Synthetic time series are typically generated not from the actual price series, but from the returns series. A naïve approach would be to model the distribution of returns, sample a sequence of returns from the model, and then convert the sequence of returns to a price series. But there are two major problems with this. Firstly, it is not straightforward to model—let alone sample from—fat-tailed (and possibly skewed) distributions. Secondly, and more importantly, even if we could successfully sample a sequence of returns, this will not replicate recurring patterns and statistical regularities such as volatility clustering and mean reversion. This is because returns sampled in this way will be independent and identically distributed, whereas in reality, returns are influenced by past returns. To capture temporal features such as volatility clustering and mean reversion we need therefore to estimate ‘conditional’ distributions; that is, distributions that take into account the previous values of returns.

While ARCH/GARCH models are used to model and forecast volatility, they have not typically been used for generating financial time series. Neural network-based approaches such as GANs (generative adversarial networks), VAEs (variational autoencoders) and RNNs (recurrent neural networks) have emerged as popular approaches, however their performance in this domain has been inconsistent, particularly lacking in their ability to capture features such as volatility clustering and mean reversion. They also suffer limitations and difficulties including training instability, the requirement for large training sets, and limited interpretability.

As with all the UNCRi tools, the UNCRi financial time series generator uses a non-parametric approach. Since there is no actual ‘training’ phase, it is more computationally tractable than parametric approaches, and far more modest in the size of the input dataset required. And because the conditional distribution of returns is explicitly estimated, it can be directly visualized, so interpretability is not a problem. Most importantly, it can easily capture long-term dependencies between returns, meaning that it can produce synthetic financial time series that are far more ‘realistic’ than those produced by parametric methods such as GANs and VAEs.