Time series forecasting quiz

Question 1

What does it mean for a time series to be weakly (covariance) stationary, and why does it matter for ARMA modeling?

Accepted Answer

Constant mean and variance, with autocovariance depending only on lag

Answer

Mean, variance, and autocovariance all change smoothly over time

Answer

The series has zero mean and unit variance at every point

Answer

All autocorrelations equal zero at every lag

Question 2

In the Box-Jenkins methodology, how do the ACF and PACF plots help distinguish an AR(p) from an MA(q) process?

Accepted Answer

AR(p): PACF cuts off at p; MA(q): ACF cuts off at q

Answer

AR(p): ACF cuts off at p; MA(q): PACF cuts off at q

Answer

Both ACF and PACF cut off at the same lag for AR and MA

Answer

Neither plot is informative for AR or MA identification

Question 3

What is the difference between the Augmented Dickey-Fuller (ADF) test and the KPSS test for stationarity?

Accepted Answer

ADF null = unit root; KPSS null = stationarity

Answer

Both tests have a null hypothesis of stationarity

Answer

Both tests have a null hypothesis of a unit root

Answer

ADF tests seasonality; KPSS tests heteroskedasticity

Question 4

Why is it incorrect to use standard k-fold cross-validation for time series, and what is the proper alternative?

Accepted Answer

Use forward-chaining / rolling-origin cross-validation

Answer

Random k-fold is fine if you set a random seed

Answer

Use leave-one-out cross-validation on shuffled data

Answer

Stratified k-fold by target quantile prevents leakage

Question 5

What is the key structural difference between SARIMA and SARIMAX, and when would you choose SARIMAX?

Accepted Answer

SARIMAX adds exogenous regressors to SARIMA

Answer

SARIMAX drops the seasonal component entirely

Answer

SARIMAX is for multivariate-only targets, SARIMA univariate

Answer

They are identical; the name differs by library

Question 6

Explain the components of Holt-Winters exponential smoothing and the difference between its additive and multiplicative forms.

Accepted Answer

Level, trend, seasonality; additive for constant, multiplicative for proportional seasonality

Answer

Only level and trend; seasonality is ignored

Answer

Additive is for growing seasonality, multiplicative for constant

Answer

It uses a single smoothing parameter for all components

Question 7

What problem does the seasonal difference (e.g., y_t - y_{t-12}) solve, and how does it differ from a first difference?

Accepted Answer

First difference removes trend; seasonal difference removes recurring seasonal patterns

Answer

Both remove only linear trend identically

Answer

Seasonal differencing removes variance heteroskedasticity

Answer

First differencing is only valid for stationary series

Question 8

Why can MAPE be a misleading forecast error metric, and what alternatives address its weaknesses?

Accepted Answer

MAPE is undefined/unstable near zero and asymmetric; MASE/sMAPE are alternatives

Answer

MAPE is always symmetric and bounded, so no alternative is needed

Answer

MAPE cannot handle multi-step horizons but RMSE can

Answer

MAPE penalizes under-forecasts more than over-forecasts

Question 9

What is the Mean Absolute Scaled Error (MASE) and why is a value below 1 desirable?

Accepted Answer

MASE < 1 means the model beats the naive benchmark

Answer

MASE < 1 means the model is worse than naive

Answer

MASE is the same as MAPE scaled by 100

Answer

MASE requires the series to be stationary to compute

Question 10

In Facebook/Meta Prophet, how is trend modeled and what are 'changepoints'?

Accepted Answer

Trend is piecewise-linear/logistic with changepoints where the slope can change

Answer

Trend is a fixed global linear slope with no breaks

Answer

Trend is modeled by an LSTM inside Prophet

Answer

Changepoints are seasonal peaks detected by FFT

Question 11

How does Prophet represent seasonality, and what does increasing the Fourier order do?

Accepted Answer

Higher Fourier order adds higher-frequency terms, fitting more complex seasonality but risking overfit

Answer

Higher Fourier order forces a smoother, simpler seasonal curve

Answer

Fourier order controls the trend changepoint count

Answer

Fourier order sets the number of holidays modeled

Question 12

What is the core architectural idea behind the N-BEATS model for forecasting?

Accepted Answer

A pure feed-forward stack of blocks with doubly-residual backcast/forecast

Answer

A recurrent LSTM with attention over exogenous features

Answer

A convolutional autoencoder for anomaly detection

Answer

A Gaussian-process kernel regression model

Question 13

How does Amazon's DeepAR differ from training a separate ARIMA model per series?

Accepted Answer

DeepAR is a single global RNN trained across many series with probabilistic output

Answer

DeepAR fits one ARIMA per series automatically

Answer

DeepAR is deterministic and gives only point forecasts

Answer

DeepAR requires every series to have identical length and no covariates

Question 14

What is a quantile loss (pinball loss) and why is it used for probabilistic forecasting?

Accepted Answer

An asymmetric loss whose minimizer is the tau-quantile, used for prediction intervals

Answer

A symmetric squared loss whose minimizer is the mean

Answer

A loss that only targets the median (tau=0.5)

Answer

A regularization penalty on autoregressive coefficients

Question 15

Why does naive 'predict the last value' (random walk) forecasting sometimes outperform complex models, and what does this imply for evaluation?

Accepted Answer

For near-random-walk series the naive forecast is hard to beat; always benchmark against it

Answer

Naive forecasts always lose to ML models, so baselines are optional

Answer

Naive forecasting only works on stationary white noise

Answer

Random-walk forecasts minimize MAPE by construction

Question 16

What is the difference between recursive (iterative) and direct multi-step forecasting strategies?

Accepted Answer

Recursive feeds predictions back into one model; direct trains a separate model per horizon

Answer

Recursive trains one model per horizon; direct reuses one model

Answer

Both strategies are mathematically identical for linear models

Answer

Direct forecasting always accumulates more error than recursive

Question 17

In the Temporal Fusion Transformer (TFT), what role do variable selection networks and interpretable multi-head attention play?

Accepted Answer

Variable selection picks relevant inputs; interpretable attention reveals influential timesteps

Answer

They replace the need for any training data

Answer

They convert the model into a pure ARIMA equivalent

Answer

They only handle static covariates and ignore time

Question 18

What is Granger causality and what is its key limitation?

Accepted Answer

It measures predictive precedence, not true causation, and can be confounded

Answer

It proves true physical causation between two series

Answer

It requires the series to be non-stationary

Answer

It is identical to Pearson correlation at lag 0

Question 19

When forecasting with a VAR model, how do you choose the lag order and verify model adequacy?

Accepted Answer

Choose lag via information criteria, then check residual autocorrelation and stability

Answer

Always use the maximum possible lag for best fit

Answer

Pick lag 1 always since VAR is first-order by definition

Answer

Use the lag that maximizes in-sample R-squared

Question 20

What does the Ljung-Box test assess on model residuals, and what outcome do you want?

Accepted Answer

You want a high p-value indicating residuals are white noise

Answer

You want a low p-value confirming residual autocorrelation

Answer

It tests residual normality, not autocorrelation

Answer

It tests for a unit root in the residuals

Question 21

How do GARCH models extend the modeling of time series, and what do they capture that ARIMA does not?

Accepted Answer

GARCH models time-varying conditional variance (volatility clustering)

Answer

GARCH models the conditional mean, ARIMA the variance

Answer

GARCH removes seasonality that ARIMA cannot

Answer

GARCH is only for stationary white noise with constant variance

Question 22

What is the danger of using future-looking features (target leakage) in time series feature engineering, and give an example.

Accepted Answer

Using a centered window or full-series scaling leaks future info and inflates backtests

Answer

Centered rolling means are safe because they reduce variance

Answer

Leakage only happens with exogenous variables, never lags

Answer

Leakage improves generalization to unseen data

Question 23

Why might you apply a Box-Cox or log transform before forecasting, and how do you produce forecasts on the original scale?

Accepted Answer

It stabilizes variance; inverting the transform needs a bias correction for the mean

Answer

It removes trend; just exponentiate the forecast with no correction

Answer

It is only cosmetic and never affects model fit

Answer

It converts additive seasonality into multiplicative

Question 24

What is the spurious regression problem when modeling two non-stationary (trending) series, and how is it addressed?

Accepted Answer

Trending series can yield spurious fits; test cointegration or difference the data

Answer

High R-squared between trending series is always genuine

Answer

Differencing always destroys real long-run relationships

Answer

Spurious regression only affects stationary series

Question 25

How does STL decomposition differ from naive (classical) additive decomposition, and what are its advantages?

Accepted Answer

STL uses Loess, allows evolving seasonality, and is robust to outliers

Answer

STL forces a fixed, unchanging seasonal pattern

Answer

STL can only decompose monthly data

Answer

STL is identical to a single moving average

Question 26

What is concept drift in time series forecasting and what strategies mitigate it in production?

Accepted Answer

Detect drift via monitoring and retrain with rolling windows / online learning

Answer

Train once and never retrain, since time series are stationary

Answer

Concept drift only affects classification, not forecasting

Answer

Adding more historical data always solves drift

Question 27

In intermittent demand forecasting (many zeros), why do standard methods fail and what is Croston's method?

Accepted Answer

Croston separately smooths demand size and inter-arrival interval

Answer

Croston's method ignores zeros and fits ARIMA to non-zeros

Answer

Intermittent series are best handled by standard exponential smoothing

Answer

Croston's method requires no demand to ever be zero

Question 28

Why is the order of operations important when scaling/normalizing features in a time series ML pipeline with cross-validation?

Accepted Answer

Fit the scaler only on each fold's training data to avoid leakage

Answer

Fit the scaler once on the full series for consistency

Answer

Scaling order never matters for tree models or linear models

Answer

Always scale using future validation statistics for accuracy

Question 29

What advantage do gradient-boosted trees (e.g., LightGBM) offer for time series forecasting, and what is their main limitation?

Accepted Answer

GBMs handle rich features but cannot extrapolate trend; detrend first

Answer

Trees extrapolate trends naturally and need no detrending

Answer

GBMs have built-in temporal memory like RNNs

Answer

GBMs require stationary Gaussian inputs only

Question 30

How does an information criterion like AIC trade off fit and complexity, and how does BIC differ?

Accepted Answer

BIC's penalty grows with sample size, favoring simpler models more than AIC

Answer

BIC penalizes complexity less than AIC

Answer

AIC and BIC always select the same model

Answer

Higher AIC indicates a better model

Test yourself