International Journal of Community Service ISSN 2961-7162 .
https://ejournal.
com/index.
php/ijcs Vol.
Issue 1, 2025 DOI : 10.
55299/ijcs.
Integrating Machine Learning into Portfolio Optimization: A Hybrid ARIMAAeGARCH Predictive Model with Genetic Algorithm Andreas P Peranginangin1 Prima Indonesia University.
PPrestasigemilang@gmail.
ABSTRACT
This article proposes a hybrid quantitative framework that integrates statistical timeAcseries modeling and evolutionary machine learning for portfolio optimization.
The approach combines an ARIMAAeGARCH model to jointly estimate conditional mean and volatility of asset returns with a Genetic Algorithm (GA) that searches for optimal portfolio weights on the basis of modelAcimplied returnAerisk profiles.
The study adopts a secondaryAcdata quantitative design, synthesising evidence from prior empirical applications of ARIMAAe GARCH forecasting and GAAcbased portfolio optimization in equity markets, including the S&P500 index and Indonesian LQ45 constituents.
Descriptive analysis confirms strong volatility clustering and leptokurtosis in daily stock index returns, justifying the use of GARCHActype volatility models.
Empirical results from the literature show that hybrid ARIMAAeGARCH models significantly outperform standalone ARIMA and buyAcandAchold strategies in terms of forecasting error and riskAcadjusted performance, while GAAcoptimized portfolios achieve superior riskAereturn tradeAcoffs compared with traditional meanAevariance optimization.
These findings support the conceptual integration of ARIMAAeGARCH forecasts and GAAcbased allocation as a promising direction for portfolio construction, particularly in emerging markets such as Indonesia.
The article concludes with implications for portfolio managers, regulators, and higherAceducation curricula in quantitative finance and dataAcdriven investment.
Keywords:
Received:
Hybrid, learning, model, predictive.
Revised:
Accepted:
Available online:
Suggested citations:
Peranginangin.
Integrating machine learning into portfolio optimization: A hybrid ARIMAAe GARCH predictive model with genetic algorithm.
International Journal of Community Service, 5 .
DOI: 10.
55299/ijcs.
INTRODUCTION
The rapid development of computational methods and data availability has transformed the portfolio management landscape.
Institutional and individual investors now operate in environments characterized by high frequency trading, complex derivative structures, and increasingly integrated global markets.
Under these conditions, the classical meanAevariance paradigm, as introduced by Markowitz, remains foundational but is often insufficient as a stand alone tool for capturing the Corresponding Author Name: Andreas P Peranginangin.
PPrestasigemilang@gmail.
International Journal of Community Service, 5 .
, 2026, pp.
| 125
nonlinear dynamics and volatility clustering observed in financial time series.
Therefore there is a growing need to integrate modern machine learning techniques with established econometric models to achieve more robust and adaptive portfolio Traditional portfolio theory models asset returns as jointly normally distributed, with risk measured by the varianceAecovariance matrix and expected returns estimated as long run sample means.
in practice ractice, empirical return distributions exhibit fat tails, skewness, and time varying volatility.
Studies on major equity indices, such as the S&P500, have shown that log returns are leptokurtic with significant volatility clustering and non Gaussian behavior, even after basic transformations.
Similar patterns have been documented in Gulf financial markets and the Indonesian stock market, including the LQ45 index constituents.
These empirical regularities undermine key assumptions of homoscedasticity and normality that underlie simple linear models, leading to biased risk estimates and potentially sub optimal portfolios (Aniket Gharpure, 2.
Against this backdrop, the Autoregressive Integrated Moving Average (ARIMA) model and Generalized autoregressive conditional heteroskedasticity (GARCH) family have become central tools in financial econometrics.
ARIMA models effectively capture linear dependence and nonAcstationarity in the conditional mean process, whereas GARCH models explicitly account for conditional heteroscedasticity in asset returns.
However, each model class hads limitations when applied in isolation.
ARIMA assumes a constant error variance, which is inconsistent with observed volatility clustering, whereas GARCH focuses on variance dynamics and does not directly model the conditional mean process.
To address these shortcomings, hybrid ARIMAAeGARCH models have been proposed, in which ARIMA captures the conditional mean and GARCH characterizes conditional variance, thereby modelling both the first and second moments of the return distribution.
Empirical evidence supports the superiority of hybrid ARIMAAeGARCH models over stand alone ARIMA or GARCH models in various financial contexts.
Studies of Gulf stock indices show that ARIMA components often provide more accurate forecasts for certain markets, whereas GARCH components dominate in others, and their hybridization can yield improved predictive performance overall.
Indonesian evidence on LQ45 stocks similarly indicates that an ARIMA.
,1,.
AeGARCH.
combination can outperform single model specifications in one step ahead price forecasts.
For the S&P500 index, a dynamic ARIMAAeSGARCH hybrid fitted using a rolling window with optimized ARIMA orders has been shown to dominate pure ARIMA forecasts and the passive buyand hold benchmark, both in error metrics and strategy performance indicators such as annualized return, volatility, maximum drawdown, and information ratio (Bakar & Rosbi, 2.
Parallel to these developments in time series forecasting, machine learning and evolutionary computation have gained prominence in portfolio optimization.
particular genetic Algorithms (GA.
have been widely used to solve complex optimization problems that are non convex, high dimensional, or subject to discrete In finance.
GAs have been employed to solve meanAevariance and related portfolio problems, often outperforming classical quadratic programming when the search space is large, constraints are combinatorial, or the objective function has .
Andreas P Peranginangin multiple local optima.
For example.
GAAcbased optimization of a meanAevariance model for Indonesian LQ45 stocks over the period February 2020 to July 2021 produced an optimal portfolio consisting of five stocks with specific allocation weights and superior expected returnAerisk characteristics.
Other studies compare GAAcbased portfolios with Markowitz solutions and alternative metaheuristics, such as Particle Swarm Optimization and Simulated Annealing, and typically find that GAs achieve higher Sharpe ratios and better diversification.
Despite these advances, the integration between time series modelling and evolutionary optimization remains relatively underdeveloped.
Many studies treat forecasting and portfolio optimization as separate problems: one strand focuses on improving return and volatility forecasts, while the other concentrates on search algorithms for asset allocation, often assuming static or historically estimated There is comparatively little work that systematically links a sophisticated forecasting engin capable of generating forward looking estimates of conditional mean and volatility with a GA that uses these estimates to evolve optimal portfolios in a dynamic, data driven manner.
However such an integration is conceptually natural:
forecasted conditional returns and covariances from ARIMAAeGARCH models provide a realistic, time varying input to the fitness function that GAs seek to maximize or minimize (Luan et al.
, 2.
This study addresses this gap by articulating a hybrid ARIMAAeGARCHAeGA framework for portfolio optimization and by grounding the proposed approach in quantitative evidence from existing empirical studies.
Methodologically, the study adopted a quantitative secondary data design.
It synthesiz ses detailed results reported in prior research on ARIMAAeGARCH forecasting for the S&P500 and GAAcbased portfolio optimization for LQ45 and other stock universes.
In doing so, the article does not claim to introduce a new proprietary dataset but rather to provide an integrative methodological blueprint that can be replicated for different markets, including Indonesia, by combining well established models and algorithms.
The objectives of thise study were fourfold First, it seeks to empirically demonstrate that financial return series exhibit distributional and dependence characteristics that justify the use of ARIMAAeGARCH models rather than simple linear models.
Second, it reviews and synthesizes empirical evidence on the forecasting performance of ARIMAAe GARCH hybrids relative to ARIMA alone and buyAcandAchold strategies.
Third, it presents evidence of the performance of GAAcbased portfolio optimization relative to traditional meanAevariance models.
Fourth, based on these strands of evidence, we proposes a conceptual and computational integration in which an ARIMAAeGARCH forecasting module is fed into a GAAcbased optimization module, yielding a hybrid machineAclearningAcinformed portfolio construction process.
The contributions of this study are methodological and pedagogical.
Methodologically, it delineates a concrete workflow for integrating time series econometrics and machine learning within a unified portfolio optimization framework.
Pedagogically, thise article is positioned to support curriculum development in Indonesian higher education, particularly in programs that seek to combine statistics, computer science, and finance.
By detailing the models, metrics, and algorithms involved, thise study provides a structured reference that can be used in coursework.
International Journal of Community Service, 5 .
, 2026, pp.
| 127
capstone projects, and applied research in quantitative finance and financial The remainder of this paper is organized as follows.
Section 2 reviews the theoretical and empirical literature on portfolio optimization.
ARIMAAeGARCH models, and Genetic Algorithms.
Section 3 describes the research method, including the data sources, model specifications.
GA configuration, and evaluation metrics.
Section 4 presents the quantitative results drawn from prior empirical studies, organized to illustrate the performance of each component of the hybrid framework.
Section 5 discusses these findings, elaborates on the implications of integrating ARIMAAeGARCH and GA, and considers their limitations.
Section 6 concludes with a synthesis of key insights and suggestions for future research, with an emphasis on applications in Indonesia and educational settings.
METODE
Thise study adopteds a quantitative research design based on secondary data and published empirical results.
Rather than collecting new primary data, it synthesizes and reinterprets existing findings on ARIMAAeGARCH forecasting and GAAcbased portfolio optimization to propose an integrated methodological framework.
The design can be characterized as explanatory and methodological: explanatory, because it uses quantitative results to support causal arguments about the benefits of hybrid modelling.
methodological, because it focuses on how to combine statistical forecasting and machine learning optimization in portfolio construction.
The empirical analysis proceeds in two stages.
The first stage examines the statistical properties of daily stock index returns and the forecasting performance of hybrid ARIMAAeGARCH models relative to ARIMA and buyAcandAchold strategies using the results reported for the S&P500 index.
The second stage analyses GAAcbased meanAe variance portfolio optimization results for LQ45 stocks in the Indonesian market, as presented in prior research.
The combination of these stages provides an empirical basis for arguing that an integrated ARIMAAeGARCHAeGA framework is both theoretically justified and practically promising (Li, 2.
Data and Variables The time series component is based on the daily prices of the S&P500 index over the period January 1 2000 to December 31 2019, as reported in prior ARIMAAeSGARCH The adjusted closing prices are transformed into daily logarithmic returns Andreas P Peranginangin where Pt denotes the adjusted closing price at time t This transformation provides additive returns and yields a series that is closer to normality than raw prices while remaining leptokurtic and exhibiting volatility clustering.
The portfolioAcoptimisation component uses data on individual stock returns from the Indonesian LQ45 index over February 2020AeJuly 2021, as reported in the GAAcbased meanAevariance optimization study.
For this study, the key variables are the estimated expected returns and covariance matrix used in the GA optimization, as well as the resulting optimal portfolio weights, expected return, and risk.
ARIMAAeGARCH Model Specification The hybrid ARIMAAeGARCH model is specified bytwo equations: a conditional mean equation and a conditional variance equation.
For the conditional mean, an ARIMA.
,d,.
model is used as follows:
where yt is the log return at time tL is the lag operator, p is the order of the autoregressive component, d is the order of differencing .
et to 1 in the cited S&P500 stud.
, q is the order of the movingaverage component, and At is the residual.
For conditional variance, a GARCH.
model is employed:
subject to 0>00>0, 1Ou01Ou0, 1Ou01Ou0, and 1 1<11 1<1 to ensure positivity and covariance-stationarity.
The innovation process is specified under a fat tailed distribution such as the generalized error distribution (GED), which captures leptokurtic behavior better than the normal distribution.
In the empirical S&P500 application.
ARIMA.
,1,.
orders are dynamically selected using a rolling window of s=1000s=1000 observations.
For each day in the out of sample period, candidate ARIMA specifications are estimated for combinations of p,qOO.
,1,2,3,4,.
p,qOO.
,1,2,3,4,.
, excluding p=q=0p=q=0.
Akaike Information Criterion (AIC) was used to select the optimal The chosen ARIMA model is then combined with an SGARCH.
variance equation, estimated with GED errors, to produce one step ahead forecasts of returns and conditional variance.
The Genetic Algorithm operates on a population of candidate portfolios, each represented as a chromosome encoding a vector of asset weights x=.
1,x2,A,x.
1,x2,A,x.
The basic portfolio optimization problem follows a meanAevariance structure:
minAx Ep2=xOVxxmin Ep2=xOVx subject to eOx=1,xiOu0,i=1,A,n,eOx=1,xiOu0,i=1,A,n.
International Journal of Community Service, 5 .
, 2026, pp.
| 129
where VV is the covariance matrix of returns and ee is a vector of ones.
In an integrated ARIMAAe GARCHAeGA framework, the VV is replaced or augmented by the forecasted conditional covariance matrix derived from GARCH type models, and the expected returns are based on ARIMA forecasts.
However, in the cited LQ45 study, the covariance matrix and expected returns wer re estimated from historical data without explicit time varying modelling.
Key components of the GA include:
A Encoding: Real valued representation of portfolio weights with normalization to ensure budget constraint eOx=1eOx=1.
A Initial population: Randomly generated portfolios satisfying non negativity and full-investment constraints.
A Fitness function: A scalar objective reflecting the desired riskAereturn trade off, such as maximizing expected return for a given risk, minimizing risk for a target return, or maximizing a risk adjusted performance measure .
Sharpe rati.
A Selection: Probabilistic selection of parent portfolios based on relative fitness using methods such as roulette-wheels or tournament selection.
A Crossover: Combination of parent portfolios to create offspring, typically using single-point or uniform crossover operators.
A Mutation: Random perturbation of portfolio weights with a low probability of maintainin diversity and avoidin premature convergence.
A Elitism: Preservation of the best solutions from one generation to the next to guarantee nonn decreasing maximum fitness.
In the LQ45 application, the GA is configured to search for a portfolio that minimizes variance while satisfying the full investment and non negativity constraints.
The algorithm converges to an optimal portfolio comprising five assets with specific weights and estimated riskAereturn Evaluation Metrics To assess forecasting performance, the following error metrics are used:
Mean Absolute Error (MAE):
MAE=1nOci=1nOAiOeFiO,MAE=n1i=1OcnOAiOeFiO.
Mean Squared Error (MSE):
MSE=1nOci=1n(AiOeF.
2,MSE=n1i=1Ocn(AiOeF.
Root Mean Squared Error (RMSE):
RMSE=1nOci=1n(AiOeF.
2,RMSE=n1i=1Ocn(AiOeF.
Mean Absolute Percentage Error (MAPE):
MAPE=1nOci=1nOAiOeFiAiO,MAPE=n1i=1OcnAiAiOeFi, where AiAi and FiFi denote actual and forecasted returns, respectively.
To evaluate investment performance of model-based strategies, the following metrics are A Annualised Return Compounded (ARC).
A Annualised Standard Deviation (ASD).
A Maximum Drawdown (MD).
Andreas P Peranginangin Information Ratio (IR = ARC / ASD).
Adjusted Information Ratio (IR*), which also incorporates MD.
For portfolio optimization outcomes, expected return and risk .
ariance or standard deviatio.
are reported along with portfolio composition .
eights on each asse.
These metrics collectively provide a quantitative basis for comparing the performance of hybrid ARIMAAeGARCH models and GA based portfolios with their respective benchmarks.
RESULTS AND DISCUSSION
Descriptive Statistics of S&P500 Prices and Returns Table 1 summarizes the descriptive statistics of the S&P500 index prices and daily log returns from January1 2000 to December 31 2019, as reported in the ARIMAAe SGARCH study.
These statistics characterize the distributional features that motivate the use of GARCH type volatility models.
Table 1.
Descriptive statistics for S&P500 prices and log returns (Jan 2000AeDec Statistic S&P500 Prices Log Returns Min Oe0.
1st Quantile Oe0.
Median Arithmetic Mean 3rd Quantile Max Skewness Oe0.
Kurtosis Oe0.
Standard Error of Mean Standard Deviation The price series exhibits strong right skewness .
and near zero kurtosis, whereas the log return series has a slight negative skewness (Oe0.
and very high kurtosis .
, indicating fat tails relative to the normal distribution.
The standard deviation of returns is 0.
0119, and the standard error of the mean is close to zero, reflecting a large sample size.
The high kurtosis of the return distribution suggests frequent extreme movements, both positive and negative, compared with a normal distribution.
The nearAczero but negative skewness implies a slightly greater propensity for large negative returns than for positive ones.
These features are consistent with the stylized facts of financial returns and justify the use of models, such as GARCH and its extensions, whiich can capture International Journal of Community Service, 5 .
, 2026, pp.
| 131
heavy tails and volatility clustering.
Thuse descriptive statistics provide empirical motivation for the ARIMAAeGARCH specification in the forecasting component of the hybrid framework.
Forecasting and Strategy Performance: ARIMA vs ARIMAAeSGARCH The next set of results concerns the relative performance of the pure ARIMA and hybrid ARIMAAeSGARCH models in forecasting S&P500 returns and driving algorithmic trading strategies.
Table 2 summarizes the key error metrics and investment performance indicators for three approaches: a buyAcandAchold benchmark.
ARIMAAcbased strategy (ARIMA 1.
, and hybrid ARIMAAeSGARCH strategy (SGARCH.
GED 1.
All models are estimated using a rolling window of 1000 observations, with ARIMA orders selected by AIC and SGARCH.
variance specification with GED innovations.
Table 2.
Forecasting error and performance metrics for ARIMA and ARIMAAeSGARCH strategies .
indow = 1.
Method
MAE
MSE
RMSE
MAPE
ARC
ASD
IR*
Buy & Hold (S&P.
ARIMA 1000
SGARCH.
GED
The hybrid ARIMAAeSGARCH strategy (SGARCH.
GED 1.
achieves lower MAE.
MSE.
RMSE, and MAPE values than the ARIMA 1000 strategy, indicating more accurate return forecasts.
The improvements, although modest in absolute terms, were consistent across all the error measures.
Importantly, the hybrid model translates these forecasting gains into substantially improved investment performance.
Its annualized compounded return (ARC) is 14.
03%, compared to 8.
08% for ARIMA 1000 and 6.
93% for buyAcandAchold.
Althoug annualized volatility (ASD) is similar across all three approaches .
8Ae18.
9%), the maximum drawdown (MD) is dramatically reduced for the hybrid strategy .
89%) relative to buyAcandAchold .
78%) and ARIMA 1000 .
01%).
The information ratio (IR) and adjusted information ratio (IR*) provide composite measures of risk adjusted performance.
The hybrid ARIMAAeSGARCH strategy attains an IR of 0.
742 and IR* of 0.
402, which is substantially higher than those of the ARIMA 1000 strategy (IR = 0.
IR* = 0.
and the buyAcandAchold benchmark (IR = 0.
IR* =
These results indicate that incorporating conditional heteroskedasticity through SGARCH.
with GED innovations materially improves both forecasting accuracy and portfolio performance when forecasts are used to generate trading signals.
From the perspective of the hybrid ARIMAAeGARCHAeGA framework,Table 2 shows that ARIMAAeGARCH models can provide more reliable and riskAcsensitive forecasts than pure ARIMA.
In an integrated setting, these forecastsAiboth conditional means and conditional variancesAiwould form the inputs to the GAAos fitness function.
Andreas P Peranginangin thereby embedding time varying information about risk and return into the optimization process.
The third set of results focuses on GAAcbased portfolio optimization in the context of the Indonesian stock market.
A study of LQ45 stocks over the period February 2020Ae July 2021 applied a GA to solve the meanAevariance model, with the goal of minimizing portfolio variance subject to full investment and non negativity constraints.
The GA converges to an optimal portfolio of five stocks.
The resulting asset weights, expected returns, and risks are summarized in Table 3.
Table 3.
Genetic AlgorithmAcoptimised meanAevariance portfolio for LQ45 stocks (Feb 2020AeJul 2.
Stock
Weight (%) ADRO
AKRA
BBCA
CPIN
EXCL
Overall portfolio characteristics:
Expected return: 0.
Risk .
: 0.
The optimal portfolio places the largest weights on AKRA .
049%) and BBCA .
749%), with moderate allocations to CPIN and EXCL and a smaller position in ADRO.
The resulting expected daily return .
exceeds the individual expected returns of many constituents when held alone, while achieving low portfolio variance .
, indicating effective diversification and risk reduction.
Although the study does not report direct comparisons with a classical quadratic programming solution on the same dataset.
GAAcbased portfolios in similar contexts have been shown to outperform MarkowitzAcoptimized portfolios when additional constraints or nonAclinearities are present.
In the context of the proposed hybrid framework.
Table 3 illustrates the ability of GAs to discover nontrivial weight vectors that effectively balance risk and return, even in the presence of multiple local optima and potential estimation errors in the input If the expected returns and covariance matrix used by the GA are derived from ARIMAAeGARCH forecasts rather than static historical estimates, the resulting portfolio is explicitly conditioned on current market volatility and return expectations.
Synthesis of Empirical Evidence for the Hybrid Framework Taken together, the results in Tables 1Ae3 provide quantitative support for each component of the hybrid ARIMAAeGARCHAeGA framework.
Descriptive statistics International Journal of Community Service, 5 .
, 2026, pp.
| 133
confirm that equity returns exhibit heavy tails and volatility clustering, thus justifying the use of GARCH type models.
The forecasting and strategy performance results indicate that hybrid ARIMAAeGARCH models can generate more accurate forecasts and materially improve riskAcadjusted returns compared to pure ARIMA and buyAcandAchold GAAcbased portfolio optimization results show that evolutionary algorithms can identify portfolios with attractive riskAereturn profiles in realistic market settings, such as the Indonesian LQ45 index.
While the empirical studies summarized here are conducted on different markets and time periods, they collectively suggest that .
modelling both conditional mean and variance is beneficial for investment decisions, and .
GAs are capable of exploiting such information to construct high quality portfolios.
The hybrid ARIMAAeGARCHAeGA approach proposed in this study builds on these findings by explicitly linking the forecasting and optimization stages ARIMAAeGARCH models provide dynamic, forward looking inputs, and the GA uses these inputs within a global search process to allocate capital across assets.
Discussion The empirical evidence summarized in the previous section has important implications for the design of portfolio optimization systems that integrate machine learning and econometric modelling.
This section discusses these implications along several dimensions: the role of ARIMAAeGARCH in capturing market dynamics, the advantages of GAAcbased optimization, the conceptual architecture of the hybrid framework, potential applications in emerging markets such as Indonesia, and implications for education and future research.
The descriptive statistics of S&P500 log returns in Table 1 and similar evidence from other markets underscore the limitations of linear models with a constant variance.
High kurtosis and volatility clustering are signatures of conditional heteroscedasticity and fatActailed distributions, which are not well captured by homoscedastic ARIMA The ARIMAAeGARCH framework addresses these limitations by modelling both the conditional mean and conditional variance processes, thereby accommodating time varying risk (Tamimu et al.
, 2.
From an investment perspective, the accurate modelling of conditional variance is as important as modelling the conditional mean.
Portfolio optimization and risk management decisions critically depent on the estimates of future volatility and Underestimating volatility can lead to excessive leverage and vulnerability to drawdowns, whereas overestimating it can result in overly conservative portfolios that sacrifice returns.
The ARIMAAeGARCH approach provides a systematic way to update volatility estimates in response to new information, making it particularly suited to dynamic portfolio strategies (Thigah, 2.
The empirical results shown in Table 2 illustrate the benefits of this approach.
The hybrid ARIMAAeSGARCH strategy not only improves error metrics (MAE.
MSE.
RMSE.
MAPE) but also delivers substantially higher annualized returns and lower maximum drawdown than both ARIMA alone and buyAcandAchold.
The reduction in maximum drawdown is especially noteworthy because it reflects the modelAos ability to adjust exposure during periods of elevated volatility, thereby limiting losses.
In an integrated ARIMAAeGARCHAeGA framework, such volatility sensitive forecasts would directly .
Andreas P Peranginangin influence the optimization stage, allowing the GA to shift capital away from assets with temporarily elevated risk.
Genetic Algorithms offer several advantages over classical optimization techniques in portfolio selection.
First, they are global search heuristics that do not rely on gradient information or convexity, making them robust to non linear, non differentiable objective This is particularly useful when incorporating realistic constraints such as cardinality, minimum lot sizes, transaction costs, and regulatory limits, which often render the optimization problem nonAcconvex (Vo & olepaczuk, 2.
Second,GAs are inherently flexible with respect to the choice of the fitness function.
In a meanAevariance context, the fitness function can be defined as a weighted combination of expected returns and variance, a Sharpe ratio, or a utility function that incorporates investor preferences.
In a hybrid ARIMAAeGARCHAeGA framework, the fitness function can be made time varying by basing it on forecasted returns and variances rather than static historical estimates.
This flexibility allows the optimization process to adapt to changing market conditions.
Third, empirical studies, including the LQ45 GA optimization reported in Table 3, demonstrate that GAs can identify portfolios with attractive riskAereturn profiles, often outperforming naive or heuristic allocations.
In some cases.
GAAcderived portfolios compare favorably with those obtained from classical quadratic programming, especially when additional constraints or non standard risk measures are introduced.
The GAAos ability to perform a global search across a wide range of feasible portfolios mitigates the risk of becoming trapped in local optima owing to estimation noise or model mis specification (Carlos A.
Villanueva, 2.
The hybrid framework proposed in this study can be conceptualized as a two layer system: a forecasting layer and an optimization layer.
Forecasting Layer (ARIMAAeGARCH):
Inputs: Historical price or return data for a set of assets.
Operations: Data cleaning, log return computation.
ARIMA order selection .
, via AIC), estimation of ARIMA.
,d,.
for the conditional mean and GARCH.
or its variants for the conditional variance.
Outputs: OneAcstepAcahead forecasts of asset returns (^t 1^t .
conditional variances and covariances (^t .
Optimisation Layer (Genetic Algorith.
Inputs: Forecasted conditional mean vector ^t 1 and covariance matrix ^t 1, along with constraints .
, full investment, non negativity, cardinalit.
and investor preferences .
isk aversion, target retur.
Operations: GAAcbased search over a feasible set of portfolio weights, including encoding, selection, crossover, mutation, and elitism.
Outputs: Optimal or near optimal portfolio weights xt 1O that maximize a chosen fitness function .
, forecasted Sharpe rati.
This architecture can be implemented in a rolling or recursive manner such that at each rebalancing date, the ARIMAAeGARCH models are re estimated or updated using a moving window of recent data, new forecasts are generated, and the GA is run to determine the updated portfolio weights.
In practice, computational considerations may necessitate approximations, such as updating models less frequently or using simplified International Journal of Community Service, 5 .
, 2026, pp.
| 135
covariance forecasts.
however, the conceptual structure remains valid (Syahaza & Kirani, 2.
The empirical results summarized in Tables 2 and 3 demonstrat this architecture.
Table 2 shows that ARIMAAeGARCH models can provide superior forecasts and trading performance, while Table 3 shows that GAAcbased optimization can construct efficient portfolios in real markets.
Integrating these components promises a portfolio construction process that is both informed by sophisticated timeseries modeling and capable of navigating complex, constrained optimization landscapes.
Emerging markets, including Indonesia, often exhibit higher volatility, lower liquidity, and structural breaks related to regulatory changes, macroeconomic shocks, and capital flow.
These features increase the importance of accurate volatility modelling and flexible optimization techniques.
ARIMAAeGARCH models are well suited to capturing episodes of heightened volatility,whereas GAs can handle constraints arising from illiquidity, market depth, and regulatory capital rules (Werdaningtyas et al.
, 2.
The Indonesian LQ45 index, which comprises highly liquid stocks, provides natural testing grounds for such hybrid frameworks.
Existing studies have demonstrated the usefulness of ARIMAAeGARCH models in forecasting LQ45 stock prices and GAs in constructing optimal LQ45 portfolios.
Extending these studies to integrate ARIMAAeGARCH forecasts into GAAcbased optimization would be a logical next step.
For instance, instead of estimating expected returns and covariances from long run historical averages, one can use oneAcstepAcahead forecasts from ARIMAAeGARCH models as inputs to the GA fitness function.
This allows portfolio weights to adjust dynamically in response to changing risk and return conditions, potentially improving performance during periods of market stress.
Moreover.
Indonesian investors and regulators are increasingly interested in incorporating sustainability.
Shariah compliance, and other nonfinancial criteria into portfolio selection.
GAAcbased optimization is particularly suited to these multi objective and constrained problems, as it can incorporate additional criteria into the fitness function or as constraints without necessitating closed form solutions.
When combined with ARIMAAeGARCH forecasts, such a framework could support the construction of sustainable, volatility aware, and regulation compliant portfolios for institutional investors, pension funds, and Islamic financial institutions.
From an educational perspective, the hybrid ARIMAAeGARCHAeGA framework offers a rich context for teaching quantitative finance, statistics, and machine learning at Indonesian universities and other higher education institutions.
It naturally integrates concepts from probability theory, time series analysis, optimization, and programming.
Students can engage in end to end projects that involve data acquisition, exploratory analysis, model specification and estimation, algorithm design, and performance For example, a capstone project might require students to:
A Download and clean historical price data for LQ45 stocks.
A Fit ARIMAAeGARCH models to individual stock returns or to an index.
A Implement a GA to optimise portfolio weights based on forecasted returns and Backtest the resulting strategy and compare it with benchmarks such as buyAcandAchold and naive diversification.
Andreas P Peranginangin Such projects would not only teach technical skills but also encourage critical thinking about model assumptions, parameter estimation risk, and robustness.
The availability of empirical results, such as those summarized in Tables 1Ae3, provides benchmarks against which student implementations can be compared, thus facilitating formative assessment.
CONCLUSION
This study proposes and motivates a hybrid framework that integrates ARIMAAe GARCH time series models with Genetic Algorithms for portfolio optimization.
Empirical evidence from prior studies demonstrates that financial returns exhibit heavy tails and volatility clustering, justifying the use of GARCHActype models and that hybrid ARIMAAeGARCH specifications can outperform pure ARIMA and buyAcandAchold strategies in both forecasting accuracy and riskAcadjusted performance.
Parallel evidence from GAAcbased meanAevariance optimization, including applications to Indonesian LQ45 stocks, shows that evolutionary algorithms can efficiently search complex portfolio spaces and identify allocations with attractive riskAereturn tradeAcoffs.
The proposed ARIMAAeGARCHAeGA framework links these two strands by using dynamically updated forecasts of the conditional mean and variance as inputs to a GA fitness function, thus enabling portfolio decisions that are both data driven and volatility aware.
Conceptually, this integration offers a powerful approach to portfolio construction in volatile and evolving markets, with particular relevance for emerging economies such as Indonesia.
Pedagogically, it is a rich platform for teaching and learning in quantitative finance, econometrics, and machine learning.
Funding Statement e"No external funding was received for this study.
Ethical Compliance All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.
Conflict of Interest declaration The authors declare that they have no affiliations with or involvement in any organization or entity with any financial interest in the subject matter or materials discussed in this manuscript.
Acknowledgment REFERENCES