Statistical Methods & Forecasting Flashcards

In a simple linear regression Y = β₀ + β₁X + ε, the ordinary least squares (OLS) estimator minimizes:

Answer: The sum of squared residuals

OLS finds coefficient estimates by minimizing the sum of squared differences between observed and predicted values.

A non-stationary time series can typically be made stationary by:

Answer: Taking first differences

First differencing removes a unit root (stochastic trend), converting a non-stationary I(1) series to a stationary I(0) series.

The Akaike Information Criterion (AIC) is used to:

Answer: Compare models while penalizing for added complexity

AIC balances model fit against parsimony by penalizing the likelihood for each additional parameter estimated.

When using regression for forecasting, the standard error of the forecast is larger than the standard error of the mean estimate because:

Answer: The forecast includes additional uncertainty from a new individual observation

A forecast interval must account for both the uncertainty in estimating the mean and the natural variability of individual values.

A market analyst observes that error variance increases with the level of the forecasted variable. This pattern is called:

Answer: Heteroscedasticity

Heteroscedasticity means the error variance is not constant but varies systematically, often growing with the scale of the variable.

Which measure expresses forecast error as a percentage of the actual value, making it useful for comparing across different scales?

Answer: MAPE

MAPE (Mean Absolute Percentage Error) divides each absolute error by the actual value, creating a scale-independent accuracy metric.

In regression analysis, omitted variable bias occurs when:

Answer: A relevant variable is excluded and correlated with included predictors

Omitting a relevant variable that correlates with included regressors causes those coefficient estimates to absorb its effect, creating bias.