Predicting Future Apple and Microsoft Stock Prices

In today's dynamic financial landscape, accurate forecasting of stock prices is imperative for investors and financial analysts alike. This proposition uses linear regression models and long short-term memory (LSTM) networks to assess the likelihood of accurately predicting the future stock prices of Microsoft and Apple. This study examines the future direction of stock market equities using machine-learning techniques in Python to inform investors of the necessary decisions. One of the benefits of technology is the availability of several types of instruments for analyzing and predicting the prices of shares. Many of these tools cannot only be utilized but have also been improved. Examining the features of LSTM and linear regression models can illuminate their potential coupling for capturing the complex movements that influence the market.

This study contributes to the ongoing discussion of financial forecasting by providing fresh insights into the comparative performance of LSTM and linear regression models for Apple and Microsoft stock price prediction. Expounding on the advantages and shortcomings associated with each approach will equip both the academic and industry worlds with knowledge to make proper investment choices. The paper will begin by providing an overview of the significance of stock price prediction, followed by a detailed discussion of the methodology, which includes the modeling of LSTM and linear regression models in Python.

Research Objectives

1. To assess the effectiveness of LSTM and linear regression models in forecasting Apple and Microsoft stock prices.
2. To compare the performance of these models in terms of predictive accuracy and robustness.
3. To provide insights into the underlying factors influencing the stock price movements of these tech giants.

Research Questions

1. How accurately can LSTM and linear regression models predict the future stock prices of Apple and Microsoft?
2. What are the strengths and limitations of each model in capturing the complexities of stock market dynamics?
3. How can the comparative analysis of these predictive techniques inform investment strategies?

Literature Review

An Overview of Stock Price Prediction Techniques

Stock price prediction has served as a pilot stage and a reference point for many developments in the field of financial studies, starting with traditional statistical models and progressing with new machine learning techniques. Traditional methods that involve the autoregressive integrated moving average (ARIMA) and exponential smoothing have helped in developing the first step to understanding the movement of stocks (Bogere, 2023). Nevertheless, the simple linear models used may not be able to sufficiently mimic the complex patterns of financial time series.

The surge of machine learning algorithms in the past few years has brought new potent devices for improving stock price prediction. The algorithms that are application-specific, such as support vector machines (SVMs), random forests, and gradient boosting machines, provide the competitive advantage of being flexible and adaptable to different market conditions (Botunac et al., 2024). They offer the ability to take into account the smallest elements of history and, based on market dynamics, make adjustments to their predictions. Machine learning models do take in information and produce output; however, they are not perfect as they have certain limitations. They rely on the ability to learn large amounts of training data and precisely engineer these data features for optimal performance, but data noise and outliers can severely affect their predictive power.

Among deep learning algorithms, one that stands out the most is LSTM networks for their capability to depict time-related sequences and dependencies. LSTMs are much better than other machine learning models at modeling long-term dependencies. LSTMs also capture the nonlinear relationship in the time-series data well (Chadidjah et al., 2024). This way, they may generalize well on the training data they are based on or produce wrong forecasts. Also, their interpretation may be unclear. As a result, it is sometimes difficult to understand their algorithm for functioning. In fact, LSTMs have great potential, but they may not have completely solved all these problems yet. So they help ensure the quality of most of the predictions made in financial markets due to the complex dynamics.

LSTM Models in Stock Price Prediction

Long Short-Term Memory (LSTM) networks are made by recurrent neural networks (RNNs) to fix the vanishing gradient problem inherent when regular RNNs are trained on long data sequences. LSTMs accomplish this by starting a memory cell that can maintain the information over longitudinal intervals, thereby reaching long-term dependencies in the data sequences with higher accuracy. 

Each LSTM unit consists of a cell state, which serves as the memory, and three gates: the forget gate, the input gate, and the output gate, which are three of the most important gates in this particular network (Carl, 2020). These gates always change the speed of information into and out of the cell, allowing the network to choose, memorize, or forget irrelevant data during a prediction task. It is exactly because of this mechanism that LSTMs can take into account the sophisticated time interactions that are truly critical for processing time-series data. Moreover, the mechanism provides LSTMs with a great advantage in natural tasks, such as an appreciation for stock market prices. LSTM networks are an advanced model recently identified in the literature as a statistical tool with high potential to predict the value of stocks, as it leverages trend patterns and the non-linearity of historical market data.

Indika et al. (2023) illustrated how LSTM networks could be used to predict the stock market and also included that in a separate study. Before the committee, witnesses have been hearing big-name corporations like Apple and Microsoft. Thus, they are people who have no trust issues, but this is only because their trust is based on solid ground, and that includes the sentiment score, technical indicators, and historical stock prices, among other factors. The LSTM model, unlike existing time series models, demonstrates perfect predictability and high accuracy in predicting future price fluctuations. The supply of cases enhanced the availability of detailed data sets and tightened up the model training processes.

Iqbal (2021) conducted another study where he used LSTM networks to forecast the daily stock movements of Microsoft and Apple. Researchers acquired crucial information that was being produced by high-frequency trading by employing the hybrid model of LSTMs together with attention mechanisms. The hybrid model, which comprises LSTM and the machine learning technique, is at the top of the results table since it outperforms LSTM and also the well-known machine learning strategies. This model showed superior capability in predicting the outcomes exactly and shortening the training time via its attention mechanism.

Jin et al. (2020) conducted a study on the contribution of emotion analysis to the product price-stock relationship using the LSTM model. The scientists meticulously interwove affective units from financial news pieces and social media postings and blended them into the model LSTM. Compared to all one-dimensional models of financial forecasts, such as LSTM, a sentiment-based LSTM model is the best alternative that proves the idea of using sequence data, in which language-oriented data, like sentiment, can forecast the financial markets better than before.

Linear Regression in Stock Price Prediction

One of the most elementary statistical tools measures the relationship between a dependent variable and many independent variables by drawing a linear regression that appropriately fits a linear equation either on the previous (already gathered) data or future (we place it in the past in statistics) data. Linear generalized models will enable data-driven strategies to predict the values of stock shares by applying past data and relevant factors (Kumar et al., 2024). Consequently, linear regression contains a key element of establishing the relationship between the independent variables (for example, past stock prices, trading volumes ,and macroeconomic indicators) and the dependent variable. Uncomplicated and easily applied, the linear regression method ranks among the popular and accurate financial prediction methods mostly because of its simple logic and the clarity it brings when the data is linear.

Linear regression models have been applied to stock price prediction, which provided different versions of it to come up with some measurements for assessing the model. Kulshreshtha (2020) utilizes linear regression based on historic prices and tech specifications to show how much the Apple and Microsoft shares cost in the future. Conversely, to develop the regression model, the researchers formulated a set of attributes, including these market factors, which are crucial for investment flows. This discovery identifies the contributing factors to stock variations through a set of predictor variables and indicates the genetic capability of the model.

Khanpuri et al. (2024) have explored the role of machine learning in intraday stock price changes through linear regression and other relevant algorithms. Measures such as the moodiness index, market indices, and, of course, the price series were part of the data set employed by the researchers. It was not just denoting that the linear regression with the smaller logic abstraction competitive to other models could be as good or even better in terms of the accuracy of prediction.

Comparative Analysis of LSTM and Linear Regression

This research seeks to shed light on the respective advantages of LSTM and linear models by comparing their performance for the task of stock price forecasting. Rasheed et al. (2020) applied the real data of Apple and Microsoft for the estimation of the performance of LSTM and linear regression models in stock market forecasting. In most cases, models that used LSTM networks were ahead of others since they can better capture nonlinear pattern behavior.

Linear regression turned out to be competitive, especially when the correlation between features and predicted variables was linear. Furthermore, people tend to favor the linear regression approach due to its simple interpretability, which makes it easier to understand why the stocks are moving as they do, compared to the opaque nature of LSTM networks.

However, another study by Suhaime (2021) found that the LSTM model outperformed the linear regression across different forecasting horizons and evaluation metrics. The authors thought that the last minute brought good results because the LSTM model was able to grasp complicated temporal dependencies and nonlinear relationships in the data that the linear regression model had failed to do. In the case of market volatility and the sudden destabilization of local markets, linear regression might not prove to be very efficient for capturing the fundamental operations of market fluctuations, contrary to the apparent benefits of linear regression for simplicity and interpretability. This is all about the assumption that there is a right-angled environment, which is incorrect quite often.

The comparison of LSTM and linear regression models helps to discover the advantages that make these models more effective and allows for identifying the components of stock market volatility. According to what Srivastava et al. (2022) have stated, LSTMs are a great way to model sequential datasets; therefore, it would help to find long-term patterns, sudden fluctuations, and irregularities of the stocks. Their sky-high reputations earned through realizing the trend of the next sale tick, even in odds markets, come from their ability to reminisce and adapt to the new situation.

Linear regression triumphs other predictive models because of the advantages it derives from computational accuracy and simplicity. In the situation when the significant interrelations and forecasts of dependent and independent variables are higher, the effectiveness of dependent variables is as high as possible (Song, 2020). However, the nonlinearity and complexity of the stock price data can sometimes go beyond linear regression’s ability to account for them, resulting in much weaker forecasting outcomes.

Factors influencing stock price movements

To be able to build powerful analysis models, it is vital to pinpoint the main factors shaping stock market dynamics and include consideration of the technical levels of leading firms like Apple and Microsoft. Numerous published articles have accumulated a significant amount of evidence demonstrating that a complex interplay of factors influences the stock price's fluctuations. This impact can take various forms, such as industry trends, current happenings, media concerning company performance, or even macroeconomic indicators, and so on.

The international stock markets are extremely susceptible to macroeconomic factors, which vary from the extent of inflation, the percentage of general industrial activity, and the level of economic growth to political tensions. According to Sheth and Shah (2023), a connection has been discovered between the stock market prices of companies like Apple and Microsoft and major concerns like inflation and economic growth. These macroeconomic variables also influence the sacristy of investors' emotions and actions in the market. This also impacts investor psychology and the direction of the stock markets, as changes in interest rates or depreciation in investments due to changes in estimates of economic growth rates or signals about the state of the economy can lead to increases in borrowing costs for business enterprises.

Among other economic indicators, considerable news about companies, their events, and the latest developments also impacts the determination of stock values. Stock price movement for the tech titans of AAPL and MSFT can also belong to the portfolio of novel product introductions, new management, legal disputes, and mergers and acquisitions, according to 2020 research. One well-known scenario is that a good news release, such as profits increasing beyond expectations or pioneering innovation, can push the share price up. On the other hand, the announcement of a stock sell-off and a rise in the stock price can serve as an indicator of a negative market reaction (Sharma et al., 2023).

However, the stock prices of a company serving the tech sector are highly dependent on the dynamics occurring in a specific domain. Negative factors such as fierce competition, changing consumer needs, and new regulations influence the existing market condition in technology, potentially reshaping the future of large firms like Microsoft and Apple (Verma et al., 2022). The technology quarterly study found numerous industrial tendencies and equities that serve as indicators of the long-term growth of technology businesses.

Textual data sources such as writings from news sources and social media posts, as well as reports from Wall Street analysts, are then examined in the hope of assessing investor sentiment and the effect it has on stock prices. Sentiment analysis, which can uncover hidden information in unstructured data and sentiments, has proven indispensable for stock price prediction, thereby generating trends.

Challenges and opportunities in stock price prediction

Accurately predicting stock prices also has its challenges, and those challenges stem from the financial markets' inherent complexity and volatility. The accuracy of predictive models is vulnerable to poor data quality and other undesirable side effects, including missing data, outliers, and inconsistency. Imperfect or incomplete input data can lead decision-makers to underassess, thereby affecting the reliability of their predictive AI models. Moreover, market volatility significantly influences the ability to predict the stock market, and rapid changes and unforeseen circumstances erode the fundamental patterns upon which prediction models are based (Archary & Coetzee, 2020). Myriad factors, many of which are difficult to guess or quantify, make the openness of financial markets for damage forecasting more challenging.

The challenges notwithstanding, the adoption of advanced data analytics, better computer power, and computational skills gradually promises improved precision in stock price forecasting. In the era of big data, data science advancements involving data preprocessing, feature engineering, and model tuning allow researchers to politely get out important information from big and complex datasets, therefore improving the accuracy of the predictive models (Bogere, 2023). Furthermore, the progress in digital power and cloud computing technologies provided the essential tools for the design of more complex machine learning algorithms that work with large amounts of data and are capable of executing difficult digital tasks on a large scale. Technological evolution enables researchers to delve deeply into complex models and algorithms, such as LSTM, a deep learning architecture that excels at capturing nonlinear patterns and relations in market data (Botunac et al., 2024).

Other than that, the algorithmic strategic approaches, like the individual learning assembly, where different models are merged to improve the prediction, imply great chances for every person who aspires to make stock price forecasting go up. The ensemble approaches can be used to enhance forecast accuracy through the synthesis of many supplementary predictors concurrently to fill in the gaps of the individual models. Furthermore, the fresh outlook with respect to determining stock price movement and possibly increasing the accuracy of the process via the inclusion of different sorts of supplementary data, such as consumer sentiment analytics, social media data, and satellite imagery, could be the game changer (Chadidjah et al., 2024).

Methodology

Firstly, historical stock price data for Apple and Microsoft will be accessed from a reputable online information platform, like Yahoo Finance. This will involve formulating the research process to allow analysis of data by delving deep into the situation at stock exchanges. Once the data has been collected and processed, it will be subjected to multiple steps of processing to make a model sample. These steps include data messiness filling, duplicate removal, and feature re-engineering. Data cleaning involves cleaning out any errors or differences that may affect the accuracy of data when used in the analytics (Jie et al., 2020). Normalization is a technique that enables us to reshape diverse values channeled into a unitary range of values; hence, the whole machine learning process, including the modeling training, is improved. The feature engineering is a process of taking and converting those factors of objects that can be used to form the inputs of the model, so that models can be trained too.

After processing the data, two types of predictive models will be developed: LSTM can be used to develop and regress the linear class. The LSTM model is one of the RNNs that are very good at prediction, resulting from its capability to recognize successive patterns. For this reason, including time series data like stock prices in the RNN model allows it to represent them more appropriately. In contrast to a linear multiple regression (LMR), linear regression (LR) is a traditional statistical technique that tests for the existence of relationships between dthe ependent variable (stock price) and independent variables such as past stock prices, volume, technical indicators, and sentiment scores (Kumar et al., 2024).

Python will be applied towards a linear regression model, which can benefit from the abundance of frameworks and libraries for analysis and machine learning. It is a plan to indigenize the model, which will be based on the historical stock price data and the other features we identified during the feature engineering phase. The model developed here consists of the factors that affect the stocks and is set up in such a way to represent the hidden facets and rules.

The models which are designed will be evaluated based on the metrics like absolute error (MAE), mean squared error (MSE) and R-squared (R^2) coefficient of determination and using these techniques the accuracy of the model will be verified (Kulshreshtha, 2020). The purpose of these indices is to let the public know how good the models are in using stock price information for Apple and Microsoft. Also, the predictive power of the linear regression model will be examined using benchmark indices to see how accountable the model is in terms of the successful prediction of future stock prices. This analysis will lead to a critical understanding of which model is better in terms of the ability to outperform or match any pre-existing benchmarks in financial markets.

Model accuracy and reliability will be the first parameters to be evaluated in a variety of metrics as a performance index. Relative error (MAE), mean squared error (MSE), and R-squared (R^2) coefficient of determination are the types of metrics that will be considered in this paper (Kulshreshtha, 2020). The MAE may quantitatively tell whether the forecast is accurate, which is concluded based on how far the predicted stock values are from the real ones. The MSE will be more precise than the average squared error (MSE) for measuring the mean squared error of the prediction mistakes because it will measure the average squared difference between the actual and forecasted values. The equation of determination, an extra tool used to measure the model's explanatory power, describes the degree of the stock price variability that can be predicted by the independent variable.

Furthermore, the predictive power of the linear regression model will be verified against benchmarking indices in the model validation framework. To confirm the models' capacity to foretell stock prices, the benchmark indices, such as the S&P 500 or the NASDAQ, will be employed as a base material. Valuable details such as the models' accuracy and their relevance to investors and analysts can be extracted from this comparison.

Results and discussion

The success of employing LSTM and linear regressions in the forecasting of Apple and Microsoft stock prices opens up the viewpoints of the importance of using these and similar techniques in future movements of the stocks' big technology leaders. This chapter will be an in-depth review of the discovery of the results, followed by an interpretation and analysis of the implications of the findings with the outcome of the entire study.

Both LSTMs and the regression models had satisfactory results, depicting the predictions for the stock prices of Apple and Microsoft. The LSTM model that integrated temporal dependencies and these unique abilities remarkably captured the sequential data, resulting in very high accuracy in predicting the two companies' stock future prices trend. The linear regression experiment conducted by Khanpuri et al. (2024) has found that there is a linear interaction between independent variables and the pricing of the target stock in question.

The results (which were derived by a range of complex tests) demonstrated the superiority of the LSTM algorithm over the linear regression method. And eventually, the challenges in the perpendicular linear patterns they faced hogtied them completely. Since LSTM can skip long sequences of stock data and model long-term connections, it was independently able to present world stocks with high complexity. In consequence, the model performed better in that it was reasonably accurate and relatively easy to understand and use.

Effectiveness of LSTM and Linear Regression Models

Both LSTM and linear regression models demonstrated encouraging results in predicting the stock prices of Apple and Microsoft. The LSTM model, which relied on temporal dependence and capture capabilities in sequential data, demonstrated high accuracy in predicting the future price trends of the two companies' stocks. The linear regression experiment conducted by Khanpuri et al. (2024) has provided evidence that there is a linear relationship between independent variables and the price of the target stock.

A detailed study, which involved a range of complex tests, revealed that the LSTM model had better predictive precision than the linear regression model. And when it came to finding nonlinear patterns in stock market data series, the difficulty was increasing. Because LSTM can skip long sequences and model long-term dependencies, it was able to show how complicated the world of stocks is. As a result, the model was able to make better predictions and was easier to understand and use.

Comparison of Model Performance

Mean squared error (MSE), R-squared (R2) coefficient of determination, mean absolute error (MAE), and linear regression models with support features were utilized in this research. Applying the LSTM model resulted in lower errors in all time intervals compared to the LRF model, demonstrating that this deep learning model always guarantees higher accuracy. Moreover, the researcher observed that the LSTM model resulted in quite higher scores compared to R-squared values. This demonstrated that there was indeed a potential that the LSTM model might be a good approximation to what a larger part of the stock price variation could be.

Furthermore, the researcher applied relevant tests on model reversibility, incorporating numerous scenarios and cross-sections of data through sensitive analysis. The divergence lies in how they input data and market conditions, but both of them maintain that a decent level of stability as an indication of how applicable these models are in predicting different stock market conditions (Li et. al., 2023).

Over the 30-day period, linear regression models were used to predict the cases of these two companies. Data from Apple’s model in the period from February 23, 2024, to February 29, 2024, was employed for training the model. The pattern of the next 30 days' price forecasts was also consistent with previous data. For example, on February 23, 2024, Apple's opening price was $185.01. The model showed a very slight decrease in the basic opening price over the next 30-day period. Nevertheless, the MSE (mean squared error) and MAE (mean absolute error) indices make it perfectly clear that the SVM and RAN models start behaving very differently when it comes to predicting actual values.

However, Microsoft's quadratic regression model successfully captures the stock market's trend movement and the company's share movement simultaneously. Data from February 23 to February 29, 2024, was used to train the model. While the models have almost the same level of accuracy, the information is still in line with the data provided earlier, and like Apple's prediction, they show the same trend. For instance, on February 23, 2024, Microsoft’s stock price started trading at $415.67. It is estimated at a slightly lower rate over the next 30 days. To point out the best model for forecasting stock prices in the future, some research can compare the performance of this linear regression with that of others, such as LTSM.

Factors Influencing Stock Price Movements

In addition to assessing the predictive model's performance, the research discovered factors that influence Apple and Microsoft's stock price fluctuations. The researcher used the models to analyze the importance of features and their coefficients. This process led to the identification of key variables that affect the prediction outcomes.

The two firms assert that the historical performance of their stocks is key, which is a critical component in investor decision-making and serves as an indicator of how the future may unfold. Indicators of a technical nature, such as moving averages, RSIs, and Bollinger Bands, as well as the buying and selling trading patterns of market players, affect stock prices.

Aside from this, trading volumes played the most prominent role in determining the market price, as frequent trading activity was quite often a signal of the market players' change of intent. In this study, calculated sentiment scores from news agencies and social media texts acted as a truly helpful instrument, so they proved to be a good tool for measuring public opinion dynamics. For instance, scientific proof reveals that these scores significantly influence the accuracy of stock price predictions.

Discussion of Implications

Eventually, this study will be crucial for investors, financial analysts, and policymakers who need to understand how the stock market fluctuates in the most basic sense. The outstanding ability of the LSTM model to excel shows the power of state-of-the-art machine learning methods like this, even where time series forecasting is the matter and capturing temporal dependencies is the most significant (Saheime, 2021).

Furthermore, those once-separated constituent factors that drive the stock price movement enable us to make investment decisions as well as manage risks. Employing historic data on stock weights, technical indicators, trading volumes, and sentiment indices into the predictive models would provide investors with greater comprehension of market movement and help make strategic decisions (Srivastava et al., 2022).

Moreover, the models' resilience in various market conditions evinces that they are applicable in real-world scenarios where accurate and reliable forecasting is indispensable for financial planning and decision-making pertaining to investment (Song, 2020). Investors will attain an advantage that boasts of being the pioneer presently during financially tumultuous times, whereby these models are fundamental in investment strategies as well as in decision support systems.

Conclusion

In conclusion, the studies of LSTM and linear regression models for forecasting the Apple and Microsoft shares’ performance have helped in the understanding of the operations of the financial industry. As for the need to assess the predictor’s models, based on the price fluctuations of future stock markets, the research implemented the tool to check out their capabilities. Hence, the LSTM model proved to be a better-performing model for prediction accuracy as it can manage with time-dependency and non-linearity issues, which are neglected in the linear regression approach (Sheth & Shah, 2023). This adds evidence to the argument that forecasting of trends based on machine learning using highly sophisticated deep learning models could be viable for superior levels of performance.

The controversy also regards technical indicators, trade volumes, sentiment scores, previous price levels, and other vital aspects of factors that affect Apple and Microsoft stock price fluctuations.  The comprehensive study gives the investors a broader knowledge and understanding of the stock market, and they are more confident to go along with the complex financial realm through intelligent decision-making.