You are given an annual time series with 40 consecutive values and asked to fit a fifth-order autoregressive model. Which of the original 40 values do you need for forecasting?
To fit a fifth-order autoregressive (AR) model, you need the original 40 values to estimate the coefficients of the model. However, for forecasting, you will only need the most recent 5 values from the time series data. This is because an autoregressive model uses a linear combination of the past values of the series to predict the future values, and the order of the model determines how many past values are included in the forecasting equation. In this case, a fifth-order AR model will only consider the most recent 5 values to generate forecasts.
