Bayesian Hierarchical Modeling for Stock Price Forecasting: Evidence from Apple Inc. (AAPL)
DOI:
https://doi.org/10.61173/d4k3c074Keywords:
Bayesian hierarchical modeling, stochastic volatility, stock return forecasting, predictive densities, uncertainty quantificationAbstract
Stock price forecasting has long been a significant research topic in finance, and the stock market has grown increasingly popular in recent years. As a popular saying goes, “even the aunts in the vegetable market are speculating on stocks.” In a rapidly changing market environment, investors need more reliable forecasting tools to assist in decision-making. Traditional prediction methods often struggle to cope with the complexity and uncertainty of the market, whereas Bayesian statistical methods offer new possibilities in this field due to their unique probabilistic framework. This study takes Apple (AAPL) as an example to explore the application of Bayesian methods in stock price prediction. We have collected the company’s historical transaction data from 2015 to 2023, including key indicators such as daily opening price, closing price and trading volume. By establishing a Bayesian hierarchical model, we try to capture the inherent laws of stock price fluctuations. The study found that the Bayesian method can better deal with uncertainty in the stock market.
References
[1] Carriero, A., Clark, T. E., & Marcellino, M. G. (2019). Large Dean&Francis ISSN 2959-6157 Bayesian vector autoregressions with stochastic volatility and non-conjugate priors. Journal of Business & Economic Statistics, 37(1), 75–90. https://doi.org/10.1080/07350015.2019.1577769
[2] Gu, S., Kelly, B., & Xiu, D. (2020). Empirical asset pricing via machine learning. The Review of Financial Studies, 33(5), 2223–2273. https://doi.org/10.1093/rfs/hhaa009
[3] Jacquier, E., Polson, N. G., & Rossi, P. E. (1994). Bayesian analysis of stochastic volatility models. Journal of Business & Economic Statistics, 12(4), 371–389. https://doi.org/10.1080/07 350015.1994.10524554
[4] Kim, S., Shephard, N., & Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. The Review of Economic Studies, 65(3), 361–393. https://doi.org/10.1111/1467-937X.00046
[5] Koop, G., & Korobilis, D. (2010). Bayesian multivariate time series methods for empirical macroeconomics. Foundations and Trends® in Econometrics, 3(4), 267–358. https://doi. org/10.1561/0800000013
[6] Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1, 206–215. https://doi.org/10.1038/s42256-019-0048-x
[7] Apple Inc. (n.d.). Investor relations — SEC filings and financials. Retrieved September 28, 2025, from https://investor. apple.com/
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