I wasn’t able to know how can we test if the data is covariance stationary? For Unit Root, we have to to conduct DF test… Not sure what should be conducted to test for covariance stationary?? Any thoughts?
I skipped Quant so unfortunately I can’t help you with this.
I may be wrong with this (I’m just going off memory), but I don’t believe there is a formal test that we have to be aware of for the purpose of the exam. Just look at the absolute value of b1, and if it’s greater than 1, the data is not covariance stationary.
Think of it this way, if you have an autoregressive model that has a unit root then it is not covariance stationary. There is a general test for covariance stationary itself however. Meaning you may have a time series model that is not autoregressive, and in that case we dont know how to test for covariance stationarity. At least CFAI doesnt offer such a test. I think the most important thing is to remember the first point I made regarding the autoregressive case and the definition of covariance stationarity itself, mainly the properties of time series like mean and the elements of the covariance matrix, which includes variances do not change overtime. Hope this helps
Just adding on to what Intelo has written with my 2 cents. CFAI has the following to check for covariance-stationarity in a time-series at scattered places in the text: 1. Visual cheking by plotting a graph: If the graph is showing a linear up or down trend or showing seasonal patterns, it fails the test for covariance-stationarity. While, up or down sloping line is okay for Linear Regressions involving 2 different variables, it is not okay, if you are regressing a variable with itself (with its lagged value), as in an autoregression. 2. Check if autocorrelations with some lagged values are present: This can checked for in the regression table, to see if autocorrelations for some lagged values are NOT significantly zero. 3. Unit Root / Random Walk: If regression has a unit root, it is not covariance-stationary. Because existence of unit root or random walk will deny a Mean Reverting Value to the forecasted value. And a covariance-stationary time series must have a Mean Reverting Value. If covariance-stationarity is found, it may be cured by transforming the series by First-Differencing it.
the absolute value of b1 must be less than 1- this is the definition for an AR model in its most basic form…from what i picked up in Kaplan and CFAI texts, the LOS doesn’t ask us to compute the modified DF test rather it would say…“we must reject the hypothesis and conclude its NOT cov. stat” doing a book 1 refresher this weekend after i finish equities will add to this if need be