![]() ![]() Proof: click here for an alternative proof. Property 7: The variance of the y i in a stationary AR(2) process is Proof: Follows from Property 4, as shown above. Property 6: The following hold for a stationary AR(2) process This value can be re-expressed algebraically as described in Property 7 below. We can also calculate the variance as follows: Create a Correlation Matrix from Historical Data 5.16. How RISK Computes Rank-Order Correlation 5.15. Excel Reports a Correlation Different from What I Specified 5.14. Changing Correlation Coefficients During a Simulation 5.12. Property 5: The Yule-Walker equations also hold where k = 0 provided we add a σ 2 term to the sum. Correlation Matrix Exceeds Excels Column Limit 5.11. These are known as the Yule-Walker equations. Here we assume that γ h = γ -h and ρ h = ρ -h if h < 0, and ρ 0 = 1. Similarly the autocorrelation at lag k > 0 can be calculated as It turns out that such a process is stationary when |φ 1| 0 can be calculated as Similar to the ordinary linear regression model, we assume that the error terms are independently distributed based on a normal distribution with zero mean and a constant variance σ 2 and that the error terms are independent of the y values. Thinking of the subscripts i as representing time, we see that the value of y at time i+1 is a linear function of y at time i plus a fixed constant and a random error term. In a simple linear regression model, the predicted dependent variable is modeled as a linear function of the independent variable plus a random error term.Ī first-order autoregressive process, denoted AR(1), takes the form ![]()
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