→ The provided equation represents an autoregressive model of order 1 (AR(1)). It describes Xt as a function of its immediately prior value (Xt−1) plus white noise.
Key identifiers:
No differencing (so not ARIMA).
No moving average term (so not ARMA).
No seasonal component (so not SARIMA).
Why the other options are incorrect:
A: ARIMA(1,1,1) includes integration and MA terms, which are absent here.
B: ARMA(1,1) includes both AR and MA terms, but only AR is present.
C: SARIMA involves seasonal and differencing components — not applicable here.
Official References:
CompTIA DataX (DY0-001) Study Guide – Section 3.5:“AR(p) models describe a variable as dependent on its previous values with no differencing or moving average.”
Time Series Analysis Textbook, Chapter 4:“Xt = ϕXt-1 + εt describes an AR(1) process when εt is white noise.”
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