Why Time Series Questions Matter
Financial data is fundamentally time series, and the methodology pitfalls in working with time series data - non-stationarity, regime change, autocorrelation, look-ahead bias - separate experienced quant researchers from candidates who've only worked with cross-sectional data. Time series interviews are particularly heavy at Two Sigma, AQR, DE Shaw, Renaissance, Citadel (research) and most systematic hedge funds.
This guide collects 15 worked examples drawn from real research interviews. For broader research-track context, see our quant research interview questions. For deeper coverage of specific topics, see our arima model explained guide.
Section 1: Stationarity and Tests (Questions 1-5)
1. Stationarity definition
What does it mean for a time series to be stationary?
Answer: Strict stationarity: the joint distribution of any subset of observations is invariant to time shifts. Weak (covariance) stationarity: mean is constant, variance is constant, and autocovariance depends only on lag (not absolute time). Most time series methods assume weak stationarity. Most financial returns are approximately weakly stationary; prices are not (random walk).
2. Augmented Dickey-Fuller test
What does the ADF test check, and what's its null hypothesis?
Answer: ADF tests for the presence of a unit root - i.e., whether the series is non-stationary (integrated of order ≥ 1). Null hypothesis: there is a unit root (non-stationary). Reject the null at p < 0.05 to conclude the series is stationary. Caveat: ADF has low power against persistent but stationary alternatives - doesn't reject the null even when it should for highly autocorrelated series.
3. KPSS vs ADF
What's the difference between KPSS and ADF tests?
Answer: Opposite null hypotheses. KPSS: null is stationarity (reject if non-stationary). ADF: null is non-stationarity (reject if stationary). Use both together for robust conclusions: if both agree (e.g., ADF rejects null AND KPSS doesn't reject null), you can be more confident the series is stationary. If they disagree, the result is ambiguous.
4. Differencing for stationarity
A series shows clear trend. How do you make it stationary?
Answer: First differencing: (Y_t - Y_{t-1}). If still non-stationary, consider second differencing or seasonal differencing (Y_t - Y_{t-12} for monthly data with annual seasonality). For prices that follow a random walk, first differences (returns) are typically stationary. For more complex non-stationarity (e.g., variance also changing over time), use additional transformations (log, Box-Cox).
5. Spurious regression
Two unrelated random walks can show R² > 0.5 over thousands of observations. What's going on?
Answer: Both processes are non-stationary (integrated of order 1, or I(1)). Standard OLS regression doesn't handle this - the t-statistics are unreliable, the R² is meaningless, the regression detects "trend matching" rather than real relationship. Solutions: (1) Regress on first differences (returns) instead of levels (prices). (2) Test for cointegration before trusting the relationship. (3) Use error-correction models if cointegrated.
Section 2: ARIMA and Forecasting (Questions 6-10)
6. AR(1) interpretation
You estimate (Y_t = 0.7 Y_{t-1} + ε_t). What does φ = 0.7 tell you?
Answer: Strong positive autocorrelation. The current value depends heavily on the previous one. Half-life of shocks is (\ln(0.5)/\ln(0.7) ≈ 1.94) periods - shocks decay relatively slowly. For comparison, white noise has φ = 0; a random walk has φ = 1.
7. ARIMA(p,d,q)
What does each parameter mean?
Answer: p = order of autoregressive (AR) terms (how many lags of Y are used). d = order of differencing (how many times the series is differenced to make it stationary). q = order of moving-average (MA) terms (how many lags of the error are used). ARIMA(0,0,0) is white noise; ARIMA(1,0,0) is AR(1); ARIMA(0,1,0) is a random walk; ARIMA(0,0,1) is MA(1).
8. Box-Jenkins methodology
Walk through the steps of identifying an ARIMA model.
Answer: (1) Test for stationarity; if non-stationary, difference until stationary (sets d). (2) Examine ACF and PACF of the differenced series. AR processes have ACF that decays slowly and PACF that cuts off; MA is reverse. (3) Estimate the model. (4) Check residuals for white noise (Ljung-Box test). (5) Validate out-of-sample.
9. AIC vs BIC for ARIMA selection
You're choosing between ARIMA(1,0,1) and ARIMA(2,0,2). AIC favours the larger; BIC favours the smaller. Which do you choose?
Answer: It depends on goals. BIC is more conservative (heavier complexity penalty) and tends to identify the true model when one exists. AIC is asymptotically optimal for prediction. For forecasting, AIC. For inference about the underlying process, BIC. In practice, also consider out-of-sample validation - either model that performs better there is the right choice.
10. Forecasting horizon
You estimate ARIMA(1,0,0) with φ = 0.5. What's the forecast at horizon 1, 5, and 100?
Answer: With φ < 1, forecasts converge geometrically to the unconditional mean. If current value is Y_T, forecast at horizon h is approximately (\bar{Y} + φ^h (Y_T - \bar{Y})). At h=1: roughly half the deviation from mean. At h=5: ~3% deviation. At h=100: essentially zero - the forecast is just the mean. ARIMA forecasts at long horizons converge to the mean.
Section 3: GARCH and Volatility (Questions 11-15)
11. Why GARCH?
What does GARCH model that ARMA can't?
Answer: Conditional heteroskedasticity - time-varying variance. ARMA models the conditional mean (level); GARCH models the conditional variance. Financial returns typically exhibit "volatility clustering" - high-vol periods cluster, low-vol periods cluster - which GARCH captures via lagged squared shocks.
12. GARCH(1,1)
What's the standard GARCH(1,1) specification?
Answer: (σ_t^2 = ω + α ε_{t-1}^2 + β σ_{t-1}^2). Variance at time t depends on yesterday's squared shock (ARCH term, weight α) and yesterday's variance (GARCH term, weight β). Long-run unconditional variance is (ω / (1 - α - β)). Stationarity requires α + β < 1. Typical equity index parameters: ω small, α ≈ 0.05, β ≈ 0.93, so very high persistence.
13. GARCH limitations
GARCH captures volatility clustering well. What does it miss?
Answer: (1) Asymmetric effects (negative shocks increase vol more than positive shocks) - addressed by EGARCH or GJR-GARCH. (2) Heavy tails of standardised residuals - addressed by GARCH with student-t or skewed-t innovations. (3) Long memory in volatility - addressed by FIGARCH. (4) Multiple regime changes - addressed by Markov switching GARCH. In practice, GARCH(1,1) with student-t errors handles most equity index data well.
14. Volatility forecasting horizons
You forecast volatility at horizon 1 day, 1 month, and 1 year. How does the uncertainty of the forecast change?
Answer: At short horizons, GARCH forecasts are highly informative (you know yesterday's vol; today is similar). At long horizons, forecasts converge to the unconditional mean. Uncertainty of cumulative return forecast grows with √h (in stationary settings). For long-horizon vol forecasting, the value-add of GARCH over simple historical mean is small.
15. Realised volatility vs GARCH
What is realised volatility, and how does it relate to GARCH?
Answer: Realised volatility (RV) is computed from intraday returns: (RV_t = \sum_i r_{t,i}^2) over high-frequency intervals. It's a much more efficient estimator of the day's true volatility than the simple squared daily return. GARCH typically uses daily squared returns, which are noisy; using RV directly (as in HAR-RV models) often produces better volatility forecasts.
How to Use This Guide
For research-track candidates at systematic firms (Two Sigma, AQR, DE Shaw, Renaissance, Citadel), all 15 questions are likely fair game. For trader and developer tracks, focus on Section 3 (GARCH and volatility) - these come up in option market making interviews even when broader time series doesn't.
For broader prep:
- Quant interview questions hub
- Quant research interview questions
- ARIMA model explained
- Machine learning finance guide
- Statistics for quantitative trading
For firm-specific interview content where time series is heavily tested:
Practise the questions Time Series Interview Questions: 15 Real Examples 2026 actually asks
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