090

Embedding dim: 2

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

WATTNet, `USDIDR`, UMAP

0102030405060708090

Embedding dim: 2

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0102030405060708090

Figure 15: UMAP of latent representation - USDIDR

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

GRU-I, `USDINR`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

LSTM-I, `USDINR`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Embedding dim: 0

Embe

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m 1

0102030405060708090

Embedding dim: 1

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m 2

WATTNet, `USDINR`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Figure 16: UMAP of latent representation - USDINR

Embedding dim: 0

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m 1

0102030405060708090

Embedding dim: 1

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m 2

GRU-I, `USDKRW`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

LSTM-I, `USDKRW`, UMAP

0102030405060708090

Embedding dim: 2

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0102030405060708090

Embedding dim: 0

Embe

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0102030405060708090

Embedding dim: 1

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m 2

WATTNet, `USDKRW`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Figure 17: UMAP of latent representation - USDKRW

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

GRU-I, `USDPHP`, UMAP

0102030405060708090

Embedding dim: 2

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

GRU-I, `USDPHP`, UMAP

0102030405060708090

Embedding dim: 2

Embe

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m 0

0102030405060708090

Embedding dim: 0

Embe

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m 1

30

40

50

60

70

80

90

Embedding dim: 1

Embe

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m 2

WATTNet, `USDPHP`, UMAP

30

40

50

60

70

80

90

Embedding dim: 2

Embe

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m 0

30

40

50

60

70

80

90

Figure 18: UMAP of latent representation - USDPHP

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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GRU-I, `USDTWD`, UMAP

0102030405060708090

Embedding dim: 2

Embe

ddin

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m 0

0102030405060708090

Embedding dim: 0

Embe

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0102030405060708090

Embedding dim: 1

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m 2

LSTM-I, `USDTWD`, UMAP

0102030405060708090

Embedding dim: 2

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m 0

0102030405060708090

Embedding dim: 0

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0102030405060708090

Embedding dim: 1

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m 2

WATTNet, `USDTWD`, UMAP

0102030405060708090

Embedding dim: 2

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m 0

0102030405060708090

Figure 19: UMAP of latent representation - USDTWD