Time Series Analysis

Time Series Analysis with ARMA Model and Forecasting on Amazon Stocks

Introduction

Stock market forecasting is a challenging yet crucial task for investors, traders, and financial analysts. Amazon, one of the world’s most influential companies, experiences significant stock price fluctuations influenced by various market factors. In this study, we leverage the Autoregressive Moving Average (ARMA) model to analyze and forecast Amazon’s stock prices using time series data.

Understanding the ARMA Model

The ARMA (p, q) model is a widely used statistical model for time series analysis, combining two key components:

• Autoregressive (AR) Model (p): Captures the relationship between a variable and its past values.
• Moving Average (MA) Model (q): Incorporates dependencies between a variable and past error terms.

This model is particularly useful when analyzing financial time series data, as it helps in understanding past price behavior and forecasting future trends.

Data Collection and Preprocessing

For this study, we obtained Amazon stock price data from a financial market dataset, covering several years of daily closing prices. The preprocessing steps included:

• Handling missing values and outliers.
• Converting the dataset into a time series format.
• Checking stationarity using the Augmented Dickey-Fuller (ADF) test.
• Differencing the data if necessary to achieve stationarity.

Model Selection and Training

1. Exploratory Data Analysis (EDA): We visualized the time series to detect patterns, trends, and seasonality.
2. Parameter Selection (p, q): We used the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots to determine optimal values of p and q.
3. Model Fitting: The ARMA model was trained using historical stock data.
4. Performance Evaluation: Metrics such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) were used to assess model accuracy.

Forecasting Amazon’s Stock Prices

Once the ARMA model was trained and validated, we used it to forecast Amazon’s stock prices for a specified future period. The predictions were visualized alongside historical data to evaluate their accuracy.

Key Findings and Insights

• The ARMA model effectively captured short-term fluctuations in Amazon’s stock prices.
• The model performed well in forecasting near-future prices but had limitations in capturing long-term trends.
• Stock prices exhibited seasonal and cyclical trends, indicating that an advanced model (such as ARIMA or LSTM) could further improve forecasts.

Conclusion

Time series analysis using the ARMA model provides valuable insights into stock price behavior. While effective for short-term forecasting, integrating additional factors such as macroeconomic indicators or utilizing deep learning models can enhance predictive accuracy.

This study highlights the potential of statistical models in financial forecasting and serves as a foundation for future research in stock market analytics.

Future Work

• Extending the model to ARIMA for better trend analysis.
• Incorporating external factors such as earnings reports and market sentiment.
• Comparing ARMA with machine learning models like LSTMs for enhanced accuracy.