Time Series Interview Questions

Sample Answer

Create a complete 15 minute time index, align observations to it, and compute lags only from past timestamps on that index. You first set the timestamp as the index, sort, then reindex to the full 15 minute grid so gaps become explicit missing values. Build lags with shift on the indexed series, and only impute using methods that do not peek forward, like forward fill or model based imputation fit on training data only. If you interpolate, do it causally, for example limit to past values, because symmetric interpolation uses future points and leaks.

Sample Answer

You could compute rolling features directly on the transaction table or you could first build a clean daily panel then engineer features on that. The transaction level approach is fragile because late corrections can reorder history and a rolling window over transactions does not correspond to a fixed 7 day period. The daily panel approach wins here because you explicitly define the day boundary, for example local market midnight in a fixed timezone, aggregate transactions into a single value per day, and version or cutoff corrections using an as of timestamp. Then compute features like $$\text{roll7}(t)=\frac{1}{7}\sum_{i=1}^{7} y_{t-i}$$ and $y_{t-7}$ so the window ends at $t-1$, never including $y_t$.

Sample Answer

You could do a log transform then difference, or difference then log. Log then difference usually wins here because it stabilizes variance first and turns growth into additive changes, so $y_t = \log x_t$ then $\nabla y_t$ approximates percent change: $\nabla \log x_t \approx (x_t - x_{t-1})/x_{t-1}$. Differencing first can leave heteroskedasticity in the differenced series when level changes are scale-dependent. You know it is correct when residuals have roughly constant variance, the ACF of the transformed series drops off quickly, and Ljung-Box style checks do not show leftover autocorrelation.

Sample Answer

First, you note the positivity and right skew, so you consider $y_t = \log(\sigma_t)$ to stabilize variance and make shocks more symmetric. Next, you check whether $y_t$ looks mean-reverting by inspecting the ACF, if it decays rather than staying near 1 for many lags, that argues for modeling in levels with an ARMA-type mean reversion rather than differencing. If the ACF of $y_t$ still decays extremely slowly and unit root tests plus a clear wandering mean suggest nonstationarity, you try $\nabla y_t$ and re-check ACF and residual whiteness. Finally, regardless of mean modeling, you check residuals for remaining conditional heteroskedasticity, because clustering can require a variance model even if the mean is stationary.

Sample Answer

This question is checking whether you can choose metrics that match the data generating quirks and communicate the tradeoffs. MAPE breaks when $y_t \approx 0$ because the denominator explodes, it also over penalizes under forecasts versus over forecasts in a way that can be misleading for intermittent demand. You can switch to sMAPE, or better, use MAE or RMSE on a stabilized scale like $\log(1+y)$, and for service level style decisions use pinball loss with quantiles. If they insist on a percentage metric, you can compute a weighted MAPE over aggregated buckets where zeros are less dominant, and you must define how you treat $y_t=0$ explicitly.

Sample Answer

The standard move is to score quantiles with pinball loss and check calibration with coverage, for example the empirical rate that $y_t \le \hat{q}_{0.9}(t)$ is close to $0.9$. But here, horizon matters because errors and uncertainty typically grow with lead time, so you compute pinball loss and coverage separately for each horizon $k=1..h$, not just averaged. You also check sharpness, the average width $\hat{q}_{0.9}-\hat{q}_{0.1}$, because a model can be calibrated but uselessly wide. Finally, you look for systematic bias in the PIT or quantile residuals over time and by segment, which flags miscalibration that a single aggregate score can hide.

Sample Answer

The standard move is to control the family wise error rate or FDR, for example Bonferroni or Benjamini Hochberg on per country p values. But here, time dependence and shared infrastructure matter because p values are not independent across countries or across minutes, so naive corrections can either over alert or miss global events. You should add hierarchical structure, for example test a global metric first, then drill down only if it triggers, or use an empirical Bayes model that shrinks noisy countries toward a global prior. Operationally, you can combine statistical control with alert grouping logic, for example one incident ticket per cluster of correlated countries within a short window.

Sample Answer

Get this wrong in production and you either roll back a good launch or ship a regression while believing the metric noise story. The right call is to reframe change point detection as a conditional problem, model conversion with covariates and look for a shift in the residual or in the treatment effect, not in the marginal rate. You can fit a segmented regression or state space model with user type and geo as predictors, then test for a post launch level shift in the intercept or coefficients. As a sanity check, run placebo change point tests on unaffected metrics and use pre period backtesting to estimate how often your method flags spurious shifts under composition changes.

Sample Answer

Get this wrong in production and you ship a strategy that only works on paper, then transaction costs and adverse selection flip your Sharpe negative. The right call is to model execution at bid or ask, include spread, commissions, slippage, and latency, and account for the fact that midprice is not a tradable price. You should also test sensitivity to fill assumptions, for example, marketable orders versus passive orders with partial fills, and include price impact that scales with participation rate. Finally, validate with out-of-sample periods and event-time stress, because microstructure regimes change and your edge can vanish around volatility spikes.

Sample Answer

Using a wide table sounds reasonable but breaks under column leakage, you can accidentally align $X_t$ with information from $t+1$ when you pivot and forward-fill. Filtering to current constituents sounds fine but does not work because it creates survivorship bias, you remove delisted names and inflate historical performance. That leaves strict point-in-time joins, timestamped availability for every feature, and an investable universe defined as of each date, including delistings and corporate actions. You also add automated leakage tests, like shifting labels backward and ensuring performance collapses, and you enforce a single data pipeline that produces both research and backtest datasets from the same as-of logic.