Analysis of data for an autoregressive forecasting model produced the following tables: The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively.The forecast value predicted by the model for July is ___.
A)36.91
B)83.67
C)218.71
D)174.41
E)191

Question

Analysis of data for an autoregressive forecasting model produced the following tables:   The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively.The forecast value predicted by the model for July is ___.
A)36.91 
B)83.67 
C)218.71 
D)174.41 
E)191

Quizplus · Accepted Answer

The autoregressive model forecasts future values based on past values in the time series. In this case, the model generated the following equation:

y_t = 102.5 + 0.346*y_(t-1)

where y_t represents the value of the time series at time t, and y_(t-1) represents the value of the time series at the previous time step.

Using this equation for July, we can substitute the actual value for June (y_(t-1) = 54) and solve for y_t:

y_t = 102.5 + 0.346*54
y_t = 102.5 + 18.68
y_t ≈ 121.18

Therefore, the forecasted value for July is approximately 121.18. However, this is not one of the answer choices provided. We can compare this forecasted value to the actual value of 191 for July, which is much higher. This suggests that the model may not be accurately capturing the behavior of the time series, or that there may be other factors influencing the time series that the model does not account for.

The answer choice closest to the actual value of 191 is C (218.71). While this value is still off from the actual value, it is the best choice among the options provided.

Analysis of Data for an Autoregressive Forecasting Model Produced the Following