# A Multi-Head LSTM Architecture for Bankruptcy Prediction with Time Series Accounting Data
## 2 Related Works  
In traditional methods to forecast bankruptcies, [PERSON]'s Z-score is the most prominent approach, but the [PERSON] quick test and [PERSON]'s model also use scoring methodologies to provide ordinal rankings of default risk [14; 15]. [PERSON], as well as [PERSON] and [PERSON], used discriminant analysis, which has been widely employed following their works, while [PERSON] was the first to introduce a binary response model using explanatory variables and applying a logistic function [16; 17]. Scoring methodologies have also been used to produce a binary response given a pre-set threshold. For example, [PERSON] suggested the use of two thresholds, 1.81 and 2.99. According to this, an [PERSON]'s Z-score above the 2.99 threshold means that firms are not predicted to default in the next two years, a score below 1.81 indicates that they are predicted to default, while a score between the two thresholds lies in a \"zone of ignorance\" where no clear decision can be taken. However, even though many practitioners use these thresholds, in [PERSON]'s view, this is an unfortunate practice since over the past 50 years, credit-worthiness dynamics and trends have changed so dramatically that the original zone cutoffs are no longer relevant [18]. Even though many authors continue to work on traditional bankruptcy models, the exploration of machine learning applications for corporate default has been more prevalent in recent years [5; 6; 12; 19; 20; 21; 22]. [PERSON] et al. showed that, on average, machine learning models exhibit 10% higher accuracy compared to traditional ones. Specifically, in this study, Support Vector Machines (SVMs), Random Forests (RFs), and bagging and boosting techniques were tested for predicting bankruptcy events and compared with results from discriminant analysis, logistic regression, and neural networks. The authors found that bagging, boosting, and RFs outperformed all other models [23]. However, [PERSON], in his recent book, discussed a trade-off between models' performance and explainability when using machine learning models, expressing skepticism as to whether practitioners would adopt \"black-box\" methods but acknowledging the superiority of the models in assessing corporate distress [18]. Considering that the results regarding the superiority of these models are still inconclusive, new studies exploring different models, contexts, and datasets are relevant. Machine learning techniques like ensembles of classifiers were first explored for default prediction by [PERSON] et al. [24]. [PERSON] et al. showed that the ensembles greatly outperformed standalone classifiers [25]. [PERSON] et al. further analyzed the performance of ensemble models, finding that bagging outperformed boosting in average accuracy for all credit databases they used, as well as type I and type II errors [26]. In [27], some evidence was presented regarding the need to consider time series for survival probability estimation over the years and bankruptcy prediction, with some benchmarks that also prove that neural networks, when properly designed, can achieve better results with time-dependent accounting variables. [PERSON] et al. also argued that a firm's failure will likely be caused by difficulties over time, not just the year before bankruptcy. To incorporate the dynamic behavior of firms, they added new variables reflecting changes in financial metrics such as growth measures and changes [23]. Findings dating back to 1966 show that firms exhibit failure tendencies as much as five years before the actual event [16]. On the other hand, in 1998, [PERSON] et al. pointed out that models are only capable of predicting bankruptcy two years before the event, which improves to three years if used for multi-period corporate default prediction [28; 29]. In most studies, ratios are analyzed backward in time starting with the bankruptcy event and going back until the model becomes unreliable or inaccurate.