Time_Series_Project

⏱️ Time Series Forecasting of Financial Asset Low Prices

📅 Date: August 2024
📈 Domain: Financial Analytics | Time Series Forecasting
🧰 Tools: R, TTR, forecast, stats, ggplot2
📂 Dataset: Shares (Stock Excel Sheet “A”)
🖱️ Portfolio: GitHub Repo Link

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📌 Project Overview

This project models and forecasts low stock prices of a financial asset using various statistical time series models including Holt-Winters, ARIMA, Auto-ARIMA, and SARIMA. It uses residual diagnostics, error metrics (RMSE, MAPE), and ACF/Ljung-Box tests to validate model assumptions and forecast accuracy.

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🎯 Objectives

• Transform raw stock data into a usable time series object
• Compare Holt-Winters, ARIMA, Auto ARIMA, and SARIMA
• Evaluate forecasts using accuracy metrics
• Validate models with residual diagnostics
• Recommend the best model based on robustness and predictive accuracy

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🧱 Step-by-Step Process

1️⃣ Data Loading & Preparation

• Installed required packages
• Loaded stock price dataset
• Selected Date and Low columns
• Converted date formats and structured into a time series object

📸 ![Load and Structure Time Series](Photo/your_structure_screenshot.png)

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2️⃣ Visualization of Raw Series

• Created line plots of raw Low prices
• Applied 150-day SMA (Simple Moving Average) using TTR
• Overlaid SMA on raw series for trend clarity

📸 ![SMA and Low Prices](Photo/your_sma_plot.png)

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🔁 Holt-Winters Smoothing

• Applied Holt-Winters method to capture level and trend
• Forecasted for 90 days
• Calculated forecast accuracy (RMSE, MAPE)
• Validated residuals using ACF & Ljung-Box test

📸 ![HW Forecast](Photo/holt_winters_forecast.png)
📸 ![HW Residual ACF](Photo/hw_residuals_acf.png)

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⚙️ ARIMA Modeling

• Differenced series to establish stationarity
• Confirmed with p-values (< 0.05 after differencing)
• Analyzed ACF and PACF plots to identify AR and MA terms
• Fitted ARIMA(1,1,1) model with good residual diagnostics

📸 ![ARIMA Diagnostics](Photo/arima_diagnostics.png)
📸 ![ARIMA Forecast](Photo/arima_forecast.png)

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⚡ AUTO ARIMA

• Used auto.arima() to optimize model via AIC/BIC
• Fitted ARIMA(2,1,2) with drift
• Forecasted 90 steps ahead
• Residuals showed mild autocorrelation, moderate fit

📸 ![Auto ARIMA Fit](Photo/auto_arima_fit.png)
📸 ![Auto ARIMA Residuals](Photo/auto_arima_residuals.png)

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❄️ SARIMA (Seasonal ARIMA)

• Used SARIMA(2,1,2) to account for seasonality
• Achieved lowest AIC/BIC and best forecast alignment
• Residuals passed randomness checks, confirming robust fit

📸 ![SARIMA Forecast](Photo/sarima_forecast.png)
📸 ![SARIMA Residuals](Photo/sarima_residuals.png)

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📊 Model Comparison

Model	RMSE	MAPE	Strengths
Holt-Winters	Medium	Medium	Simplicity, short-term patterns
ARIMA(1,1,1)	Low	Low	Captures trend well
Auto ARIMA	Medium	Medium	Automated, moderate fit
SARIMA	Low	Low	Best overall fit and seasonal control

SARIMA outperformed others in forecast reliability and residual independence.

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✅ Conclusion

This project demonstrates a complete time series forecasting workflow, from raw data to final model selection. SARIMA showed the most reliable and accurate results, while ARIMA and Holt-Winters offered complementary insights.

🧠 Future Work: Integrate ML-based models (e.g., XGBoost, LSTM) for improved long-range forecasting.

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🔗 Repository & Assets

• 📁 GitHub Repository
• 🖼️ Visualizations stored in /Photo/ folder