A second-order autoregressive model for annul average mortgage rate is:
Rate i = 0.5 + 1.0(Rate) i-1 - 0.5 (Rate) i-2
If the average mortgage rate in 2015 was 2.0, and in 2014 was 4.0, the forecast for 2017 is
To forecast the average mortgage rate in 2017 using the given second-order autoregressive model, we need to substitute the values for 2015 and 2014 into the equation:
Rate(2015) = 2.0
Rate(2014) = 4.0
Using the equation:
Rate(2017) = 0.5 + 1.0 * Rate(2015) - 0.5 * Rate(2014)
Substituting the values:
Rate(2017) = 0.5 + 1.0 * 2.0 - 0.5 * 4.0
Rate(2017) = 0.5 + 2.0 - 2.0
Rate(2017) = 0.5
Therefore, the forecast for the average mortgage rate in 2017 is 0.5.
To forecast the average mortgage rate in 2017 using the given second-order autoregressive model, we need to substitute the previous two rates into the equation.
Given:
Rate in 2015 = 2.0
Rate in 2014 = 4.0
Let's calculate the forecast for 2017 step by step:
Step 1: Substitute the known values into the equation:
Rate 2015 = 2.0
Rate 2014 = 4.0
Rate 2016 = 0.5 + 1.0(2.0) - 0.5(4.0)
Step 2: Calculate the forecast for 2017 using the equation:
Rate 2017 = 0.5 + 1.0(Rate 2016) - 0.5(Rate 2015)
Let's substitute the calculated value of Rate 2016 into the forecast equation:
Rate 2017 = 0.5 + 1.0(0.5 + 1.0(2.0) - 0.5(4.0)) - 0.5(2.0)
Step 3: Simplify the equation:
Rate 2017 = 0.5 + 0.5 + 2.0 - 1.0 - 1.0 + 1.0
Step 4: Calculate the result:
Rate 2017 = 2.0
Therefore, the forecasted average mortgage rate for 2017 using the given second-order autoregressive model is 2.0.
To find the forecast for 2017, we will use the second-order autoregressive (AR) model provided. The model suggests that the mortgage rate in any given year (Rate i) depends on the rates in the previous two years (Rate i-1 and Rate i-2). Here's how we can find the forecast for 2017:
Step 1: Substitute the known values into the model.
Rate 2015 = 2.0
Rate 2014 = 4.0
Rate 2015 = 0.5 + 1.0(Rate 2014) - 0.5(Rate 2013)
Step 2: Rearrange the equation to solve for Rate 2013.
Rate 2013 = (Rate 2015 - 0.5 - 1.0(Rate 2014)) / -0.5
Step 3: Calculate the forecast for 2017 using the obtained value for Rate 2013.
Rate 2017 = 0.5 + 1.0(Rate 2016) - 0.5(Rate 2015)
Step 4: Substitute Rate 2013 as Rate 2016 in the forecast equation.
Rate 2017 = 0.5 + 1.0(Rate 2013) - 0.5(Rate 2015)
By following these steps, you can calculate the forecasted mortgage rate for 2017 based on the given second-order autoregressive model and the known rates for 2015 and 2014.