Classical Forecasting Interview Questions

Q: Explain AR, MA, and ARMA models. How do you determine the orders?

Short interview answer

An AR model regresses the current value on past values, an MA model regresses the current value on past shocks, and ARMA combines both. For a stationary series, I typically inspect ACF and PACF, fit a few candidate orders, and compare AIC, BIC, and residual diagnostics.

Core formulas

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AR(p):    y_t = c + φ_1 y_(t-1) + ... + φ_p y_(t-p) + ε_t

MA(q):    y_t = μ + ε_t + θ_1 ε_(t-1) + ... + θ_q ε_(t-q)

ARMA(p,q):
          y_t = c + φ_1 y_(t-1) + ... + φ_p y_(t-p)
                + ε_t + θ_1 ε_(t-1) + ... + θ_q ε_(t-q)

How to identify order

• For a pure AR(p), the PACF tends to cut off after lag p while the ACF tails off.
• For a pure MA(q), the ACF tends to cut off after lag q while the PACF tails off.
• For mixed ARMA behavior, both ACF and PACF may tail off, so I fit several candidates and compare information criteria.

What a strong candidate says next

• Stationarity is required for ARMA.
• Residuals should look like white noise after fitting.
• Order selection should combine plots, information criteria, and out-of-sample validation.

Q: What is the difference between ARIMA and SARIMA?

Short interview answer

ARIMA adds differencing to ARMA so we can model non-stationary series. SARIMA extends ARIMA with seasonal AR, seasonal differencing, and seasonal MA terms.

Core formulas

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ARIMA(p,d,q):
Φ(B) (1 - B)^d y_t = c + Θ(B) ε_t

SARIMA(p,d,q)(P,D,Q)_s:
Φ(B) Φ_s(B^s) (1 - B)^d (1 - B^s)^D y_t
    = c + Θ(B) Θ_s(B^s) ε_t

Where:

• B is the backshift operator, so B y_t = y_(t-1).
• d is the non-seasonal differencing order.
• D is the seasonal differencing order.
• s is the seasonal period, such as 12 for monthly data with yearly seasonality.

How I choose between them

• Use ARIMA if the series has trend but no clear seasonal cycle.
• Use SARIMA if the series has repeated seasonal structure.
• Confirm with seasonal plots, seasonal ACF spikes, and performance on rolling backtests.

Q: What are exponential smoothing methods?

Short interview answer

Exponential smoothing forms forecasts as weighted averages of past observations, where recent observations get larger weights. Different variants model level, trend, and seasonality.

Core formulas

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Simple Exponential Smoothing:
l_t = α y_t + (1 - α) l_(t-1)
ŷ_(t+h) = l_t

Holt's Linear Trend:
l_t = α y_t + (1 - α)(l_(t-1) + b_(t-1))
b_t = β (l_t - l_(t-1)) + (1 - β) b_(t-1)
ŷ_(t+h) = l_t + h b_t

Holt-Winters Additive:
l_t = α (y_t - s_(t-m)) + (1 - α)(l_(t-1) + b_(t-1))
b_t = β (l_t - l_(t-1)) + (1 - β) b_(t-1)
s_t = γ (y_t - l_t) + (1 - γ) s_(t-m)
ŷ_(t+h) = l_t + h b_t + s_(t-m+h)

Interview follow-up

• Additive seasonality is appropriate when seasonal amplitude is roughly constant.
• Multiplicative seasonality is better when seasonal amplitude scales with the level.
• ETS is often a strong baseline because it is simple, interpretable, and fast.

Q: When would you choose a classical model over a deep model?

Strong answer

• The dataset is small.
• The signal is mostly trend plus seasonality.
• Interpretability matters.
• Training and inference must be cheap and stable.
• You need a trustworthy baseline before trying more complex architectures.

Good line to say

I usually start with seasonal naive, ETS, ARIMA, or Prophet-like baselines, because if a complex model cannot beat them on rolling-origin backtests, it is not production-worthy yet.