=Paper=
{{Paper
|id=Vol-3762/538
|storemode=property
|title=VolTS Augmented: An Improvement of a Volatility-based Trading System to Forecast Stock Markets Trends
|pdfUrl=https://ceur-ws.org/Vol-3762/538.pdf
|volume=Vol-3762
|authors=Ivan Letteri
|dblpUrl=https://dblp.org/rec/conf/ital-ia/Letteri24
}}
==VolTS Augmented: An Improvement of a Volatility-based Trading System to Forecast Stock Markets Trends==
https://ceur-ws.org/Vol-3762/538.pdf
VolTS Augmented: An Improvement of a Volatility-based
Trading System to Forecast Stock Markets Trends
Ivan Letteri1,*
1
University of L’Aquila, Coppito (AQ), 67100, Italy
Abstract
In this study, we proposed an improvement to a previous strategy of the work called VolTS. It is a module
of the AITA framework that integrates statistical analysis with machine learning techniques for forecasting
stock market trends. The main goal is to verify the cointegration in volatility-based trading strategies within
financial markets, and then to devise a methodology that leverages market dynamics to yield profits. This
methodology improvement incorporates the Dynamic Time Warping to assess the similarity of trend sequences,
even when they exhibit temporal misalignment coupling it. With the K-Nearest Neighbors algorithm, which
identifies the most akin price patterns, we construct a sophisticated model spotlighting stocks among the nine
largest ones listed on both the NYSE and Nasdaq exchanges that exhibit analogous price movements to our
portfolio stocks. From volatility assets pointofview, it is applied the Granger Causality Test to the dataset
containing the same mid-range volatility clusters of the chosen stocks, thus identifying them with robust
predictive relationships. These “predictor” stocks were pivotal in shaping our trading strategy, serving as trend
indicators to inform decisions on target stock trades. The empirical findings demonstrated the effectiveness of
our method in identifying, small but not rare, profitable day-trading opportunities. This success was attributed
to the predictive insights from volatility clusters, the Granger causality relationships, and Co-integration
trends identified among the stocks. In conclusion, our research has significantly contributed to the realm
of volatility-based trading strategies by introducing a methodology that mixes statistical techniques with
machine learning.
Keywords
Dynamic Time Warping, K-Nearest Neighbour, Technical Analysis, Stock Market Prediction, Algorithmic
Trading, Backtesting
1. Introduction enced stocks, can Dynamic Time Warping (DTW)
[2] be paired with K-Nearest Neighbours (KNN) to
This article explores the emerging field of volatility- spotlight stocks that “fluctuate” to the same tune
based trading strategies, which is encountering exploiting the delay among them?
promising growth in the financial sector. Artificial This study aimed to formulate trading strategies
intelligence (AI) has emerged as a pivotal player, based on predictive connections affecting influen-
offering robust tools for analysing market volatil- tial stocks as trend indicators. The proposed time
ity and leveraging it for profitable outcomes. AI series study, related to the prices and volatility-
models, trained to estimate mean volatility, offer driven trading strategy was then rigorously evalu-
valuable insights into the inherent uncertainty and ated through backtesting and performance analysis
risk linked to individual securities or the overall to validate its reliability. Through empirical evi-
market [1]. dence, this research has given an improvement to
Our research was primarily driven by the follow- the previous volatility-based trading strategies [3].
ing key questions: 𝑅𝑄1 : Can k-means clustering The augmented AI trading strategy utilised k-
effectively determine the mean volatility of promi- means clustering of average volatility data [4]. This
nent stocks? 𝑅𝑄2 : defined the stocks with the same data encompassed nine major stock markets. Our
mid-term volatility, can the Granger Causality Test initial objective was to identify distinct volatility
be employed to identify predictive influences be- patterns within the market and subsequently group
tween stocks? 𝑅𝑄3 : Established the subset of influ- assets accordingly. Following this, the Granger
Causality Test (GCT) [5] was leveraged to pinpoint
Ital-IA 2024: 4th National Conference on Artificial In-
telligence, organized by CINI, May 29–30, 2024, Naples, stocks that significantly predicted others within our
Italy analysis. Then, we pairwise compare two time series
*
Corresponding author. to find the closest match between them via DTW.
$ ivan.letteri@univaq.it (I. Letteri) Then, the future trend is predicted as the average
0000-0002-3843-386X (I. Letteri)
© 2024 Copyright for this paper by its authors. Use permitted under of the trends of the 𝐾 neighbours. These predictive
Creative Commons License Attribution 4.0 International (CC BY
4.0). relationships were then utilised to establish buy, sell,
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
or hold trading decisions. The Parkinson (PK) estimator incorporates the
Our previous research focused on technical trad- stock’s daily high and low prices as follow:
ing strategies that emphasised technical indicators ⎯
[1],[6]. This current exploration delves, first into
⎸ 𝑁 (︂ (ℎ)
)︂2
⎸ 1 ∑︁ 𝑥
Historical Volatility estimators as a dataset for iden- 𝑃𝐾 = ⎷ 𝑙𝑛 𝑡(𝑙) .
4𝑁 𝑙𝑛(2) 𝑥𝑡
tifying medium volatility selecting stocks for the 𝑖=1
Granger Causality Test asset cointegration approach
It is derived from the assumption that the true
[7]. Second, within the context of investment timing,
volatility of the asset is proportional to the loga-
we predict it via DTW paired with KNN. (ℎ) (𝑙)
This paper is organised as follows: Section 2 rithm (𝑙𝑛) of the ratio of the high 𝑥𝑡 and low 𝑥𝑡
summarize fundamental concepts within our AITA prices of 𝑁 observations.
framework [8], highlighting the Volatility Trading The Garman-Klass (GK) estimator as-
System (VolTS) module [3]. Section 3 outlines sumes that price movements are log-
the improvement with the VolTS Augmented (in normally
√︃ distributed calculated as follows:
𝑁
(︂ )︂2 𝑁
(︂ )︂2
short VolTS-Aug) module, which analyses securi- 1
∑︀ 1 𝑥𝑡
(ℎ) ∑︀ (𝑐)
𝑥𝑡
ties’ volatility averages and price trends establishing 𝑁 2
𝑙𝑛 (𝑙) − (2𝑙𝑛(2) − 1) 𝑙𝑛 (𝑜)
𝑥𝑡 𝑥𝑡
𝑖=1 𝑖=1
predictive relationships. It then delves into the im-
The Rogers-Satchell (RS) estimator uses the
plementation of the trading strategy and includes
range of prices within a given time interval as a
a thorough empirical analysis of its performance
and robustness. Section 4 presents practical find- √︃ for the volatility of the asset as follows: 𝑅𝑆 =
proxy
(︂ )︂ (︂ )︂ (︂ )︂ (︂ )︂
𝑁 (ℎ) (ℎ) (𝑙) (𝑙)
ings achieved through backtesting followed by a 1
∑︀
𝑙𝑛
𝑥𝑡
𝑙𝑛
𝑥𝑡
+ 𝑙𝑛
𝑥𝑡
𝑙𝑛
𝑥𝑡
𝑁 (𝑐) (𝑜) (𝑐) (𝑜)
discussion. Finally, Section 5 concludes the study 𝑡=1
𝑥𝑡 𝑥𝑡 𝑥𝑡 𝑥𝑡
by summarising the effectiveness and applicability RS assumes that the range of prices within the
of the proposed method. interval is a good proxy for the volatility of the
asset, additionally, the estimator may be sensitive
to outliers and extreme price movements.
2. BACKGROUND The Yang-Zhang (YZ) estimator [9] in-
corporates OHLC prices as follows: 𝑌 𝑍 =
2.1. Price Action √︀ 2 2 2
𝜎𝑂𝑣𝑒𝑟𝑛𝑖𝑔ℎ𝑡𝑉 𝑜𝑙 + 𝑘𝜎𝑂𝑝𝑒𝑛𝑇 𝑜𝐶𝑙𝑜𝑠𝑒𝑉 𝑜𝑙 + (1 − 𝑘)𝜎𝑅𝑆 ,
𝑁 +1 2
The price action (PA) influences Historical Volatil- where 𝑘 = 0.34/1.34 + 𝑁 −1 , 𝜎𝑂𝑝𝑒𝑛𝑇 𝑜𝐶𝑙𝑜𝑠𝑒𝑉 𝑜𝑙 =
ity (HV), and in turn, HV can provide insights into 𝑁
(︂
(𝑐) (𝑐)
)︂2
𝑥𝑡 𝑥𝑡 2
future PA. When the PA exhibits strong price move- 𝑁 1−1
∑︀
𝑙𝑛 (𝑜) − 𝑙𝑛 (𝑜) , and 𝜎𝑂𝑣𝑒𝑟𝑛𝑖𝑔ℎ𝑡𝑉 𝑜𝑙 =
𝑥𝑡 𝑥𝑡
ments, such as wide trading ranges, breakouts, or 𝑖=1
(︂ )︂ 2
𝑁 (𝑜) (𝑜)
rapid directional changes, it tends to increase. 1
∑︀ 𝑥𝑡 𝑥𝑡
𝑙𝑛 − 𝑙𝑛 . YZ exhibits notable
VolTS-Aug, as an improvement of the VolTS mod- 𝑁 −1 𝑖=1 (𝑐)
𝑥𝑡−1
(𝑐)
𝑥𝑡−1
ule within the AITA framework, adheres to these performance across a broad spectrum of scenarios,
principles. Low HV signifies a period of consolida- including those characterised by jumps and non-
tion or low price volatility, indicating a potential normality in the data. However, this estimator has
upcoming spike in volatility or a shift in the PA. limitations, and its effectiveness may be constrained
On the other side, high HV suggests a higher proba- in certain contexts.
bility of sharp market movements or trend changes. In this research, our attention is centred on mid-
Also into VolTS-Aug, the PA is encoded as OHLC, volatility. This focus allows us to either close open
i.e., the open, high, low, and close prices of the positions or refrain from entering a position when
assets. the anticipated volatility coefficient is high, thereby
For each timeframe 𝑡, the OHLC of an asset mitigating the risk of losses. On the other hand, if
is represented as a 4-dimensional vector 𝑋𝑡 = the expected volatility is too low, it does not offer
(𝑜) (ℎ) (𝑙) (𝑐) (𝑙) (𝑙) (ℎ)
(𝑥𝑡 , 𝑥𝑡 , 𝑥𝑡 , 𝑥𝑡 )𝑇 , where 𝑥𝑡 > 0, 𝑥𝑡 < 𝑥𝑡 any potential for gains.
(𝑜) (𝑐) (𝑙) (ℎ)
and 𝑥𝑡 , 𝑥𝑡 ∈ [𝑥𝑡 , 𝑥𝑡 ].
2.3. Trading Strategy
2.2. Historical Volatility Time Series In this experiment, we used the Trend Following
The construction of the dataset is composed by time (TF) strategy. It is one way to engage in trend
series from the following HV estimators: trading, where a trader initiates an order in the
direction of the breakout after the price surpasses
the resistance line as follows: let 𝑃𝑡 the price at
time 𝑡, and let 𝑀 𝐴 denote the Moving Average of 3. THE EXPERIMENT
the asset price over a certain period. If 𝑃𝑡 ≥ 𝑀 𝐴𝑡
indicates an upward trend to take a long position 3.1. Asset Collections
otherwise it is a downward trend to take a short
AITA automatically downloads the OHLC prices
position.
via an internal Python library connected to an API,
Then, our strategy is compared only with the
using the MetaTrader5 (MT5)1 . The data collected
Buy and Hold (B&H) strategy considering it as a
for this study includes the OHLC prices of the stocks
benchmark.
listed in Table 1.
2.4. Backtesting Metrics Table 1
AITA framework considers the following profit and List of the main 9 stocks selected for the experimentation.
risk metrics to evaluate the potential profitability Ticker Company Market
of investments and manage risk exposure. MSFT Microsoft Corporation Nasdaq
Drawdown (DD). It is a measure of the peak-to- GOOGL Alphabet Inc. Nasdaq
trough decline in the value of a trading account MU Micron Technology, Inc. Nasdaq
before a new peak is attained. DD is defined as NVDA NVIDIA Corporation NYSE
follows: 𝐷𝐷 = 𝑃 −𝑇 , where 𝑃 is the highest value AMZN Amazon.com, Inc. NYSE
𝑇
or peak of the portfolio. 𝑇 is the lowest value META Meta Platforms, Inc. NYSE
QCOM QUALCOMM Incorporated Nasdaq
or trough after the peak. Maximum Drawdown
IBM Int. Business Machines Corp. NYSE
(MDD) is the most significant loss from peak to
INTC Intel Corporation NYSE
trough during a(︁specific period calculated
)︁ as follows:
𝑃𝑖 −𝑚𝑖𝑛𝑗:𝑖≤𝑗≤𝑁 𝑇𝑗
𝑀 𝐷𝐷 = 𝑚𝑎𝑥𝑖 𝑃𝑖
, where 𝑃𝑖 is the
highest value or peak of the portfolio time 𝑖. 𝑇𝑗 is
the lowest value or trough after the peak up to time
3.2. Historical Volatility Time Series
𝑗. 𝑁 is the total number of data points. The History Volatility Clustering process of our
Sortino ratio (SoR). It is a risk-adjusted profit approach determines the stocks with intermediate
measure, which refers to the return per unit of volatility. First calculate the average of historical
𝑅 −𝑅
deviation as follows: 𝑆𝑜𝑅 = 𝑝𝜎𝑑 𝑓 , where 𝑅𝑝 is volatility time series among the aforementioned esti-
the expected portfolio return, 𝑅𝑓 the risk-free rate mators (see sect. 2.2). Next, the resulting volatility
of return, and 𝜎𝑑 denotes the downside deviation of series are clusterized using the KMeans++ algo-
the portfolio returns. rithm. In particular, we split into three clusters
Sharpe ratio (SR). It is a variant of the risk- (𝐾 = 3) high, middle, and low volatility.
adjusted profit measure, which applies 𝜎𝑝 as a risk Figure 1 shows the results displayed through a
𝑅 −𝑅
measure: 𝑆𝑅 = 𝑝𝜎𝑝 𝑓 where 𝜎𝑝 is the standard plot of the time series belonging to the middle clus-
deviation of the portfolio return. ter where we are focused on our strategy. It is worth
Calmar ratio (CR) is another variant of the risk- noting that, the main region is in the time window
adjusted profit measure, which applies MDD as risk from 1st January 2021 to 1st March 2024.
𝑅 −𝑅
measure: 𝐶𝑅 = 𝑀𝑝 𝐷𝐷𝑓 . So, we use this interval as the dataset, and then
To check the goodness of trades, we mainly fo- from the intermediate cluster (confined between
cused on the Total Returns 𝑇 𝑅𝑘 (𝑡) for each stock the two red dashed lines in fig 1). The candidate
(𝑘 = 1, ..., 𝑝) in the time interval (𝑡 = 1, ..., 𝑛) assets selected are NVDA, META, AMZN, MU and
with the price 𝑃 , defined as follows: 𝑇 𝑅𝑘 (𝑡) = QCOM.
𝑃𝑘 (𝑡+Δ𝑡)−𝑃𝑘 (𝑡)
𝑃𝑘 (𝑡)
.
Furthermore, we analyzed the standardized re- 3.3. Causality Analysis
turns 𝑟𝑘 = (𝑇 𝑅𝑘 −𝜇𝑘 )/𝜎𝑘 , with (𝑘 = 1, ..., 𝑝), where Co-integration refers to the long-term stable lin-
𝜎𝑘 is the standard deviation of 𝑇 𝑅𝑘 , e 𝜇𝑘 denote ear combination between two or more time series,
the average overtime for the studied period. although individual series may be non-stationary.
In the context of volatility-based trading, the
VolTS-Aug module performs the GCT to examine
this relationship between the lagged volatility of
1
https://www.metatrader5.com/
Figure 1: Stocks selected in the range, from 1st January 2021 to 1st March 2024, are MU, NVDA, AMZN, QCOM,
META from the Historical Volatility estimators dataset.
one asset and the future volatility of another asset 3.4. The Algorithm
by applying the following steps:
Three are the main steps followed by VolTS-Aug:
Step 1. Significant Granger causality: Let 𝑋 and
Regression step: For each pair of time series
𝑌 be the pair stocks time series volatility to check,
(𝑋𝑖 , 𝑌𝑗 ), where 𝑖 ̸= 𝑗, we construct a linear regres-
where 𝑋 represents the potential causal variable
sion model: 𝑋𝑖 = 𝛽0,𝑖𝑗 + 𝛽1,𝑖𝑗 𝑌𝑗 + 𝜖𝑖𝑗 , where 𝛽0,𝑖𝑗 is
and 𝑌 represents the potential effect variable. The
the intercept, 𝛽1,𝑖𝑗 is the regression coefficient, and
null hypothesis (H0) states that 𝑋 does not Granger
𝜖𝑖𝑗 is the error term. We calculate the F-statistic
cause 𝑌 , while the alternative hypothesis (H1) states
to evaluate the overall adequacy of the model.
that 𝑋 does Granger cause 𝑌 . The F-test is defined
GCT step: For each pair of time series (𝑋𝑖 , 𝑌𝑗 ), we
as follows:
perform the Granger causality test. The model for
[(𝑅𝑆𝑆𝑌 (𝑡) − 𝑅𝑆𝑆𝑌 𝑋(𝑡) )/𝑝] the
∑︀𝑛 Granger test can be∑︀expressed as 𝑋𝑖 (𝑡) = 𝛼𝑖𝑗 +
𝐹 − 𝑡𝑒𝑠𝑡 = , 𝑛
𝛽 𝑋 (𝑡 − 𝑘) + 𝑘=1 𝛾𝑘,𝑖𝑗 𝑌𝑗 (𝑡 − 𝑘) + 𝜖𝑖𝑗 (𝑡),
[(𝑅𝑆𝑆𝑌 𝑋(𝑡) )/(𝑛 − 𝑝 − 𝑘)] 𝑘=1 𝑘,𝑖𝑗 𝑖
where 𝑋𝑖 (𝑡) is the current value of 𝑋𝑖 , 𝑋𝑖 (𝑡 − 𝑘)
where 𝑅𝑆𝑆 is the Residual Sum of Squares for the and 𝑌𝑗 (𝑡 − 𝑘) are the lagged values of 𝑋𝑖 and 𝑌𝑗 ,
two AutoRegressive models: 𝑌 (𝑡) = 𝑐𝑌 +𝛽𝑌1 *𝑌 (𝑡− respectively, and 𝜖𝑖𝑗 (𝑡) is the error term. If the
1) + 𝛽𝑌2 * 𝑌 (𝑡 − 2) + · · · + 𝛽𝑌𝑝 * 𝑌 (𝑡 − 𝑝) + 𝜖𝑌 (𝑡) , coefficients 𝛾𝑘,𝑖𝑗 are statistically different from zero,
and 𝑋 : 𝑌 (𝑡) = 𝑐𝑌 𝑋 + 𝛽𝑌 𝑋1 * 𝑋(𝑡 − 1) + 𝛽𝑌 𝑋2 * we reject the null hypothesis and conclude that 𝑌𝑗
𝑋(𝑡 − 2) + · · · + 𝛽𝑌 𝑋𝑝 * 𝑋(𝑡 − 𝑝) + 𝜖𝑌 𝑋(𝑡) , with 𝑝 Granger causes 𝑋𝑖 .
the lag order, 𝑛 the number of observations, and DTW-KNN step: (i) For each pair of time se-
𝑘 the number of parameters in the models. It in- ries (𝑋𝑖 , 𝑌𝑗 ), where 𝑋𝑖 has length 𝑛 and 𝑌𝑗 has
dicates how much the regression coefficients of the length 𝑚, the DTW distance ∑︀𝑛 𝑑(𝑋∑︀𝑚𝑖 , 𝑌𝑖 ) is given by
lagged time series help to explain the variation in 𝑑(𝑋𝑖 , 𝑌𝑖 ) = 𝑚𝑖𝑛𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 𝑖=1 𝑗=1 𝑐(𝑖, 𝑗), where
the target time series. 𝑐(𝑖, 𝑗) is the distance between points 𝑋𝑖 [𝑖] and 𝑌𝑗 [𝑗],
Step 2. Causality Direction: If the volatility of and the optimization is performed overall possible
Stock 𝑋 Granger causes the volatility of Stock 𝑌 , alignments. (ii) The process of finding the best
it suggests that changes in Stock 𝑋 volatility can parameters delta time 𝛿𝑡 involves the KNN whit 𝑘
be used to predict changes in Stock 𝑌 volatility. A optimization through grid search.
low p-value suggests the presence of a causal rela-
tionship between the time series. 3.5. Metrics observed
Step 3. Delta Time Trends: VolTS-Aug performs
the DTW paired with KNN to examine the interval Profit and risk metrics are pivotal considerations
time necessary for profitable trades: (i) The DTW in trading AITA framework evaluates the following,
distance between two time series is the sum of differ- for the potential profitability of the investments and
ences between their corresponding points, optimally to manage the risk exposure.
aligned. (ii) The KNN classifier, aimed at finding (i) The Maximum drawdown (MDD) measures the
the most similar neighbours for each observation largest decline from the peak in the whole trading
based on DTW distance. period, to show the worst case, as follows: 𝑀 𝐷𝐷 =
𝑚𝑎𝑥𝜏 ∈(0,𝑡) [𝑚𝑎𝑥𝑡∈(0,𝜏 ) 𝑛𝑡𝑛−𝑛𝑡
𝜏
]. Tab. 2 contains further details about the perfor-
(ii) The Sharpe ratio (SR) is a risk-adjusted profit mance metrics of the strategy and shows how the
measure, which refers to the return per unit of total amount in the portfolio is increased to 3241.57$
deviation as follows: 𝑆𝑅 = E[𝑟] [𝑟]
. (8.05%), which is a positive sign of profitable trad-
(iii) The Sortino ratio (SoR) is a variant of the ing, also considering the fixed commission of 9$ per
risk-adjusted profit measure, which applies DD as trade. Notice that, the managing of the budget
risk measure: 𝑆𝑜𝑅 = 𝐷𝐷 E[𝑟]
. is set in compounded mode, so the full amount is
(iv) The Calmar ratio (CR) is another variant reused for each trade.
of the risk-adjusted profit measure, which applies
MDD as risk measure: 𝐶𝑅 = 𝑀E[𝑟] 𝐷𝐷
. 4.2. Backtesting
To check the goodness of trades, we mainly fo-
cused on the (v) Total Returns 𝑅𝑘 (𝑡) for each stock The analysis of individual stocks’ performance is
(𝑘 = 1, ..., 𝑝) in the time interval (𝑡 = 1, ..., 𝑛), presented in figure 3 about META co-integration.
The trades of AMZN bought following the META
where 𝑇 𝑅 = 𝑅𝑘 (𝑡) = 𝑍𝑘 (𝑡+Δ𝑡)−𝑍 𝑍𝑘 (𝑡)
𝑘 (𝑡)
, and fur-
trend given a profit of 59.98$, with a winrate of
thermore analysing the standardized returns 𝑟𝑘 =
75%, a MDD of 0.035%, and a return of 5.98%,
(𝑅𝑘 − 𝜇𝑘 )/𝜎𝑘 , with (𝑘 = 1, ..., 𝑝), where 𝜎𝑘 is the
which outperforms the B&H strategy with return
standard deviation of 𝑅𝑘 , e 𝜇𝑘 denote the average
of 0.998%. The trades of MU bought following
overtime for the studied period.
the META trend given a profit of 146.68$, with a
winrate of 100%, a MDD of 0%, and a return of
4. RESULTS AND DISCUSSIONS 34.91%, which outperforms the B&H strategy with
return of 3%. The trades of NVDA bought following
4.1. The Experiment the META trend given a profit of 39.11$, with a
winrate of 75%, a MDD of 0.11%, and a return of
3.98%, which is similar to the B&H strategy with
return of 4.02%.
Figure 3: Trades during the 21 testing days (1st March -
Figure 2: Best Granger Causality Test with 21 lags.
5th April).
The VolTS algorithm iterates the daily lags in
a range from 2 to 30 days to determine the best Figure 3 shows all the 7 positions applied at the
testing range time. The best result is achieved same time on NVDA, MU and AMZN with buy-
with lags=21, where ’best’ is considered when there ing/selling trades following the co-integration with
is direction coherency among the stocks with the META trend determined with VolTS-Aug algorithm.
lowest p-value, with the maximum cardinality of The trades on MU stock outperforms all the oth-
the set of stocks previously filtered, and not create ers stocks increasing notably the portfolio gain (see
cyclic graph in the connections. On other words, Table 2).
the GCT suggests buying AMZN, MU and NVDA
when META has a positive trend and vice versa 5. Conclusions
(see fig. 2).
The experiment results indicate that the strategy In this paper, we propose VolTS-Aug an improve-
resulted in a total gain of 241.57$ in 21 days of ment of the AITA framework module calle VolTS.
market opening, starting with an initial budget of VolTS-Aug handle volatility in trading strategy com-
1000$ per stock. bining causality by the Historical Volatility Granger
Causality Test and DTW & KNN to determine
Table 2
Results of the backtesting in the experiment.
Stock #Trades 𝜇 WinRate (%) 𝜇 TR ($) 𝜇 SR 𝜇 SoR CR
META ->AMZN, NVDA, MU 7 83.33 241.57 3.03 8.75 15.941
a profitable stock pairings improving on previous and error correction: Representation, estima-
work [10, 1]. tion, and testing, Econometrica 55 (1987)
The novelty of the approach implemented in 251–276. URL: http://www.jstor.org/stable/
VolTS-Aug lies in a better trades timing. To vali- 1913236.
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