A grocery chain maintains demand histories for three products.

A data analyst must select one model for each product.

Which mapping is most appropriate?

A warehouse forecasts seasonal monthly demand using Holt-Winters. During testing, the predictions reproduce the broad annual seasonal pattern but consistently underestimate demand during the final three months.

The analyst proposes the following actions.

I. Examine whether the demand level or trend changed during the test period.

II. Immediately increase γ to its maximum value, without further analysis.

III. Compare residuals across time to identify systematic bias.

IV. Confirm that seasonal periodicity was specified correctly.

Which combination is the most defensible?

A student uses the following code to fit and evaluate Holt-Winters forecasting on monthly demand data:

from statsmodels.tsa.holtwinters import ExponentialSmoothing

from sklearn.metrics import mean_squared_error

model = ExponentialSmoothing(

    data,

    trend="add",

    seasonal="add",

    seasonal_periods=12

).fit()

forecast = model.forecast(6)

rmse = mean_squared_error(data[-6:], forecast) ** 0.5

Assume data contains 60 monthly observations, and the objective is to evaluate the model on the final six months.

What is the most serious methodological problem?

A demand forecasting system uses Holt-Winters with optimized smoothing parameters. Consider the following statements.

I. A high α generally makes the level component more responsive to recent observations.

II. A low β guarantees that future forecasts will have almost no trend.

III. A low γ makes the seasonal component update more slowly.

IV. Optimizing α, β and γ guarantees the lowest possible RMSE on the test dataset.

Which statements are correct?

Two SES models forecast tomorrow’s inventory demand. Both start with a forecast of 100 units. Actual demand over the next two days is 140 and 100 units, respectively.

• Model A uses α = 0.8.

• Model B uses α = 0.2.

After incorporating both actual demand observations, which statement about the forecast for Day 3 is correct?

Consider the following code:

from statsmodels.tsa.holtwinters import ExponentialSmoothing

model = ExponentialSmoothing(

    train,

    trend=None,

    seasonal=None

).fit(optimized=True)

prediction = model.forecast(5)

Which statement best describes this model?

Three models are tested on the same demand observations.

A supply chain manager wants to minimize the influence of occasional unusually large forecasting errors.

Which recommendation is most justified by these results?

A company's monthly demand has a repeating annual seasonal pattern. Its average demand increases significantly over several years, but the absolute magnitude of seasonal variations remains nearly unchanged.

Assertion (A): Additive seasonality may be more suitable than multiplicative seasonality.

Reason (R): Multiplicative seasonality is generally appropriate when seasonal effects change proportionally with the series level.

A retail store experiences a steady upward trend in demand. The manager uses Simple Exponential Smoothing with α = 0.9 and observes that the fitted values closely follow recent demand.

Assertion (A): Increasing α sufficiently allows SES to model a persistent upward trend in the same way as Holt’s model.

Reason (R): A larger α increases the influence of the most recent observation on the updated level estimate.

Choose the correct option.

Consider the following practices when comparing SES, Holt and Holt-Winters models on monthly warehouse shipment data.

I. Using chronological training and testing periods preserves the forecasting order.

II. A model with lower training RMSE must also have lower test RMSE.

III. A model with lower MAE can nevertheless have higher RMSE than another model.

IV. Seasonality should be determined entirely by whichever model has the most parameters.

Choose the correct combination.