锯齿状时间序列信号预测及维护调度影响分析模型选型咨询

Hey there! Let's walk through the best models for your sawtooth time series—since your pattern is directly tied to maintenance events, we need tools that can explicitly account for those triggers, not just raw time trends. Here are my top recommendations, tailored for someone new to time series:

1. Facebook Prophet #

• This is hands down the best starting point for you. Prophet was built specifically to handle time series with external events (like your maintenance cycles) and clear recurring patterns.
• You’ll just add a custom column to your data (e.g., maintenance_flag) where you mark 1 on days maintenance occurs, and 0 otherwise. Prophet will automatically learn the sharp upward jump after maintenance, plus the gradual downward trend until the next event.
• It’s super beginner-friendly, has great built-in visualization, and lets you easily test "what-if" scenarios (like shifting maintenance dates) to see how they impact your signal—exactly what you need for analyzing maintenance scheduling effects.
• You can implement it in Python with the prophet library in just a few lines of code.

2. SARIMAX (Seasonal ARIMA with Exogenous Variables) #

• If you notice your maintenance cycles follow a fixed seasonal pattern (e.g., every 30 days), SARIMAX is a solid step up from basic ARIMA.
• The "X" in SARIMAX stands for exogenous variables—you’ll feed in that same maintenance_flag feature to let the model explicitly link maintenance events to signal spikes.
• Since you’ve already experimented with cross-correlation, this model plays nicely with that intuition: it uses auto-correlation to capture the decay trend after maintenance, while the exogenous variable fixes the gap cross-correlation couldn’t fill (accounting for the maintenance trigger itself).
• Start simple with a non-seasonal ARIMAX first, then add seasonal components if your maintenance schedule is regular. Use Python’s statsmodels library for this.

3. ETS with Exogenous Variables (ETSX) #

• Exponential Smoothing (ETS) is another beginner-friendly option that’s great for capturing trend and level changes.
• By adding your maintenance flag as an exogenous variable, you can teach the model to expect a sudden level jump every time maintenance occurs, then let the smoothing component handle the gradual decline.
• It’s less flexible than SARIMAX or Prophet, but it’s easy to understand and implement—perfect for building intuition about your data before moving to more complex models.

4. Rule-Based Regression (Quick Prototype) #

• If you want to start super simple and validate your pattern first, try splitting your data into individual maintenance cycles (from one event to the next).
• For each cycle, fit a regression model (linear or polynomial) to predict the signal based on "days since last maintenance".
• You can then stitch these predictions together using your future maintenance schedule. This approach is totally transparent, so you’ll see exactly how each maintenance event drives the signal—great for learning the basics before diving into ML models.

• Feature Engineering is Critical: Don’t just stop at a maintenance flag—add a days_since_maintenance feature too. This helps models learn the exact decay rate after each event.
• Use Time-Series Validation: Avoid random train-test splits! Use rolling window validation instead, where you train on past data and predict on the next time segment—this mimics real-world forecasting and gives you more accurate performance metrics.
• Test "What-If" Scenarios: Once you have a model, tweak your future maintenance schedule (e.g., move an event up by 5 days) and see how the predicted signal changes. This is exactly how you’ll analyze scheduling impacts.

内容的提问来源于stack exchange，提问作者Zikry Kickbuttowski