Auto-Correlation on Unadjusted (Raw) Returns through lag 48
Here is the Auto-Correlation Function (ACF) of raw returns out through lag 48. We see a pattern here that suggests that values of Returns follow a pattern that is strong with t=12. As we know, home prices are seasonal, ex. Home prices tend to be higher in summers than winters, below ACF chart clearly depicts this relation.
Auto-Correlation on Adjusted Returns through lag 48
Here is the Auto-Correlation Function (ACF) of Adjusted returns out through lag 48. Now, we see a very high correlation of Rt with Rt-1 and it keeps declining as we go backwards. AR(1) model should fit well for these adjusted returns.
Applying AR(1) model and checking Residuals
After importing the adjusted returns we execute the below commands in Matlab to fit an AR(1) model. Beta value returned is 0.6917 with 0 intercept.
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