Time Series Interview Questions
Time series questions in quant interviews cluster into a handful of recurring flavors: stationarity and unit-root reasoning, ACF/PACF model identification, GARCH-family volatility, cointegration and pairs logic, and state-space filtering.
The common thread: observations arrive in order and depend on their own past — every technique is machinery for modeling that dependence without fooling yourself.
Last updated 3 July 2026 · sub-areas, difficulty mix and firm attributions on this page are compiled directly from the 57 time-series problems in the QuantVault bank; firm tags are candidate-reported, not employer-verified, and no individual author is named in our source data.
- Core sub-areas
- Stationarity & unit roots · ARMA identification · volatility models · cointegration · state-space & regimes
- Typical difficulty
- Skews hard — 4 easy, 17 medium and 36 hard across the 57-problem set
- Who leans on it
- Research-heavy interview loops — problems here carry candidate tags from Two Sigma, Citadel, Jane Street, JPMorgan and others
- Practice pool
- 57 problems in the bank · 4 free to open with the full worked solution
Where time series shows up: mostly in quant-research phone screens, onsites and data-challenge take-homes, where a model-identification or volatility question doubles as a test of whether you can be trusted with a backtest. For how it sits inside specific funnels, see the Two Sigma interview questions guide and the Citadel interview questions guide.
The surfaceThe time series sub-areas quant interviews test
Six families cover essentially every time-series question in the bank. Each row pairs a sub-area with the recurring question shape and a representative type — a flavor drawn from real problems, not a leaked wording — so you can see where the difficulty actually lives.
| Sub-area | Recurring shape | Representative type (flavor, not a real question) |
|---|---|---|
| Stationarity, unit roots & random walks | Decide whether the statistical properties hold still; difference or detrend before modeling | “Is a random walk stationary?” escalating into unit-root tests with structural breaks and the spurious-regression trap. |
| ARMA identification & forecasting | Read the ACF/PACF fingerprint, recover coefficients, forecast with error bands | Derive the ACF of an AR(1) or ARMA(1,1); recover AR(2) coefficients from autocorrelations via Yule-Walker. |
| Volatility modeling (GARCH, EWMA, realized vol) | Persistence, unconditional variance and forecast comparison | GARCH(1,1) conditional vs. unconditional variance; EWMA half-life; GARCH vs. HAR-RV forecasting bake-offs. |
| Cointegration & pairs logic | Separate correlation from cointegration; build an error-correction spread | An Engle-Granger two-step on a pair of prices, or a Johansen trace test, ending in “is this spread tradeable?” |
| State-space & regime models | Run the filter recursion; infer the hidden state | A Kalman filter on a latent mean-reverting signal, or a two-state volatility HMM with the Hamilton filter. |
| Inference & backtesting on dependent data | Correct for autocorrelation before trusting a statistic or a backtest | Effective sample size under autocorrelation; time-series cross-validation without lookahead; drawdown and Sharpe computations in code. |
What’s confirmed vs. what varies: the sub-areas and the difficulty mix above come straight from the problem set, so they are stable. Which firm asks which flavor is candidate-reported through problem tags — treat the firm attributions as directional, and expect research tracks to see the estimation and state-space families far more often than trading or SWE tracks.
The patternsSignature time series question patterns
Three derivations generate a large share of correct answers in this topic. Each worked box below is a 60–90 second micro-example in the interview’s actual cadence — the reasoning template, applied to a generic setup rather than any firm’s wording.
Stationarity first — why a random walk fails the test
Takeaway: a random walk is the canonical non-stationary series — its variance grows linearly in time, so nothing downstream is valid until you difference.
Shape. Is the random walk \(X_t = X_{t-1} + \varepsilon_t\), with i.i.d. shocks of variance \(\sigma^2\), stationary? What must you do before modeling it?
1. Compute the variance. Iterating gives \(X_t = X_0 + \varepsilon_1 + \cdots + \varepsilon_t\), so \(\mathrm{Var}(X_t) = t\sigma^2\) — it grows without bound. The mean is constant; the variance is what fails.
2. Difference it. The first difference \(\Delta X_t = \varepsilon_t\) is i.i.d. noise — stationary by construction. One differencing pass is exactly what “integrated of order one” means.
3. Respect the warning. Regress one independent random walk on another and you will still see large t-statistics and a healthy R² — the spurious-regression trap. Stationarity testing is what makes every later inference mean anything.
The move: test for the unit root first, difference to stationarity, then model — never the reverse.
ACF/PACF — reading the model’s fingerprint
Takeaway: the ACF and PACF jointly identify the model — AR cuts off in the PACF, MA cuts off in the ACF, and a mixed ARMA tails off in both.
Shape. Returns follow an AR(1), \(X_t = \phi X_{t-1} + \varepsilon_t\) with \(|\phi| < 1\). What do the ACF and PACF look like, and how does that identify the model?
1. Derive the ACF. Multiply by \(X_{t-k}\) and take expectations: \(\gamma_k = \phi\,\gamma_{k-1}\), so \(\rho_k = \phi^k\) — geometric decay that never quite reaches zero.
2. Read the PACF. Once \(X_{t-1}\) is in the regression, older lags add nothing: the PACF is \(\phi\) at lag 1 and zero beyond — a clean cutoff.
3. Invert the logic. An MA(1) is the mirror image — ACF cuts off after lag 1, PACF decays — and when both tail off you are looking at a mixed ARMA, the pattern the free ARMA(1,1) problem below makes you prove.
The fingerprint: the cutoff names the order, the decay names the family.
GARCH(1,1) — persistence sets everything
Takeaway: the three GARCH parameters answer three questions — the constant sets the base level, the ARCH term the reaction to news, the GARCH term the memory — and their sum tells you how long shocks last.
Shape. Daily returns follow GARCH(1,1): \(\sigma^2_t = \omega + \alpha\varepsilon^2_{t-1} + \beta\sigma^2_{t-1}\) with \(\omega = 2\times 10^{-6}\), \(\alpha = 0.08\), \(\beta = 0.90\). What is the long-run volatility, and how persistent are shocks?
1. Check stationarity. \(\alpha + \beta = 0.98 < 1\), so the variance process is covariance-stationary and a long-run level exists.
2. Solve for the level. Set \(\sigma^2_t = \sigma^2\) on both sides: \(\sigma^2 = \omega/(1-\alpha-\beta) = 2\times10^{-6}/0.02 = 10^{-4}\) — a daily vol of 1%, roughly 16% annualized.
3. Time the decay. Deviations from that level shrink by the factor \(\alpha+\beta\) each day, so the half-life is \(\ln 0.5 / \ln 0.98 \approx 34\) trading days. That slow decay is volatility clustering, quantified.
The move: persistence \(\alpha+\beta\) is the headline number — the long-run level and the shock half-life both fall out of it.
Free practiceFree time series practice questions
An honesty note up front: the free pool here is small — 4 of the 57 problems, one medium and three hard, with the easy tier entirely in the paid set. The list below is short but real: every link opens the complete worked solution, so you can check your reasoning line by line. For the remaining 53 — the GARCH, cointegration and Kalman material the table above maps out — head to the full Time Series problem bank.
Diagnostics, memory & model identification
- Detecting the Direction of Time in a Price SeriesRandom-walk diagnosticsmediumfree
- ACF and PACF of an ARMA(1,1) ProcessARMA identificationhardfree
- Estimating the Hurst Exponent via Rescaled Range AnalysisLong memoryhardfree
Coding on price series
- Maximum Drawdown in a Sliding WindowStreaming algorithmshardfree
The planHow to prepare for time series questions
Five techniques to make reflexive, in the order they pay off. The first three cover the worked patterns above; the last two are what research interviewers use to separate candidates.
- Make the stationarity check your first instinct. Before any modeling claim, ask what the mean, variance and autocovariance are doing over time, and difference or detrend until they hold still. Knowing why a random walk fails — variance \(t\sigma^2\) — is table stakes.
- Memorize the ACF/PACF fingerprint table. AR(p): PACF cuts off at lag p. MA(q): ACF cuts off at lag q. Mixed ARMA: both tail off. Then practice recovering coefficients from a correlogram — the Yule-Walker equations for a low-order AR are a two-line computation.
- Drill the GARCH algebra until it is mechanical. Unconditional variance \(\omega/(1-\alpha-\beta)\), persistence \(\alpha+\beta\), shock half-life — interviewers use these as speed checks before the harder quasi-likelihood and risk-measure questions.
- Learn cointegration as “correlation is not a spread”. Two trending series can be highly correlated yet not cointegrated; the Engle-Granger two-step and the error-correction interpretation are what make a pairs trade defensible in front of an interviewer.
- Treat dependence as the enemy of naive inference. Autocorrelation shrinks your effective sample size, backtests need walk-forward splits, and any bootstrap must be a block bootstrap. Then work the free practice problems above and take the interactive time series playlist on a clock.
FAQTime series interview questions — frequently asked
How important is time series for quant interviews?
Core material for quant-research roles: forecasting returns and volatility is the day job, and interviews test the machinery directly. Trading and software tracks see it less often, but a stationarity or drawdown question can surface in any loop that touches market data.
What time series topics should I focus on?
Stationarity and unit roots, ACF/PACF-based ARMA identification and GARCH-family volatility cover the bulk of what gets asked. Research desks add cointegration, Kalman filtering and honest inference on dependent data — the walk-forward and block-bootstrap hygiene that separates a backtest from a story.
How hard are time series interview questions?
This set skews hard: of the 57 problems, 36 are hard, 17 medium and only 4 easy, and most are proof-style derivations. The difficulty is cumulative rather than trick-based — each result leans on the last, which is why drilling the core derivations pays off fast.
Are these real quant interview questions?
They are representative, not verbatim. The problems are curated from our bank to match the time-series shapes candidates report from quant interviews, rewritten for clarity with worked solutions we author ourselves — we never claim any wording is a leaked question.