Time Series Fundamentals
What is a time series, and how does it fundamentally differ from cross-sectional data?
What is time series forecasting, and can you give an example of a real-world application?
Explain autocorrelation and its significance in time series analysis.
What is time series analysis?
Why does the choice of frequency or granularity of a series matter for modeling and forecasting?
How would you read a time plot, seasonal-subseries plot, and lag plot to understand a series before modeling?
How are time series problems different from other regression problems?
What is cross-correlation and when would you use it?
Stationarity & Unit Roots
What is stationarity in a time series, and why is it a crucial assumption for many classical forecasting models?
How do you check for stationarity in a time series, both visually and statistically?
What is differencing, why does it help in achieving stationarity, and when would you use seasonal differencing?
What is white noise, how is it different from a stationary process, and why are residuals expected to be white noise?
What is the difference between strict (strong) stationarity and weak (covariance) stationarity, and which conditions on the mean, variance, and autocovariance define the weak form?
What is a random walk, and how do a random walk with drift and one without differ in behavior?
What are the costs and symptoms of over-differencing a time series?
How would you combine the results of the ADF and KPSS tests, given that they have opposite null hypotheses?
Explain the concept of a unit root and its relation to non-stationarity.
Explain the null and alternative hypotheses for the Augmented Dickey-Fuller (ADF) and KPSS tests, and how you would interpret their results.
What is the difference between a trend-stationary and a difference-stationary series, and why is it a mistake to detrend one when you should difference the other?
How does the Phillips-Perron test differ from the ADF test, and when might you prefer it?
What do the stationarity and invertibility conditions mean for AR and MA models, and why do they matter?
Components Decomposition & Seasonality
Explain the concept of trend in time series analysis.
Walk me through the steps of classical time series decomposition.
What is the difference between a cycle and seasonality in a time series?
What is seasonality in time series analysis, and how do you detect and handle it?
Explain the different components of a time series (trend, seasonality, cycle, irregular) and how they are distinguished.
What is the difference between additive and multiplicative decomposition models, and when would you use each?
What is STL decomposition, and what robustness and flexibility advantages does it have over classical decomposition?
What is seasonal adjustment, and why are official statistics often published in seasonally adjusted form?
How do you decide whether a series follows an additive or a multiplicative seasonal structure?
How do you handle a series with multiple or nested seasonalities, such as daily data with both weekly and yearly patterns?
What is a periodogram, and how does the Fourier/spectral view help identify seasonality?
How would you model daily power consumption data exhibiting strong weekly and yearly seasonal patterns along with long-term growth, and which model would be most suitable?
Arima & Related Models
What is ARIMA, and what do the p, d, and q parameters represent?
What are the key assumptions of the ARIMA model?
How do you determine the appropriate p, d, and q values for an ARIMA model?
Given a time series with a steady upward trend but no repeating yearly pattern, which model (e.g., ARIMA, SARIMA) would you choose and why?
How do AIC, AICc, and BIC help with ARIMA order selection, and how do they differ?
What does auto-ARIMA do, and what are the risks of relying on it blindly?
Walk through the Box-Jenkins methodology for identifying, estimating, and validating an ARIMA model.
What is SARIMAX, and how do exogenous regressors enter an ARIMA model?
Autocorrelation & Model Identification
Explain the concept of an autoregressive (AR) model.
On a correlogram, what do the significance bands represent and how do you decide a spike is meaningful?
Explain autocorrelation and partial autocorrelation, and how ACF and PACF plots help identify the order of AR and MA components.
How do you interpret ACF and PACF plots to understand the underlying patterns such as AR vs MA behavior and seasonality?
What is a moving average (MA) model, and how does it differ from a simple moving average smoother?
What is the Ljung-Box test, and how do you use it to check whether model residuals are white noise?
What is the lag (backshift) operator, and how is it used to express time series models?
What is an ARMA model, and how does it combine AR and MA components?
What is the Durbin-Watson statistic, and what does it tell you about residual autocorrelation?
Why might linear regression assumptions fail with time-series data?
Validation & Data Leakage
How should you properly validate a time series forecasting model, and what is rolling-origin (walk-forward) cross-validation?
Why is k-fold cross-validation inappropriate for time series data, and what are the risks of data leakage in time series?
What is backtesting in a forecasting context, and how does an expanding window differ from a sliding window in time series cross-validation?
What are the most common data leakage mistakes in time series modeling, and how can they be prevented?
What are purging and embargo gaps in time series cross-validation, and why are they needed?
Forecast Horizon & Multi Step Strategies
Explain the concept of forecast horizon and why accuracy typically decays with it.
What is the difference between one-step-ahead and multi-step-ahead forecasting, and what strategies exist for multi-step forecasting?
Why do prediction intervals widen as the forecast horizon increases?
How do you reframe a forecasting problem as a supervised learning problem?
What are the recursive, direct, and multi-output strategies for multi-step forecasting, and what are their trade-offs?
What is hierarchical forecasting, and how do bottom-up, top-down, and middle-up reconciliation approaches differ?
Exponential Smoothing Methods
What is simple exponential smoothing, and what role does the smoothing parameter alpha play?
What is the Holt-Winters method, and how does it differ from ARIMA?
What is Holt's linear trend method, and why would you use a damped trend variant?
When would you choose Exponential Smoothing models over ARIMA models, and vice versa, and what are their strengths and weaknesses?
What is the ETS taxonomy, and how does it organize exponential smoothing models?
Forecast Evaluation & Metrics
What are the standard naive baselines (last-value, seasonal naive, drift, mean), and why must any forecasting model be compared against them?
How do you evaluate point forecasts, and what are the pros and cons of metrics like MAE, RMSE, and MAPE?
What is MASE, and why is it considered a scale-free error metric?
What are the failure modes of MAPE, and how do sMAPE and WAPE attempt to address them?
Why is it important to track forecast bias (mean error), and what does a persistent bias tell you?
How do you compare forecast accuracy fairly across series that have very different scales?
What is the difference between a point forecast and a distributional or quantile forecast, and when do you need the latter?
How do you evaluate probabilistic forecasts and prediction intervals?
What is pinball (quantile) loss, and when would you use it to evaluate a forecast?
How do you choose an error metric that reflects the business cost of over-forecasting versus under-forecasting?
How do you decide whether a series is even forecastable, and when should you choose not to forecast?
Data Preprocessing & Transformations
What does downsampling versus upsampling a time series mean, and when is each valid?
How do you handle missing values in time series data, and what imputation strategies apply?
How do you transform time series data with log, Box-Cox, or scaling, and why are these transformations useful?
How do irregular or unevenly-spaced timestamps complicate time series modeling, and how do you handle them?
For a gapped series, when would you use forward-fill versus interpolation versus seasonal imputation to fill missing timestamps?
Prophet & State Space Models
Explain the core components of Facebook Prophet (trend, seasonality, holidays, changepoints) and how it works.
What are the strengths and criticisms of Prophet, and when would you choose it over other models?
What is the Kalman filter, and how is it conceptually applied to time series for state estimation or smoothing?
Explain the core steps of the Kalman filter (prediction and update) at a conceptual level.
What is a state-space model, and what do the local level and local linear trend models represent?
Volatility Modeling
Explain the concept of realized volatility and how it relates to GARCH models.
What are the limitations of GARCH models, and how can they be addressed?
How does the uncertainty of a volatility forecast change with different forecasting horizons (e.g., 1 day, 1 month, 1 year)?
What is heteroskedasticity and volatility clustering in a time series, and what motivates ARCH/GARCH models?
Anomaly Drift & Changepoints
How would you approach anomaly detection in time series data?
Explain how time series forecasting can be leveraged for anomaly detection.
How do you detect concept drift in a time series?
What is intermittent (sparse) demand, and how does Croston's method handle it?
How do you distinguish a genuine outlier from a level shift or structural break in a time series?
What is changepoint detection, and how do approaches like CUSUM or structural break tests work conceptually?
What is the difference between a centred and a trailing moving average, and what lag/endpoint trade-offs come with smoothing filters like the Hodrick-Prescott filter?
When and why should you retrain a forecasting model, and how does regime change factor into that decision?
Feature Engineering & Ml Forecasting
How would you engineer time-based features for a time-series prediction model, including lag features, rolling statistics, and seasonal decomposition?
Why do gradient-boosted trees on lag features struggle to extrapolate a trend, and how do you address this?
What are Fourier terms, and how are they used to represent seasonality in a regression or ML model?
What is the difference between global (cross-series) and local (per-series) forecasting models, and when is each preferred?
When would a neural forecaster outperform a classical statistical model, and what do models like DeepAR, N-BEATS, or TFT bring to forecasting?
How do you window and scale sequences when preparing time series data for a neural forecasting model?
Multivariate & Causal Analysis
How would you model trend and seasonality using deterministic regression with trend terms and seasonal dummies?
What is panel (longitudinal) data, and how does it differ from a single univariate time series?
What is Granger causality, and what does it imply and not imply about relationships between time series?
What is a VAR model, and when would you use it for multivariate time series?
What is an impulse response function in the context of a VAR model?
What is cointegration, and how does an error-correction model use it?
What is spurious regression between two trending time series, and how do you avoid it?
Why are OLS standard errors wrong when residuals are autocorrelated, and how do Newey-West/HAC standard errors help?