Diagnostics and Stationarity Interview Questions

Q: What is stationarity, and why does it matter?

Short interview answer

A weakly stationary series has time-invariant mean, variance, and autocovariance that depends only on lag, not calendar time. Many classical models assume this because their parameter estimates and forecast equations rely on stable dynamics.

Core conditions

1
2
3

E[y_t] = μ
Var(y_t) = σ^2
Cov(y_t, y_(t-k)) = γ_k

These should not change with t.

Q: How do you check stationarity?

What interviewers want

They usually want more than “I run ADF.” A strong answer combines visual checks, transformations, and two complementary tests.

Workflow

1. Plot the series and rolling mean/variance.
2. Inspect ACF and PACF.
3. Apply log transform if variance grows with level.
4. Difference if trend or seasonality is present.
5. Run ADF and KPSS together.

How to interpret ADF and KPSS

• ADF null hypothesis: unit root, so the series is non-stationary.
• KPSS null hypothesis: the series is stationary.

Strong interview line

If ADF rejects non-stationarity and KPSS fails to reject stationarity, that is strong evidence the transformed series is stationary enough for ARIMA-style modeling.

Q: What is white noise, and how is it different from stationarity?

Short interview answer

White noise is stronger than weak stationarity. A white-noise process has zero autocorrelation at all non-zero lags, while a stationary process may still have serial dependence.

Core conditions

1
2
3

E[ε_t] = 0
Var(ε_t) = σ^2
Cov(ε_t, ε_(t-k)) = 0   for k ≠ 0

Why it matters

After fitting a classical time-series model, I want the residuals to look like white noise. If residual autocorrelation remains, the model has left structure unexplained.

Q: What residual diagnostics would you run after fitting a forecasting model?

Strong answer

• Plot residuals over time.
• Check residual ACF.
• Use Ljung-Box to test joint autocorrelation.
• Inspect residual histogram or Q-Q plot if probabilistic assumptions matter.
• Check whether residual variance changes over time.

Ljung-Box test idea

1

H0: residual autocorrelations up to lag h are jointly zero

If the p-value is small, the model likely missed temporal structure.

Q: Why does differencing help?

Short interview answer

Differencing removes low-frequency trend and can convert an integrated process into a stationary one.

Formula

1
2
3
4
5

First difference:
Δ y_t = y_t - y_(t-1)

Seasonal difference:
Δ_s y_t = y_t - y_(t-s)

What a strong candidate adds

Over-differencing is harmful because it can inject unnecessary noise and make the series harder to model. I usually choose the smallest differencing order that yields acceptable stationarity and residual behavior.