Autoregressive Model Forecasting

XYZ Corp. has conducted an analysis of its quarterly sales over the past five years to assess forecasting possibilities. The sales data is represented as a time series, and the company is interested in modeling its future sales using an autoregressive model. The autoregressive model installed is a simple AR(1) model given by the equation:

Sales_t = α + β Sales_t-1 + ε_t

Where:

• Sales_t = sales in the current quarter
• α = constant term
• β = coefficient of the lagged sales
• ε_t = error term

After analyzing their data, the company estimates α to be 200 and β to be 0.7. If the sales for the last quarter were $1500, what is the forecasted sales for the next quarter?