Question 1

What are trend, seasonality, and residual in time series decomposition, and how do you extract them?

Accepted Answer

Decomposition separates a series into a trend component (long-run direction), a seasonal component (periodic, fixed-period pattern), and a residual (everything left over). Additive decomposition sums the three; multiplicative decomposition multiplies them, which is appropriate when seasonal swings grow with the level.

Question 2

Why can't you shuffle a time series before splitting into train and test sets?

Accepted Answer

Shuffling destroys temporal order, so the model trains on future data and is evaluated on the past — a direct information leak. Time series observations are serially correlated, meaning past values predict future ones, and any random split obliterates that structure entirely.

Question 3

How do you read ACF and PACF plots, and what do they tell you about AR and MA orders?

Accepted Answer

The ACF measures correlation between a series and its own lags including indirect effects; the PACF strips out those indirect effects to show direct correlation at each lag. A cut-off in the PACF after lag p signals an AR(p) process; a cut-off in the ACF after lag q signals an MA(q) process.

Question 4

What is the difference between ARIMA and SARIMA, and when do you use each?

Accepted Answer

ARIMA(p,d,q) models non-seasonal series by combining autoregression, differencing, and a moving average of errors. SARIMA extends it with a second set of seasonal parameters (P,D,Q,s) that operate at the seasonal lag s, handling periodic patterns that ARIMA alone cannot capture.

Question 5

How do you choose p, d, and q for an ARIMA model?

Accepted Answer

Choose d by differencing until the ADF test confirms stationarity; choose p from the PACF cutoff and q from the ACF cutoff on the differenced series; then confirm with AIC or BIC to guard against over-fitting. In practice, an automated grid search over a small range of candidates with information criteria is more reliable than visual inspection alone.

Question 6

What is exponential smoothing, and how does Holt-Winters extend it to handle trend and seasonality?

Accepted Answer

Simple exponential smoothing computes a weighted average of all past observations where weights decay geometrically, controlled by a single smoothing parameter alpha. Holt's method adds a trend component with a second parameter beta; Holt-Winters (ETS) adds a seasonal component with a third parameter gamma, making it a strong baseline for series with both trend and seasonality.

Question 7

How do you engineer lag and rolling features for a time series ML model, and what leakage risks arise?

Accepted Answer

Lag features shift the target or exogenous variables backward by k steps so the model sees past values as inputs; rolling features (rolling mean, std, min, max) summarise a window of past observations. Both must be computed strictly on past data — any feature that incorporates information from the current or future rows leaks the target and inflates metrics.

Question 8

When would you use MAPE versus MASE to evaluate a forecast, and what are the failure modes of each?

Accepted Answer

MAPE (Mean Absolute Percentage Error) is intuitive and scale-free but breaks when actuals are near zero and penalises under-forecasts more than over-forecasts. MASE (Mean Absolute Scaled Error) solves both issues by scaling errors against a naive seasonal benchmark, making it valid even with zero values and comparable across series with different scales.

Question 9

When would you choose Prophet over ARIMA for a forecasting problem?

Accepted Answer

Prophet is a curve-fitting model that decomposes the series into trend, seasonality, and holidays; it handles missing data, multiple seasonalities, and non-uniform time grids with minimal tuning and is accessible to non-statisticians. ARIMA is a statistical model based on autocorrelation structure; it is more appropriate when the series is short, noise is small, and you need principled uncertainty intervals from an explicit stochastic process.

Question 10

What is walk-forward validation, and why is it the correct cross-validation strategy for time series?

Accepted Answer

Walk-forward validation (also called time-series cross-validation or expanding-window CV) creates successive train/test folds where each fold's test set is always strictly in the future relative to its training set. It mimics real deployment — you fit on what you knew then and evaluate on what happened next — unlike random k-fold, which lets future data contaminate training.

Question 11

What is stationarity in a time series, and how do you test for it?

Accepted Answer

A stationary series has a constant mean, constant variance, and autocovariance that depends only on lag — not on when you look. Most classical models (ARIMA, VAR) require it. The Augmented Dickey-Fuller (ADF) test is the standard check; a p-value below 0.05 lets you reject the unit-root null and conclude the series is stationary.

Question 12

What is a VAR model, and when would you use it instead of a univariate ARIMA?

Accepted Answer

A Vector Autoregression (VAR) model extends ARIMA to multiple time series simultaneously: each variable is regressed on its own past values and the past values of all other variables in the system. Use VAR when the series have mutual predictive relationships (Granger-causality) and you want to model those interactions; ARIMA is sufficient when one series can be forecast in isolation.