if anyone interested in chatting, pls add me pepphell @ gmail. com I am studying Quant and am in need of help. Book says for time series model to be valid, it must be Covariance stationary. But then it say that for a time series that is covariance stationary, the OLS procedure for AR (1) won’t work. Why the f is going on? First they tell you to use it then say it wont work.
also is AR, and AR(1) same thing? autoregressive of first order?
ya they are the same. AR(1) is just one type of AR models.
I just skip quant, really hard to understand about the time series thing…
AR(1) first order, AR(2) second order…AR(n) n order… these are just corresponding to the time period in the lag… i.e., t-1 is 1 lag… t-2 is a 2 lag not sure if you were talking baout this… but for a random walk model ( Xt = Xt-1) then yes you are not able to use it, and need to either use first differencing or Unit Root test…reason being is that covariance stationarity requires a ‘mean-reverting level’ which this clearly doesn’t have ( b0 / 1 - b1) since this slope intercept is 1 (can’t divide by zero and hence not covariance stationarity)… not a problem though IF the two time series are cointegrated. not sure if this makes sense, or is accurate… half asleep about to hit the hay
I seem to be in a differant boat than most and like quant so I will try and shed some light on it for you. AR is not that hard if you can get your head around it. If you think of a normal regression, you are predicting a value from some variable, lets say you are predicting stock returns from stock P?E ratios. So you get y=mx+b. Ok hope we all have that from alg 1. We also have multi reg in CFAI and that is just using P/E’s and what ever else to determine value, so just add mx’s. SO getting wordy but to the point. An AR model is trying to predict, lets say, stock price, from a previous value of itself. So dont get confused, we are just saying is there a relationship between the stock price in Q1 and Q2. Or its saying can we take the Q1 price and fit a regression to it to predict the next periods value. Something CFA loves here is seasonality. So maybe there is not a lot of predictive power in the AR(1) model, which in our case is the previous quarters price, but let say we are looking at a toy stores earnings. We may be able to predict a toy stores earnings based of an AR(4) model which just says we are trying to predict earnings in this quarter based of the earnings 4 quarters ago. So for toy store that would be regressing Q4 agains the previous Q4 data or Q1 against previous Q1. Dont bother yourself with know what the implications of covariance stationarity are just know that if AR models dont have a mean reverting level, they are not stationary and can not be used. You can correct them with first differancing however. A whole nother topic. Too much studying hope this helps though.
Spent an hour on understanding time series…Use the last LOS from Schweser or CFAI…Its really helpful…Also read the CFAI summaries…
Yea I get it too now, although a bit late now.