## 4 Related Work: Generative FTS Models  
The application of generative approaches to modelling FTS data is a more recent development. Most research papers so far have tended toward an applied experimental approach for generating synthetic stock returns or foreign exchange (FX) rate data. The papers experimented with training generative models for different tasks, including:  
1. **'In-filling' data out of sample** (i.e., prediction tasks). [PERSON] et al. [9], [PERSON] et al. [10] trained GANs to make short-term stock price predictions for univariate FTS. 2. **Density estimation**. Though GANs implicitly learn latent data densities, [PERSON] and [PERSON] [17] demonstrate that a restricted Boltzmann machine (RBM) with stochastic Bernoulli activations [49] could estimate joint densities and higher moments of the DGP for multivariate FX log-return data, as well as reproduce desired autocorrelation and non-stationary behaviours via a controlled early stopping 'thermalisation' parameter. 3. **Generating synthetic data**. Other approaches explored for generative FTS modelling included denoising autoencoders and style transfer for FX data [50] and multivariate Gaussian sequence mixtures [51]. FTS GAN models in the literature used various network topologies for generator and discriminator networks. [PERSON] et al. [11] developed FIN-GAN, which used an ensemble product of CNN and MLP outputs to model US equities. [PERSON] et al. [12] developed Quant GAN, which used a TCN with skip layers to jointly learn generative models for drift and volatility stochastic processes akin to GARCH model classes for the S&P500. Only a few papers [13; 14; 15] applied cGANs for FTS generative modelling. [PERSON] et al. [13] used single-hidden-layer MLP networks to train cGANs conditioned on 1 year (252 days) of historical returns to generate 5 years of synthetic data (1260 days) for 573 different assets spanning equities, fixed income, and FX. [PERSON] [14] used deep CNNs with combinations of WGAN-GP [35] and relativistic average critic losses (RaGAN) [52] and conditioning on the previous 100 days of S&P500 returns to jointly simulate 100 days of S&P500 and VIX synthetic data. [PERSON] et al. [15] used a three-layer MLP architecture with WGAN [33] critic loss and conditioning on regime category (normal versus crisis) to generate next-day synthetic data for two US financial stocks. More recently, [PERSON] [16] explored the generative modelling of very-high-dimensional FTS correlation matrices using a deep convolutional GAN (DCGAN) [24]. As of the time of writing, it is the only study known to us that has evaluated GAN performance based on its ability to simulate characteristics of empirically studied multivariate FTS behaviour. There are unique challenges to evaluating the quality and variety of synthetic data. Designing an automated approach to evaluate the FTS GAN output still remains elusive. In the image domain, methods such as inception score [38] that rely on the existence of a deep, pre-trained classification model such as the ImageNet domain do not exist for the FTS domain. As such, no single measure yet exists to describe the quality of synthetic FTS data. To evaluate the performance of generative FTS models, three general approaches were observed among the studies mentioned above. One common approach, **stylised facts**[41; 42; 43], describe well-studied and accepted heuristics for the time series behaviour of financial asset returns. Many other contributions to stylised fact research from the field of empirical finance [53; 54; 55; 56; 57; 58; 59] are discussed further below in Section 5.4. This evaluation approach was taken by [PERSON] et al. [11] and [PERSON] et al. [12] and, in the multivariate case, by [PERSON] [16].