ARIMA (AutoRegressive Integrated Moving Average)

ARIMA is a classical statistical model designed for time series forecasting. It models a time series based on its own past values (autoregression), the differencing of data points to make the series stationary (integration), and past forecast errors (moving average).

The model is typically denoted as ARIMA(p, d, q), where:

• p: number of autoregressive terms, capturing dependence on past values
• d: number of differencing steps needed to make the series stationary
• q: number of lagged forecast errors in the prediction equation

ARIMA works well for linear patterns and stationary time series and has been widely used in economics and finance for decades. Model parameters are usually chosen using statistical criteria such as the Akaike Information Criterion (AIC).

LSTM (Long Short-Term Memory Networks)

LSTM is a type of recurrent neural network (RNN) specially designed to capture long-term dependencies in sequential data. Unlike classical models, LSTM can model complex nonlinear relationships and patterns in time series.

LSTMs use special memory cells with gates to control the flow of information, enabling them to remember important context over long sequences while ignoring irrelevant data. This makes them particularly powerful for stock price prediction where patterns can be complex and non-linear.

LSTM models require tuning architecture parameters (number of layers, neurons) and training with optimization algorithms like gradient descent on large datasets.

Collecting Data

The foundation of any forecasting system is high-quality data. For stock prices, we collect historical data (e.g., daily open, high, low, close prices, and trading volume) from sources like Yahoo Finance. This data forms a time series—a sequence of values recorded over time. For example, we might gather five years of daily prices for a stock like Apple (AAPL) to identify trends and patterns.

Data collection involves handling issues like missing values (e.g., no data on holidays) or stock splits, which can distort prices. We also ensure the data is consistent, with the same time intervals (e.g., daily) across all stocks. This step is critical because inaccurate or incomplete data can lead to poor predictions.

Feature Engineering

Raw stock prices provide a starting point, but we need to create additional “features” to help our models make better predictions. Features are like clues that reveal more about the market. Common features include:

- Technical Indicators: The Simple Moving Average (SMA) averages prices over a period (e.g., 20 days) to smooth out fluctuations and reveal trends. The Relative Strength Index (RSI) measures whether a stock is overbought (too high) or oversold (too low), helping predict reversals.

- Volatility: We calculate the standard deviation of prices over a window (e.g., 20 days) to measure how much the stock fluctuates, which can indicate risk.

- Lagged Values: Past prices (e.g., yesterday’s or last week’s price) are used as inputs, especially for ARIMA and LSTM, to capture temporal relationships.

These features are normalized (scaled to a standard range, like 0 to 1) to ensure compatibility with models, especially LSTMs, which are sensitive to data scales. Feature engineering is crucial because it provides the context needed for accurate forecasts.

Model Training & Testing

With data and features ready, we train our ARIMA and LSTM models. Training involves feeding historical data to the model so it can learn patterns. For ARIMA, we select the best p, d, q orders using statistical tests like the Akaike Information Criterion (AIC). For LSTMs, we define the network architecture (e.g., number of layers and neurons) and train it using optimization techniques like gradient descent.

To test the models, we use walk-forward validation. We train on a portion of the data (e.g., 2020–2023), predict a short period (e.g., one month in 2024), and compare the predictions to actual prices. We then slide the training window forward and repeat. This mimics real-world forecasting, where we don’t know future prices. We evaluate models using metrics like Mean Absolute Error (MAE) to measure accuracy.

Deploying the Model

The final step is deploying the models in an interactive app (like this one!). Users can select a stock, choose ARIMA or LSTM, and specify a forecast horizon (e.g., 30 days). The app displays predictions as charts, with confidence intervals showing the range of likely outcomes. This makes the system accessible, allowing you to explore how different models perform and visualize market trends.

Deployment also involves monitoring model performance over time. Markets change, so models may need retraining to stay accurate. The app provides tools to compare predictions, analyze errors, and understand model strengths and weaknesses.