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But producing a set of synthetic stock price data is even more of a challenge because not only do the above do the above requirements apply, but we also need to ensure that the open, high, low and closing prices are internally consistent, i. These basic consistency checks have been overlooked in the research thus far.
Econometric Methods One classical approach to the problem would be to create a Vector Autoregression Model, in which lagged values of the Open, High, Low and Close prices are used to predict the current values see here for a detailed exposition of the VAR approach. While a VAR model potentially has the ability to model long memory and even GARCH effects, it is unable to produce stock prices that are guaranteed to be consistent, in the sense defined above.
Another approach favored by some researchers is to stitch together sub-samples of the real data series in a varying time-order. This is applicable only to return series and, in any case, can introduce spurious autocorrelations, or overlook important dependencies in the data series. Besides these defects, it is challenging to produce a synthetic series that looks substantially different from the original — both the real and synthetic series exhibit common peaks and troughs, even if they occur in different places in each series.
Deep Learning Generative Adversarial Networks In a previous post I looked in some detail at TimeGAN, one of the more recent methods for producing synthetic data series introduced in a paper in by Yoon, et al link here. Generating Synthetic Market Data TimeGAN, which applies deep learning Generative Adversarial Networks to create synthetic data series, appears to work quite well for certain types of time series.
But in my research I found it be inadequate for the purpose of producing synthetic stock data, for three reasons: i The model produces synthetic data of fixed window lengths and stitching these together to form a single series can be problematic. For both TimeGAN and DoppleGANger, the researchers have tended to benchmark performance using classical data science metrics such as TSNE plots rather than the more prosaic consistency checks that a market data specialist would be interested in, while the more advanced requirements such as long memory and GARCH effects are passed by without a mention.
The conclusion is that current methods fail to provide an adequate means of generating synthetic price series for financial assets that are consistent and sufficiently representative to be practically useful. Important if we are looking to mass-produce synthetic series for a large number of assets, for a variety of different applications.
Some deep learning methods would struggle to meet this requirement, even supposing that transfer learning is possible. In some case we want synthetic price series that are highly correlated to the original; in other cases we might want to test our investment portfolio or risk control systems under extreme conditions never before seen in the market.
After researching the problem over the course of many years, I have at last succeeded in developing an algorithm that meets these requirements. Before delving into the mechanics, let me begin by illustrating its application. Synthetic Price Series Generating ten synthetic series using the algorithm takes around 2 seconds with parallelization. I chose to generate series of the same length as the original, although I could just as easily have produced shorter, or longer sequences. The first task is to confirm that the synthetic data are internally consistent, and indeed is guaranteed to be so because of the way the algorithm is designed.
For example, here are the first few daily bars from the first synthetic series: This means, of course, that we can immediately plot the synthetic series in a candlestick chart, just as we did with the real data series, above. While the real and synthetic series are clearly different, the pattern of peaks and troughs somehow looks recognizably familiar.
Obviously this is a much more bullish scenario that we have seen in reality. Here, too, we see several very large drawdowns, especially in the period from , but there is also a general upward drift in the process that enables the Index to reach levels comparable to those achieved by the real series: Price Correlations Reflecting these very different price path evolutions, we observe large variation in the correlations between the real and synthetic price series.
For example: As these tables indicate, the algorithm is capable of producing replica series that either mimic the original, real price series very closely, or which show completely different behavior, as in the second example. Dimensionality Reduction For completeness, as have previous researchers, we apply t-SNE dimensionality reduction and plot the two-factor weightings for both real yellow and synthetic data blue.
We observe that while there is considerable overlap in reduced dimensional space, it is not as pronounced as for the synthetic data produced by TimeGAN, for instance. However, as previously explained, we are less concerned by this than we are about the tests previously described, which in our view provide a more appropriate analysis benchmark, so far as market data is concerned.
Furthermore, for the reasons previously given, we want synthetic market data that in some cases tracks well beyond the range seen in historical price series. Returns Distributions Moving on, we next consider the characteristics of the returns in the synthetic series in comparison to the real data series, where returns are measured as the differences in the Log-Close prices, in the usual way.
A more detailed look at the distribution characteristics for the first four synthetic series indicates that there is a very good match to the real returns process in each case the results for other series are very similar : We observe that the minimum and maximum returns of the synthetic series sometimes exceed those of the real series, which can be a useful characteristic for risk management applications. The median and mean of the real and synthetic series are broadly similar, sometimes higher, in other cases lower.
Only for the standard deviation of returns do we observe a systematic pattern, in which returns volatility in the synthetic series is consistently higher than in the real series. This feature, I would argue, is both appropriate and useful. Standard deviations should generally be higher, because there is indeed greater uncertainty about the prices and returns in artificially generated synthetic data, compared to the real series.
Moreover, this characteristic is useful, because it will impose a greater stress-test burden on risk management systems compared to simply drawing from the distribution of real returns using Monte Carlo simulation. Put simply, there will be a greater number of more extreme tail events in scenarios using synthetic data, and this will cause risk control parameters to be set more conservatively than they otherwise might. This same characteristic — the greater variation in prices and returns — will also pose a tougher challenge for AI systems that attempt to create trading strategies using genetic programming, meaning that any such strategies are more likely to perform robustly in a live trading environment.
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