Time Series Analysis

1: Understanding Temporal Dependencies and Data Structure

• Begin with the definition: a time series is a sequence of observations indexed in time order (e.g., daily sales, hourly temperature).
• Understand components — trend, seasonality, cyclic behavior, and residuals.
• Learn how autocorrelation captures the relationship between past and present values.
• Visualize data to detect non-stationarity (e.g., using rolling mean/variance).

Deeper Insight: Time-based leakage is one of the most common interview traps. Never shuffle time series data — always use chronological order for training/testing splits.

2: Stationarity & Differencing

• Grasp the concept of stationarity — the statistical properties (mean, variance, covariance) should not change over time.
• Learn to test stationarity using:
  • Rolling statistics (plot moving averages)
  • ADF (Augmented Dickey-Fuller) Test
• Apply differencing (subtracting previous observations) to stabilize mean levels and remove trends.

Probing Question: “How do you handle a series that is trend-stationary but not variance-stationary?”
Be ready to discuss log transforms, Box-Cox, and power transforms for variance stabilization.

3: ACF and PACF — Model Identification Tools

• Learn Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots:
  • ACF → measures overall correlation with lagged versions.
  • PACF → isolates direct correlations, removing intermediate effects.
• Use them to identify AR (AutoRegressive) and MA (Moving Average) order parameters.

Deeper Insight: Interviewers might ask you to interpret real ACF/PACF plots — practice identifying AR(1), MA(1), ARMA(1,1) signatures. The “cut-off” behavior is the key diagnostic signal.

4: ARIMA — The Statistical Workhorse

• Understand ARIMA(p, d, q) model:
  • p: number of AR terms
  • d: degree of differencing
  • q: number of MA terms
• Learn the Box-Jenkins methodology for model identification, estimation, and validation.
• Implement an ARIMA model using statsmodels.tsa.arima.model.ARIMA.
• Evaluate with residual diagnostics — residuals should look like white noise.

Probing Question: “What happens if residuals show autocorrelation?”
Answer: “Model is underfitted — revisit ACF/PACF or increase complexity (e.g., add seasonal terms).”

5: SARIMA — Handling Seasonality

• Extend ARIMA to SARIMA(p, d, q)(P, D, Q, s):
  • Seasonal terms capture repeating cycles (like weekly or yearly patterns).
• Identify seasonality using seasonal decomposition and ACF spikes at lag multiples of s.
• Implement SARIMA via statsmodels.tsa.statespace.SARIMAX.

Deeper Insight: Interviewers love to ask “What is the difference between SARIMA and ARIMA?”
Answer: SARIMA explicitly models seasonality with periodic lags; ARIMA doesn’t.

6: Facebook Prophet — Practical Forecasting at Scale

• Understand Prophet’s additive model:
  \( y(t) = g(t) + s(t) + h(t) + \epsilon_t \)
  where \( g(t) \) is trend, \( s(t) \) is seasonality, \( h(t) \) is holiday effects.
• Learn how Prophet auto-detects changepoints and handles irregular intervals.
• Implement Prophet for business-friendly forecasting and interpret output plots.

Probing Question: “Why would you prefer Prophet over ARIMA?”
Mention Prophet’s scalability, ease of use, and robustness to missing data and outliers — ideal for production pipelines.

7: Feature Engineering for Time Series ML

• Engineer lag features (e.g., lag_1, lag_7), rolling mean/variance, and time-based encodings (day, month, quarter).
• Learn about windowing and sliding windows for supervised ML transformation.
• Avoid leakage — use only past information for each timestamp.

Deeper Insight: For large-scale ML systems, time-based feature pipelines are implemented using feature stores and backfills to maintain temporal integrity.

8: Forecast Evaluation Metrics

• Use time-series-specific metrics:
  • MAE (Mean Absolute Error)
  • RMSE (Root Mean Squared Error)
  • MAPE (Mean Absolute Percentage Error)
  • SMAPE (Symmetric MAPE)
• Understand pros and cons — MAPE fails when true values are near zero; RMSE penalizes large errors more.

Probing Question: “Why not use accuracy for forecasting?”
Because forecasting is continuous-valued, and the goal is minimizing error magnitude, not classification accuracy.

9: Scaling to Real-World Systems

• Learn about rolling retraining and time-based cross-validation (e.g., TimeSeriesSplit in scikit-learn).
• Understand concept drift — data patterns changing over time — and mitigation strategies (retrain schedules, online learning).
• Explore model monitoring for drift detection and performance degradation.

Deeper Insight: Expect interviewers to ask about deployment. For example:
“How do you ensure your time series model remains valid after a sudden event (like a pandemic or server outage)?”
Highlight adaptability: dynamic retraining, drift detection, or regime-switching models.

10: From ARIMA to Deep Learning

• Bridge from classical to modern models:
  • RNNs / LSTMs / GRUs for long temporal dependencies.
  • Temporal Convolutional Networks (TCNs) for parallelism.
  • Transformers for Time Series (Temporal Fusion Transformer) for multivariate forecasting.
• Understand trade-offs: interpretability (ARIMA) vs. representation power (LSTM).

Probing Question: “When would you still prefer ARIMA over LSTM?”
When data is small, interpretability is required, or training compute is constrained.