ARIMA Models

Question 1

ARIMA Models purpose

Answer 1

Models time series data using autoregression (AR), integration (I), and moving average (MA)

Question 2

A time series is covariance stationary if:

Answer 2

1. Mean Reversion: Fluctuates around a constant long-run mean
2. Constant Variance: Variance does not change over time
3. Decaying Autocorrelation: Correlation between values diminishes over time

Question 3

If a time series is non-stationary:

Answer 3

• Classical regression results are invalid (spurious regression)
• Shocks are permanent, meaning effects do not dissipate over time

Question 4

AR(1) Model:

Answer 4

is a Gaussian error term
The current value depends on its previous value

Question 5

AR(p) Model

Answer 5

A general AR(ρ) model has ρ lagged terms
The roots of the characteristic equation must be greater than 1 in absolute value

Question 6

Strict Stationarity

Answer 6

The joint distribution remains the same regardless of time shifts

Question 7

Covariance Stationarity:

Answer 7

Only the mean, variance, and autocovariance remain constant over time

Question 8

Augmented Dickey-Fuller (ADF) Test

Answer 8

tests for unit roots (non-stationarity)
Critical values vary based on trend vs. purely covariance stationarity

Question 9

If a series has a unit root:

Answer 9

Shocks have permanent effects → No mean reversion

• Predicting future values is difficult**
• Transforms needed (e.g., differencing) to make data stationary for valid regression