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fin.Box-Jenkins-AR1-forecast Calculator
Generates 1-step and 2-step-ahead forecasts from an AR(1) (first-order autoregressive) model fitted to a time series. AR(1) models are the simplest econometric forecasting tool — mean reversion is the implication when the AR coefficient is between 0 and 1.
Inputs
Mu
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Y Last
Reference formula or conversion factor shown for context.
Sigma E
Average spread around the mean. In a normal distribution: 68% within ±1 SD, 95% within ±2 SD, 99.7% within ±3 SD.
Results
1-step-ahead forecast ŷ(t)
Reference formula or conversion factor shown for context.
2-step-ahead forecast ŷ(t+2)
Reference formula or conversion factor shown for context.
95% prediction interval lower
Sample size or count used in the calculation.
95% prediction interval upper
Sample size or count used in the calculation.
ŷ(t) = μ + φ₁·(y_{t−1} − μ)
Reference formula or conversion factor shown for context.