Amazon & Uber Interview

Time Series: ARIMA, LSTM, Prophet & Stationarity

Forecasting the future from the past

Interview Question

"Explain the concept of stationarity in time series. What is ARIMA and how does it handle non-stationary data? Compare ARIMA with LSTM for time series forecasting."

Difficulty: Hard | Frequently asked at Amazon, Uber, Google

Theoretical Foundation

Stationarity

A time series is stationary if its statistical properties don't change over time:

Constant mean: $E[X_t] = \mu$
Constant variance: $\text{Var}(X_t) = \sigma^2$
Constant autocovariance: $\text{Cov}(X_t, X_{t+k}) = \gamma(k)$

Why stationarity matters: Most time series models assume stationarity.

Making Non-Stationary Data Stationary

Differencing: $Y_t = X_t - X_{t-1}$ (first order)
Log transform: Stabilizes variance
Seasonal differencing: $Y_t = X_t - X_{t-s}$

ARIMA (AutoRegressive Integrated Moving Average)

Components:

AR(p): AutoRegressive - depends on past values
I(d): Integrated - differencing order
MA(q): Moving Average - depends on past errors

Model:

X_t = c + \sum_{i=1}^{p} \phi_i X_{t-i} + \sum_{j=1}^{q} \theta_j \epsilon_{t-j} + \epsilon_t

Parameters:

$p$ : Number of AR terms
$d$ : Number of differences
$q$ : Number of MA terms

ARIMA vs LSTM Comparison

Aspect	ARIMA	LSTM
Assumptions	Linear, stationary	None (learns patterns)
Features	Univariate only	Multivariate
Non-linear	No	Yes
Data Required	Less	More
Interpretability	High	Low
Computation	Fast	Slow
Long-term Dependencies	Limited	Captures well

Facebook Prophet

Model: Additive decomposition:

y(t) = g(t) + s(t) + h(t) + \epsilon_t

$g(t)$ : Trend (piecewise linear or logistic)
$s(t)$ : Seasonality (Fourier series)
$h(t)$ : Holidays and events

Properties:

Handles missing data
Robust to outliers
Interpretable components
Automatic changepoint detection

ℹ️

Key Insight: ARIMA works well for short-term forecasts of stationary linear processes. LSTM excels when there are complex non-linear patterns and sufficient data. Prophet is great for business time series with known seasonal patterns.

Code Implementation

Real-World Applications

Amazon: Demand Forecasting

Inventory Management: Predicting product demand
Supply Chain: Forecasting logistics requirements
Pricing: Dynamic pricing based on demand patterns

Uber: Ride Demand Prediction

ETA Prediction: Forecasting arrival times
Surge Pricing: Predicting demand spikes
Driver Allocation: Matching supply with demand

💡

Amazon Interview Tip: Be prepared to discuss handling multiple seasonalities (daily, weekly, yearly) and the importance of feature engineering in time series.

Common Follow-Up Questions

Q1: How do you choose p, d, q for ARIMA? Use ACF/PACF plots, information criteria (AIC/BIC), or auto-ARIMA. d is determined by differencing until stationary.

Q2: When does LSTM outperform ARIMA? When there are complex non-linear patterns, multiple input features, or long-term dependencies that ARIMA cannot capture.

Q3: How do you handle missing values in time series? Forward fill, interpolation, or model-based imputation. Some models (Prophet) handle missing data natively.

Q4: What is the difference between time series regression and forecasting? Forecasting predicts future values using only past values. Time series regression uses external features (weather, events) to predict the target.

Time Series: ARIMA, LSTM, Prophet & Stationarity

Time Series: ARIMA, LSTM, Prophet & Stationarity

Interview Question

Theoretical Foundation

Stationarity

Making Non-Stationary Data Stationary

ARIMA (AutoRegressive Integrated Moving Average)

ARIMA vs LSTM Comparison

Facebook Prophet

Code Implementation

Real-World Applications

Amazon: Demand Forecasting

Uber: Ride Demand Prediction

Common Follow-Up Questions

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