Build a Time Series Forecasting Model with Trend and Seasonality Analysis

You are a data scientist specializing in time series analysis and forecasting. I need you to build a comprehensive forecasting model for the following business metric. **Forecasting Target:** - **Metric to Forecast:** [METRIC, e.g., monthly revenue, daily website traffic, weekly inventory demand] - **Historical Data Range:** [START_DATE] to [END_DATE] ([NUM_PERIODS] data points) - **Forecast Horizon:** [HORIZON, e.g., next 3 months, next 90 days, next 12 weeks] - **Data Granularity:** [GRANULARITY, e.g., daily, weekly, monthly] - **Known Patterns:** [PATTERNS, e.g., strong weekly seasonality, holiday spikes in December, upward growth trend] - **External Factors:** [EXTERNAL_FACTORS, e.g., marketing spend, weather data, competitor pricing — or 'none'] - **Business Use Case:** [USE_CASE, e.g., budget planning, inventory management, capacity planning] Please provide the following comprehensive analysis: 1. **Exploratory Data Analysis (EDA):** Outline the EDA steps to perform — trend visualization, seasonal decomposition (additive vs. multiplicative), stationarity testing (ADF test, KPSS test), and autocorrelation analysis (ACF/PACF plots). Describe what to look for at each step. 2. **Data Preprocessing:** Detail the preprocessing pipeline including handling missing values (interpolation strategies), outlier detection and treatment, and any necessary transformations (log, differencing, Box-Cox). 3. **Model Selection:** Compare at least 4 candidate models appropriate for this data: - Classical statistical (ARIMA/SARIMA, Exponential Smoothing/ETS) - Modern ML-based (Prophet, XGBoost with lag features) - Deep learning if applicable (LSTM, N-BEATS) For each, explain pros/cons and suitability for this specific use case. 4. **Feature Engineering:** If using ML models, define lag features, rolling statistics, calendar features (day of week, holidays, month), and how to incorporate [EXTERNAL_FACTORS]. 5. **Validation Strategy:** Describe the time series cross-validation approach (expanding window vs. sliding window), the number of folds, and why random splits are inappropriate. 6. **Evaluation Metrics:** Calculate and interpret MAPE, RMSE, MAE, and SMAPE. Define acceptable error thresholds for [USE_CASE]. 7. **Implementation Code:** Provide Python code using [LIBRARY, e.g., statsmodels, Prophet, scikit-learn] that trains the best model and generates forecasts with prediction intervals. 8. **Forecast Output:** Format predictions as a table with date, point forecast, lower bound, and upper bound at [CONFIDENCE_LEVEL]% confidence. Include visualization recommendations and a model monitoring/retraining schedule.