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Article Not peer-reviewed version
Machine Learning to Forecast the
Financial Bubbles in Stock Market:
Evidence in Vietnam
Kim Long Tran , Hoang Anh Le * , Cap Phu Lieu , Duc Trung Nguyen
Posted Date: 30 September 2023
doi: 10.20944/preprints202309.2150.v1
Keywords: financial bubbles; machine learning algorithms; Vietnamese stock market
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Article
Machine Learning to Forecast the Financial Bubbles
in Stock Market: Evidence in Vietnam
Kim Long Tran 1, Hoang Anh Le 1,*, Cap Phu Lieu 1 and Duc Trung Nguyen 1
1 Ho Chi Minh University of Banking, No. 36 Ton That Dam Street, Nguyen Thai Binh ward, District 1, Ho
Chi Minh City, 700000, Vietnam; longtk@hub.edu.vn (K.L.T.); phulc@hub.edu.vn (C.P.L.);
trungnd@hub.edu.vn (D.T.N.)
* Correspondence: anhlh_vnc@hub.edu.vn
Abstract: Financial bubble prediction has been a significant area of interest in empirical finance, garnering
substantial attention in the literature. This study aimed to detect and forecast financial bubbles in the
Vietnamese stock market from 2001 to 2021. The PSY procedure, which involves a right-tailed unit root test to
identify the existence of financial bubbles, was employed to achieve this goal. Machine learning algorithms
were then utilized to predict real-time financial bubble events. The results revealed the presence of financial
bubbles in the Vietnamese stock market during 2006-2007 and 2017-2018. Additionally, the empirical evidence
supported the superior performance of the Random Forest and Artificial Neural Network algorithms over
traditional statistical methods in predicting financial bubbles in the Vietnamese stock market.
Keywords: financial bubbles; machine learning algorithms; Vietnamese stock market
1. Introduction
Financial bubbles can have profound effects on a economy and the livelihoods of its citizens.
Consequences such as financial and debt crises, as seen in the dot-com bubble of 1999-2001 and the
U.S. subprime mortgage crisis of 2007-2009, often originate from the abnormal escalation of asset
prices in the stock market or the real estate market. When a bubble bursts, it can lead to the collapse
of major financial institutions, pushing countries to the brink of bankruptcy and triggering
comprehensive financial and economic crises. Governments are forced to allocate substantial
resources to bailout packages and recovery programs in the wake of such crises.
Moreover, the social costs remain significant, and the restoration of public confidence in the
market poses a particularly formidable challenge. Inexperienced investors, lacking the knowledge to
manage risks, are among the most severely impacted [1]. They often hold assets during the late stages
of a bubble, making them particularly vulnerable to the adverse effects of the bubble's burst.
Therefore, for governments and market supervisors, researching and forecasting the status of
financial bubbles is extremely important. This enables the implementation of necessary interventions
to mitigate adverse impacts of financial bubbles on the market and society, especially in the context
of globalization where risks can easily spread between markets. However, research relating to
financial bubbles in the context of Vietnam remains relatively limited, especially in studies employing
quantitative methodologies and machine learning algorithms. The effectiveness of forecasting tools
utilizing machine learning algorithms continues to be a subject of skepticism and debate within the
academic community.
The main objective of our research is to detect financial bubbles in the Vietnamese stock market
from 2001 to 2021 and subsequently forecast financial bubble occurrences based on macroeconomic
indicators. We employed the PSY procedure to identify market phases with bubble-like
characteristics and use machine learning algorithms for prediction. Furthermore, we have
implemented the SMOTE method to rectify data imbalances within the dataset and leveraged the
PCA method to reduce data dimensionality, thereby enhancing the quality of our forecasting
outcomes. We aim to determine the best-performing model among the methods used. We anticipate
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© 2023 by the author(s). Distributed under a Creative Commons CC BY license.
2
that our study can contribute empirical evidence regarding the application of machine learning for
real-time forecasting of financial bubbles. This can provide early warning signals for policymakers
and investors to make informed financial decisions.
The remaining sections of this research paper are organized as follows: Section 2 introduces the
theoretical framework for detecting financial bubbles and the application of machine learning in
forecasting. Section 3 outlines our data sources and methodologies, including the PSY procedure and
machine learning techniques. Section 4 presents our research findings and thoroughly discusses their
implications. Finally, Section 5 provides a concise conclusion, summarizing key insights and
suggesting avenues for future research.
2. Literature Review
2.1. Definition of Financial Bubbles
In theory, the concept of financial bubbles is often referred to by various terms like asset price
bubbles or speculative bubbles, and is an intriguing research topic. There exist various perspectives
on financial bubbles and their identification. However, attempting to classify and provide a clear-cut
definition remains a controversial subject within the academic community. Generally, the
classification of financial bubbles falls into two primary categories: classical bubbles and modern
bubbles.
Classical bubbles are primarily driven by irrational investor behavior. Shiller [2] posits that
bubbles in the market are a psychological phenomenon. He suggests that the occurrence of these
bubbles is a result of amplified feedback-trading tendencies, which are caused by the attention given
to them by news media. The reason for this is that as more investors show interest in a particular
asset, news media tend to expand their coverage of it, which in turn attracts even more potential
investors. This leads to an increase in demand for the asset, which causes its price to rise, thereby
attracting even more attention from the news media. This cyclical process reinforces the feedback-
trading tendency in the market, ultimately leading to the occurrence of bubbles. This phenomenon is
often referred to as 'herd mentality', and its consequences can lead to a severe market collapse,
subsequently exerting a profound impact on the overall economy. Kindleberger, Aliber and Solow
[3] proposed an approach to understanding financial bubbles from the perspectives of irrational
exuberance and psychological expectations. According to these authors, financial bubbles were
created by the irrational exuberance and blind faith of investors, leading to a series of reckless
investment decisions and ultimately culminating in a market collapse and asset value correction.
Stiglitz [4] suggested that the phenomenon of a financial bubble occurs when investors believe that
current prices already reflect high levels of expectations, and the fundamental factors supporting
those prices are no longer in place. In other words, when investors believe that current prices no
longer offer them the potential for future profits and this sentiment becomes widespread, a bubble
begins to form. When investors have faith that the upward trend will continue and fear missing out
on potential gains if they do not buy at the present moment, the bubble inflates. However, a bubble
will be prone to burst when investors start to believe that prices can no longer rise further, demand
wanes, and this can trigger a significant sell-off, causing prices to fall rapidly [5].
The second approach is the modern bubble, described by Tirole [6] as a situation in which the
price of an asset exceeds its fundamental value. The fundamental value of an asset is typically based
on its expected future cash flows, such as dividends, coupon payments, or rental income. According
to the author, bubbles occur when investors are willing to pay a higher price for an asset that can be
resold immediately than if they were obligated to hold onto it for a longer period. This view
recognizes that an asset's perceived value is not always tied to its true value, but rather to its potential
for short-term profits. In the derivatives market, a bubble is considered to exist if the market value of
a derivative consistently exceeds the cost of creating similar derivatives. This means that the price at
which the derivative is trading in the market is higher than the cost of creating a comparable
derivative. An illustration of such a bubble can be observed in the price disparity in option pricing.
Specifically, a bubble may occur when a combination of put and call options, designed to replicate
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 September 2023 doi:10.20944/preprints202309.2150.v1
3
the movements of a stock, is traded at a price differential compared to the price of the underlying
stock. This price differential must also take into account factors such as interest rates and the cost of
borrowing the stock. Therefore, the existence of bubbles in various forms highlights the complexity
of market dynamics and raises the challenges associated with maintaining economic stability.
Additionally, the concept of bubbles can be classified into two categories: rational bubbles and
partially rational bubbles. The rational bubble theory proposes that investors knowingly purchase
overpriced assets with the understanding that they can sell them at a profit in the future. This theory
posits that even when faced with prices that are clearly overvalued, expectations of future profits can
drive investment behavior. In other words, investors in rational bubbles willingly engage in the
bubble, motivated by the prospect of profiting from price increases before the bubble eventually
bursts. Shiller [7] introduced the concept of partially rational bubbles, which posits that stock prices
are influenced by a combination of rational and irrational behavior among investors. He suggested
that individual investors were prone to irrational exuberance, often driven by sensationalized media
reports, but this does not mean that investors are consistently irrational or 'crazy'. Rather, the stock
market is influenced by social trends and short-term desires, which may either lead to the formation
of bubbles or not. In essence, partially rational bubbles recognize that market behavior can be
influenced by both rational and irrational elements that stem from societal trends and collective
beliefs, and these factors contribute to the persistence of bubbles. This perspective provides a more
nuanced understanding of the dynamics that drive financial bubbles.
Fama [8], who advocates the Efficient Market Hypothesis (EMH), offers an alternative
perspective on financial bubbles. According to Fama, the extreme price fluctuations of assets can be
anticipated, and as a result, there are no bubbles in asset prices. While this stance is still subject to
debate, it provides a framework for delving into the identification of factors or causes that could lead
to the predictable formation of bubbles. Fama's view challenges the perception that financial bubbles
are irrational and uncontrollable, and proposes that there may be underlying patterns and elements
that can be used to predict or understand the emergence of bubbles. This perspective has given rise
to further research into the predictability of bubbles and the factors that contribute to their formation.
In this article, we approach bubbles from the perspective of irrational bubbles, which are
characterized by a sudden surge in prices within a short time frame followed by a rapid decline in
the VNINDEX. Besides, we also recognize the presence of external factors that influence market
dynamics beyond investor behavior, as posited by Fama's perspective.
2.2. Literature review on Detecting Financial Bubbles
Throughout history, a multitude of research studies have been conducted with the objective of
identifying bubbles in financial markets that are characterized by speculation, including but not
limited to stock markets, foreign exchange markets, real estate markets, and more recently,
cryptocurrency markets. However, within the context of this article, we will provide a concise
overview of studies conducted solely within the sphere of the stock market, with a particular focus
on those that utilize statistical models on time series data.
Shiller [9] introduced a novel method called Variance Bounds Tests, which he applied to sample
data of the S&P price index from 1871 to 1979, revealing evidence of bubble existence. However,
Shiller's approach is often deemed less reliable when applied to small sample sizes. Blanchard and
Watson (1982) explained rational bubbles as the discrepancy between asset prices and their
fundamental values, suggesting that speculative bubbles do not adhere to rational behavior. The
impact of irrational factors adds complexity to assessing bubbles in the stock market.
West [10] employed Euler equations and ARIMA models on annual stock price and dividend
data of the S&P 500 from 1871 to 1980 and the Dow Jones index from 1928 to 1978, providing robust
statistical evidence of the existence of stock market bubbles in the United States.
Phillips, Wu and Yu [11] proposed the Sup Augmented Dickey-Fuller test (SADF), also known
as the PWY method, to assess the presence of rational bubbles in financial markets. This approach is
based on the null hypothesis of a unit root, analogous to the conventional Dickey-Fuller test, but with
a right-tailed alternative hypothesis. Rejecting the null hypothesis in this test indicates the presence
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4
of explosive behavior in the price series, thereby providing empirical evidence for the existence of a
bubble. The right-tailed SADF unit root tests are conducted using rolling window forms. Homm and
Breitung [12] applied this test to detect stock market bubbles, and after a process of simulation and
evaluation criteria comparison, the authors found that the SADF test was the most optimal among
the methods employed. The SADF test is effective when there is a single bubble event, but in practical
applications, there may be multiple bubbles appearing in sufficiently large samples. While this
method successfully identified famous historical bubbles, the SADF test failed to detect the 2007-2008
debt crisis bubble.
Phillips, Shi and Yu [13] developed the Generalized sup ADF (GSADF) test as an improvement
over the SADF method, also referred to as the PSY procedure, to overcome its limitations. The GSADF
test is an iterative application of the right-tailed ADF test based on the rolling-window SADF test that
aims to detect explosive patterns in sample sequences. Compared to the SADF, the GSADF is more
flexible in terms of rolling windows, making it a valuable tool for investigating price explosion
behavior and confirming the presence of market bubbles. In this study, they applied both the SADF
and GSADF tests to the S&P 500 index from 1871 to 2010, revealing that the GSADF successfully
identified two bubble periods: the Panic of 1873 (from October 1879 to April 1880) and the Dot-com
bubble (from July 1997 to August 2001). When restricting the bubble duration to over 12 months, the
results showed that there were three existing bubble periods: the post-1954 war period, Black
Monday in 1987, and the Dot-com bubble in 2000.
Based on the findings outlined above, it is evident that the GSADF test is an effective approach
for detecting the presence of market bubbles. Hence, in this study, we have employed the PSY
procedure to identify the existence of bubbles in the Vietnamese stock market.
2.3. Literature Review on Machine Learning Applied in Economic Forecasting
In macroeconomics, machine learning techniques are commonly used for classification problems
such as predicting stock market trends and corporate bankruptcies. While the use of machine learning
for identifying financial bubbles in the stock market is a relatively new approach and has been the
subject of limited research, most studies on financial crises in banking, securities markets, and public
debt have focused on predicting general economic crises rather than forecasting individual financial
bubbles. To date, only one recent study by Başoğlu Kabran and Ünlü [14] has been conducted on
predicting financial bubbles. The authors used a support vector machine (SVM) approach to forecast
bubbles in the S&P 500 index and compared it with other methods. The results demonstrated that
SVM has superior performance in predicting financial bubbles.
For forecasting financial crises, several notable studies have been conducted. Alessi and Detken
[15] constructed a warning system using random forest to identify systemic risk from a dataset of
banking crises in the EU, using macroeconomic indicators as predictors. Their results demonstrated
that the random forest model provided excellent predictive performance and holds promise for
macroeconomic forecasting. Beutel, List and von Schweinitz [16] compared the out-of-sample
predictive performance of various early warning models for systemic banking crises in advanced
economies and found that while machine learning methods often exhibit high in-sample fits, they
were outperformed by the logit approach in recursive out-of-sample evaluations. Chatzis, Siakoulis,
Petropoulos, Stavroulakis and Vlachogiannakis [17] utilized a wide range of machine learning
algorithms to forecast economic risks across 39 countries. They demonstrated that deep neural
networks significantly improved classification accuracy and provided a robust method to create a
global systemic early warning tool that is more efficient and risk-sensitive compared to established
methods. Ouyang and Lai [18] proposed an Attention-LSTM neural network model to assess systemic
risk early warning in China. They found that the model exhibited superior accuracy compared to
other models, suggesting that it could be a valuable tool for systemic risk assessment and early
warning in the Chinese context.
In default prediction, machine learning models have also demonstrated superiority in handling
non-linear relationships compared to traditional models. Shin, Lee and Kim [19] employed SVM to
forecast bankruptcy for 2,320 medium-sized enterprises in the Korean Credit Guarantee Fund from
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 September 2023 doi:10.20944/preprints202309.2150.v1
5
1996 to 1999. The study's outcomes exhibited that SVM provided superior predictive outcomes
compared to other models, including artificial neural network (ANN) models. Zhao, Xu, Kang, Kabir,
Liu and Wasinger [20] conducted a research to develop a credit scoring system based on ANN
employing a credit dataset from Germany. The study's results demonstrated that ANN could forecast
credit scores more accurately than traditional models, obtaining an accuracy rate of 87%. Geng, Bose
and Chen [21] utilized machine learning models to predict financial distress for companies listed on
the Shanghai and Shenzhen stock exchanges from 2001 to 2008. The study's findings revealed that
the ANN model yielded better results when compared to decision trees, SVM, and random forest
models. Barboza, Kimura and Altman [22] applied SVM, ensembles, boosting, and random forest
methods to predict bankruptcy for 10,000 companies in the North American market from 1985 to
2013. The authors contrasted these models with traditional statistical models and examined their
predictive performance. The results indicated that ensemble methods like bagging, boosting, and
random forests outperformed other approaches. Specifically, machine learning models achieved an
average accuracy that was approximately 10% higher than traditional models. The random forest
model displayed the highest accuracy, reaching up to 87%, whereas traditional models ranged from
50% to 69% accuracy. Fuster, Goldsmith-Pinkham, Ramadorai and Walther [23] examined mortgage
default cases in the United States and found that the random forest model achieved higher predictive
accuracy than logistic regression. These results highlight the effectiveness of ensemble methods,
particularly random forests, in financial distress prediction compared to traditional models. A recent
study conducted by Tran, Le, Nguyen and Nguyen [24] incorporated the Sharpe ratio to clarify the
forecasting outcomes of complex machine learning models on a dataset of listed companies in
Vietnam from 2010 to 2021. The study's results showed that the extreme gradient boosting and
random forest models outperformed other models. One interesting point is that based on Shapley
values, the authors can determine the influence of each feature on the prediction results and provide
additional insights into relationships that are not present in the theory.
The literature suggests that machine learning algorithms have exhibited better outcomes than
statistical models in both classification and time series regression problems. Nevertheless, the
forecasting results across models can differ considerably depending on the dataset used, and there is
no one-size-fits-all superior approach. Several factors can significantly impact forecasting results,
such as data imbalance, the presence of outliers in the dataset, and the selection of parameters within
the models. In this case, the choice of the forecasting model is of utmost importance and can
significantly impact the output results. Therefore, the primary aim of this research is to identify and
select the most appropriate model for forecasting financial bubbles in the Vietnamese stock market.
To our best knowledge, there has been no prior research conducted on this topic.
3. Methodology
3.1. Research Design and Data Preprocessing
Our study is divided into two primary phases. Phase 1 involves the detection of financial bubbles
in the stock market, while Phase 2 employs machine learning algorithms to predict the appearance
of financial bubbles. The details of each phase are as follows:
In Phase 1, we focus on identifying financial bubbles in the Vietnamese stock market, utilizing
historical stock market data, specifically the VNINDEX, from 2001 to 2021. This timeframe
encompasses significant economic events and global economic fluctuations, particularly during the
2006-2008 and 2017-2018 periods, as noted by economic experts. Our goal is to identify financial
bubble phenomena on a monthly basis during this time frame. We obtained daily stock index data
from FiinPro, a reputable financial data provider in Vietnam.
In Phase 2, we use various machine learning techniques to predict the presence of financial
bubbles. We utilize macroeconomic indicators of Vietnam during the same timeframe to forecast
financial bubble occurrences. The target variable is the financial bubble status for each month, as
detected in Phase 1. We label months as 1 if a financial bubble occurred and 0 for other months. The
forecasting time frame is one month prior. The features include macroeconomic variables collected
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 September 2023 doi:10.20944/preprints202309.2150.v1
6
from the World Bank data, representing crucial aspects of the economy, such as GDP growth,
Consumer Price Index, broad money, foreign direct investment, interest rate, etc. In total, we selected
55 important macroeconomic indicators extracted from the World Bank dataset, considering them as
features for forecasting. Most of the data is reported quarterly or annually, so we employed the cubic
spline interpolation method to convert them into monthly data while preserving the characteristic
features of the variables.
The dataset utilized in our study was collected over a period of twenty years, spanning from
December 2001 to December 2021, and comprises a total of 252 data points. Out of these, 33 months
were identified as having financial bubbles. To facilitate the training and testing of our model, the
data was partitioned into two main sets - the training set and the test set. The time chosen to split the
dataset was January 2018, ensuring that the proportion of months with bubble phenomena in the
training and test sets was 2/3 and 1/3, respectively. The objective here is to ensure that the training
and testing datasets contain sufficient data for model development and evaluation.
In financial datasets, class imbalance is a commonplace phenomenon where the occurrence of
financial bubbles is relatively infrequent compared to non-bubble periods. Our dataset also exhibited
class imbalance, and to mitigate this issue, we employed the Synthetic Minority Over-sampling
Technique (SMOTE). This approach was chosen due to its suitability for financial datasets where rare
class occurrences are prevalent. SMOTE generates synthetic samples for the minority class,
addressing the imbalance while preserving the data distribution characteristics. In financial markets,
the accurate detection of financial bubbles is of utmost importance, and SMOTE assists in reducing
bias, improving model generalization, and enhancing performance metrics such as precision and
recall. This technique ensures that the model can reliably identify critical financial bubble events with
greater accuracy.
Given the presence of 55 macroeconomic indicator features in our dataset, we recognized the
need to adopt a judicious strategy to mitigate the risk of overfitting. In this regard, we employed
Principal Component Analysis (PCA) as a systematic means to condense the dimensions of our
dataset. By transforming the original features into a smaller set of principal components, we retained
the critical information essence while addressing the perils associated with excessive dimensions.
This approach not only provides a practical solution to tackle the dimensionality conundrum but also
serves as a catalyst for enhancing the efficacy of our machine learning model training, thereby
augmenting prediction accuracy. It is important to note that during the PCA process, feature scaling
is applied through standardization using the StandardScaler tool from scikit-learn.
The identification of financial bubbles in the VNINDEX series was carried out by using the
'psymonitor' package in R to execute the PSY procedure as proposed by Phillips, Shi, Caspi and Caspi
[25]. Furthermore, for data analysis, Python and several associated packages such as Numpy, Pandas,
Scikit-learn, and Seaborn [26-29] were utilized.
3.2. PSY Method for Bubbles Detection
Within the scope of our research, we utilize the Phillips, Shi, and Yu (PSY) methodology, which
employs recursive regression techniques to investigate the presence of a unit root in the face of an
alternative right-tailed explosive hypothesis. This technique, which was introduced by Phillips, Shi
and Yu [30], has been tailored to identify multiple bubble periods in a time series dataset. Rejecting
the null hypothesis in this test is regarded as empirical evidence of the existence of financial asset
price bubbles. The critical values for these tests are determined through Monte Carlo simulations,
and the outcomes of these tests aid in defining the start and end dates of the bubbles.
The objective is to compute statistical measures on the right tail of the Augmented Dickey-Fuller
(ADF) test with regard to a time series. Through a comparison of the maximum values that are
derived from the test statistics with corresponding threshold values obtained from the distribution,
analysts can draw inferences regarding the explosiveness of the observed values. The null hypothesis
assumes that a time series follows a random walk process with an extremely small drift coefficient,
as expressed by the equation:
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 September 2023 doi:10.20944/preprints202309.2150.v1
7
Δ
𝑦
=
𝜇
+
𝜎
𝑦
+
𝜙
Δ
𝑦
+
𝑒
(1)
Where 𝑦 represents stock prices at time 𝑡; 𝜇 is the intercept; 𝑝 is the maximum lag; 𝜙 are
the regression coefficients corresponding to different lags; and 𝑒 is the error term.
The recursive model is proposed as follows:
Δ
𝑦
=
𝛼
,
+
𝛽
,
𝑦
+
Σ
𝜙
,
Δ
𝑦
+
𝜀
,
𝜀
∼
.
.
𝑁
(
0
,
𝜎
,
)
(2)
When conducting the test, the authors assume a sample time frame of [0,1]. The symbols
𝛿,and 𝐴𝐷𝐹, represent the estimated coefficients according to Equation (2) and the
corresponding ADF test within the data window [𝑟,𝑟]. Let r_w denote the window size, so 𝑟=
𝑟−𝑟. The starting points r_1 can vary within the range [0,𝑟−𝑟].
The maximum ADF test statistic for the right tail is expressed by the following formula:
𝐵𝑆𝐴𝐷
𝐹
(
𝑟
)
=
sup
∈
[
,
]
(
𝐴𝐷
𝐹
}
(3)
The PSY procedure assumes that the errors in the regression model, represented by 𝜖, have
constant error variance. Based on this, the estimates of bubble periods using GSADF are determined
by the following formulas:
𝑟
=
inf
∈
[
,
]
(
𝑟
:
𝐵𝑆𝐴𝐷
𝐹
>
𝑐
𝑣
)
(4)
𝑟
=
inf
∈
[
,
]
(
𝑟
:
𝐵𝑆𝐴𝐷
𝐹
>
𝑐
𝑣
)
(5)
Where 𝑐𝑣
is the 100(1−𝛽)% critical value of the SADF statistic based on observations
𝑇,𝑟.
𝐵𝑆𝐴𝐷𝐹 with 𝑟∈[𝑟,1] is the delayed SADF statistic related to the GSADF statistic by the
following relationship:
𝐵𝐺𝑆𝐴𝐷𝐹
(
𝑟
)
=
sup
∈
[
,
]
(
𝐵𝑆𝐴𝐷
𝐹
(
𝑟
)
)
(6)
In the PSY method, 𝑟 represents the minimum size, 𝑟 is the starting point, and 𝑟 is the
ending point for each sample. The starting point 𝑟 is fixed, and 𝑟 varies from 0 to 𝑟 − 𝑟.
3.3. Machine Learning Methods to Predict Financial Bubbles
3.3.1. Logistic regression
Logistic regression is a widely used statistical method for predictive modelling in scenarios
where the response variable is binary. In the present study, the focus is on predicting financial
distress. Based on the input features, the model generates a probability estimate of financial distress.
This probability is computed through equation (7).
𝑃
(
𝑦
=
1
)
=
1
1
+
𝑒
(
⋯
)
(7)
Logistic regression is a commonly employed benchmark in research studies that investigate
different forecasting methods. One of the key advantages of this technique is its ease of interpretation,
which makes it accessible to most users. Therefore, logistic regression is frequently utilized in
practical applications within financial institutions, owing to its high explanatory power.
3.3.2. Support vector machine
Support vector machines (SVMs) are a type of machine learning algorithm that relies on the
concept of defining hyperplanes to partition observations in high-dimensional feature spaces. Linear
SVM models prioritize the maximization of the margin between positive and negative hyperplanes.
The classification decision is made using equation (8).
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8
y
=
+
1
if
b
+
α
𝑥
≥
+
1
−
1
if
b
+
α
𝑥
≤
−
1
(8)
where b is the bias.
In cases where the relationship between features and outcomes is nonlinear, a kernel function is
employed to transform the features into a higher dimensional space. A commonly used kernel
function is the Gaussian radial basis function, which is expressed as equation (9).
𝐾
(
𝑥
,
𝑥
)
=
exp
−
𝛾
|
𝑥
−
𝑦
|
(9)
One of the strengths of Support Vector Machines (SVMs) is their ability to avoid overfitting with
small sample sizes and to remain robust to unbalanced distributions.
3.3.3. Decision tree
Decision tree algorithms use a tree structure to extract insights from data and derive decision
rules. The algorithm determines the optimal allocation for each split with maximum purity, using a
measure such as the Gini coefficient or Entropy. The root node, representing the most distinguishing
attribute, is located at the top of the tree, while the leaf nodes represent classes that correspond to the
remaining attributes.
One of the main advantages of decision tree models is that they are intuitive and easy to
interpret. However, there is a risk of overfitting during the feature domain division or branching
process, which represents a potential drawback.
3.3.4. Random forest
The random forest technique, which was developed by Breiman [31], is based on the decision
tree model. In random forests, decision trees are grown using a subset of randomly selected features.
This random selection of both samples and features ensures the diversity of the basic classifiers. The
forest is constructed from multiple subsets that generate an equal number of classification trees. The
preferred class is identified based on a majority of votes, which results in more precise forecasts and,
importantly, protects against overfitting the data.
3.3.5. Gradient boosting (GB)
Gradient boosting is a machine learning technique commonly used in regression and
classification tasks. It produces a prediction model in the form of an ensemble of weak prediction
models, typically decision trees. Gradient Boosting is a robust boosting algorithm that combines
several weak learners into strong learners. In this technique, each new model is trained to minimize
the loss function, such as mean squared error or cross-entropy, of the previous model using gradient
descent. During each iteration, the algorithm calculates the gradient of the loss function with respect
to the predictions of the current ensemble and then trains a new weak model to minimize this
gradient. The predictions of the new model are then added to the ensemble, and this process is
repeated until a stopping criterion is met. This method has been proven to be effective in improving
the prediction accuracy of models.
3.3.6. Artificial neural network
An artificial neural network, also known as a neural network, is a machine learning algorithm
that is designed based on the structure and connections between neurons in the brain. This algorithm
is capable of solving complex problems by mimicking the brain's structure. An artificial neural
network consists of many layers of artificial neurons, which are connected to one another. Each layer
is composed of an input layer, output layer, and hidden layer. These artificial neurons simulate the
role of real neurons through mathematical models. Each artificial neuron receives an input signal,
𝑥,𝑥,...,𝑥, consisting of binary numbers (0 or 1). It then calculates the weighted sum of the signals
it receives based on their weights, 𝑤,𝑤,...,𝑤. The signal is only transmitted to the next artificial
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neuron when the sum of the weights of the received signals exceeds a certain threshold. An artificial
neuron can be represented as the equation (10).
y=output=
⎩
⎪
⎨
⎪
⎧
0
if
𝑤
𝑥
≤
threshold
1
if
𝑤
𝑥
>
threshold
(10)
Based on historical data, neural network optimization is performed by determining the
appropriate weights and activation thresholds. This process involves training the network using a set
of input data and corresponding output data, which is used to adjust the weights and thresholds of
the artificial neurons until the desired level of accuracy is reached. Through this iterative process, the
neural network can learn to accurately predict outcomes for new input data.
3.4. Evaluation of model performance
To evaluate the performance of classification algorithms, it is important to avoid focusing on a
single class. Instead, a more comprehensive approach is preferred, which involves analyzing multiple
metrics. The metrics are accuracy, precision, and sensitivity (recall).
Accuracy measures the proportion of correct classifications in the evaluation data and is
calculated as follows:
Accuracy = (TP + TN) / (TP + TN + FP + FN) (11)
Precision measures the proportion of true positives among the predicted positives and is
calculated as follows:
Precision = TP / (TP + FP) (12)
Sensitivity (recall) measures the proportion of positives that are correctly predicted and is
calculated as follows:
Sensitivity (recall) = TP / (TP + FN) (13)
In these equations, TP represents true positives, FP represents false positives, FN represents false
negatives, and TN represents true negatives. By analyzing these metrics, the performance of different
classification algorithms can be compared and evaluated.
In the case of imbalanced datasets, accuracy alone may not be a reliable metric for evaluating
classification models. To provide a more comprehensive evaluation, the F1-score and the ROC curve
are often used.
The F1-score is the harmonic mean of precision and sensitivity, ensuring that the F1-score is
higher only when both components are higher. The F1 Score is calculated as follows:
F1 Score = 2 × (Precision × Recall) / (Precision + Recall) (14)
The ROC curve plots the true positive rate against the false positive rate, with the horizontal
coordinate representing the false positive rate and the vertical coordinate representing the true
positive rate. To quantify the characteristics of the ROC curve, the area under the curve (AUC) is
introduced. The AUC value represents the area of the shadow part at the lower right of the ROC
curve. The larger the shadow area, the greater the AUC value and the closer the ROC curve is to the
upper left, indicating that the classification model is more accurate.
4. Result and Discussion
4.1. Overview of the Vietnamese Stock Market
The Vietnamese stock market was established in July 2000 with the launch of the Ho Chi Minh
City Stock Exchange. The market experienced significant growth from 2006 to 2007, thanks to foreign
investment inflows following Vietnam's entry into the WTO and the enactment of the Securities Law
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in 2006. However, there was a sharp decline in 2008, followed by a recovery in 2009, leading to stable
growth until 2016. From 2017 to the present, the Vietnamese stock market has been characterized by
significant volatility, with the VNIndex surpassing the 1000-point mark in 2018, followed by a sharp
decline in 2020, and continued fluctuations from 2021 to 2022. Vietnam Stock Market Capitalization
accounted for 205.153 USD billion in July 2023, which is equivalent to 65% of GDP. There are over
1600 listed companies in the market, with the majority operating in the financial, real estate, and
essential consumer goods sectors, accounting for over 80% of the total market capitalization.
Figure 1. The Vietnamese Stock Market from 2001 to 2021. Source: Author (2023). Based on data
from FiinPro (2023).
4.2. Results of Financial Bubble Detection
In this study, we employed the PSY procedure to detect the presence of financial bubbles in the
Vietnamese stock market from January 2001 to December 2021, on a monthly basis. The VNINDEX
was determined on the last trading day of each month. The PSY procedure has the minimum window
that includes at least 38 observations, as determined by the rule of 𝑡𝑚𝑖𝑛 = 0.01𝑇 + 1.8√𝑇. The
monitoring process starts from January 2001 onwards.
Table 1 displays the results of the financial bubble identification, providing the start and end
dates for each bubble. The analysis identified a total of 33 months as having experienced financial
bubbles, which are highlighted with dark gray vertical lines in Figure 2. Notably, two significant
periods with multiple bubbles emerged during 2006-2007 and 2017-2018. These findings confirm the
observations of financial experts regarding the overvaluation of stock prices in the stock market
during these periods. Following the obtained results, we proceeded to label the months that were
identified as bubble, thereby preparing the dataset for the subsequent stage of supervised machine
learning.
Table 1. Statistics of Financial Bubbles Occurrences.
Start Date End Date
1 2006-02-28 2006-04-28
2 2006-06-30 2006-06-30
3 2006-12-29 2007-09-28
4 2017-11-30 2018-04-27
5 2018-06-29 2018-07-31
Source: Author (2023).
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Figure 2. Bubbles in Vietnam Stock market from January 2001 to December 2021.
4.3. Results of Forecasting Financial Bubbles Using Machine Learning Algorithms
Our study involved the implementation of various machine learning algorithms, including
Logistic Regression, Decision Trees, Random Forest, Neural Networks, Gradient Boosting, and
Support Vector Machine (SVM). The following table summarizes the performance of these models:
The results from Table 2 show that both Random Forest and Neural Network models outperform
other algorithms in terms of AUC, accuracy, and F1 score. The Neural Network model stands out
with the highest AUC (0.968), accuracy (0.915) and sensitivity (1.00), indicating its proficiency in
accurately classifying periods marked by financial bubbles. However, the relatively lower F1 score
(0.75) suggests a potential trade-off between precision and recall. This observation implies that while
the Neural Network excels in correctly classifying positive instances, it may benefit from adjustments
to maintain a balance between precision and recall.
Table 2. The performance results of classifiers.
Algorithms Hyper-Parameter AUC F1 score Accuracy Precision Sensitivity
Neural Networks hidden_layer_sizes
=100,
max_iter = 300,
activation = "relu",
solver = 'adam',
alpha = 0.0001
0.968 0.750 0.915 0.600 1.000
Random Forest max_depth=5,
n_estimators= 50
0.953 0.800 0.894 1.000 0.667
Gradient Boosting max_depth=3,
learning_rate=0.1,
n_estimators= 100
0.957 0.727 0.872 0.800 0.667
Logistic Regression C = 1 0.943 0.700 0.872 0.700 0.700
Support Vector Machine C = 1, kernel = 'rbf',
class_weight =
'balanced'
0.965 0.696 0.851 0.800 0.615
Decision Trees max_depth = 5 0.819 0.667 0.830 0.800 0.571
Source: Author (2023).
Besides, the Random Forest algorithm delivers commendable results with a high AUC (0.953)
and perfect precision (1.00), indicating its capacity to identify periods marked by financial bubbles
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precisely. However, its slightly lower sensitivity (0.667) implies a higher likelihood of missing some
actual instances of financial bubbles. This trade-off underscores the need to consider the practical
implications of false positives and false negatives in real-world financial decision-making.
Decision Trees underperformed in comparison, with an AUC of 0.82 and lower F1 scores. This
serves as a baseline for evaluating the machine learning models' performance.
Figure 3. ROC curve of classifiers.
The AUC ROC graph also provides similar outcomes. Among the machine learning algorithms
we employed, Artificial Neural Network emerged as the top-performing model with an AUC score
of 0.968. This score reflects its ability to achieve a high true positive rate while keeping the false
positive rate low. In essence, it excels at distinguishing bubble periods from non-bubble periods in
the stock market. Other models, including Logistic Regression, and Decision Trees, demonstrated
competitive but relatively lower AUC scores. While these models may still provide useful insights,
their performance fell slightly behind that of Neural Networks, Random Forest, Gradient Boosting
and SVM in this specific task.
Our research results differ from the findings of Başoğlu Kabran and Ünlü [14], which
demonstrated that SVM yielded the best forecasting results for the S&P 500 index in the United States.
We attribute this discrepancy to differences in the selected features incorporated into the models, as
well as variations in the scale of the datasets used in the two studies. However, it is noteworthy that
this study represents the first attempt to apply machine learning to forecast bubbles in an emerging
market. In the future, we aspire to conduct empirical research across a broader range of markets.
Our research demonstrates the potential of machine learning algorithms in forecasting financial
bubbles. The choice of the most suitable algorithm depends on the specific goals and constraints of
the application, with Neural Network and Random Forest showing strong promise in this context.
The results of this study have practical implications for financial policymakers, investors, and
institutions. The ability to forecast financial bubbles can serve as an early warning system, enabling
timely interventions to mitigate the adverse effects of market crashes. Policymakers can use these
insights to develop more informed regulatory strategies, and investors can adjust their portfolios to
reduce risks associated with bubble bursts.
In terms of future research directions, further studies could enhance the interpretability of
forecasting results and analyze causal relationships to uncover the root causes of financial bubbles.
Additionally, comparing and investigating the duration as well as the impact of financial bubbles on
different asset markets is another promising research avenue.
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5. Conclusions
In this study, we employed the PSY procedure to identify the presence of financial bubbles and
forecast this phenomenon in the Vietnamese stock market using data from 2001 to 2021. The results
indicated that financial bubbles occurred during the periods from 2006 to 2007 and from 2017 to 2018.
Regarding predictive results, the Neural Network and Random Forest models exhibited superior
forecasting performance with high F1 scores of 0.80 and 0.75, respectively. Based on the study's
findings, policymakers, governments, and market regulatory agencies now have a valuable tool to
detect and predict the emergence of financial bubbles on the real time basis, enabling them to
formulate appropriate policies to mitigate their adverse effects. From an academic perspective, this
research also opens up potential avenues for applying machine learning tools to prediction tasks in
the field of economics.
Author Contributions: Assoc Prof. Duc Trung Nguyen conceived the idea and wrote the Introduction. Dr.
Hoang Anh Le wrote Literature review. Dr. Kim Long Tran and Dr. Cap Phu Lieu wrote the Methodology,
Results and discussions, and Conclusion.
Funding: The research topic was supported by The Youth Incubator for Science and Technology Programme,
managed by Youth Promotion Science and Technology Center - Ho Chi Minh Communist Youth Union and
Department of Science and Technology of Ho Chi Minh City. The contract number is "25/2022/ HĐ-KHCNT-
VU" signed on 30th December, 2022.
Data Availability Statement: The data for this study can be found on our GitHub page:
https://github.com/kimlongdhnh/long.tran.git (accessed on 02 September 2022).
Conflicts of Interest: The authors declare no conflict of interest.
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