Which of the following statements regarding a mean reverting time series is least accurate? A) If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease. B) If the time-series variable is x, then xt = b0 + b1 xt. C) If the current value of the time series is above the mean reverting level, the prediction is that the time series will increase. Your answer: C was correct! If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease; if the current value of the time series is below the mean reverting level, the prediction is that the time series will increase. ----------- I get why C is incorrect, but why is B a correct statement? Shouldn’t x be equal to x, then xt = b0 + b1 xt-1?
Because there’s nothing wrong with the formula xt = b0 + b1 xt. b0 and b1 are there, which are needed to calculate the mean-reverting level.
so B has a unit root, but since the equation is put together properly, theres nothing “incorrect” about it? you can still calculate a mean reverting level, its just that it give s u a unit root? is that the right logic
the show NY, the formula you were thinking of was an autoregressive model which runs a regression on the lag of itself (xt = b0 + b1 xt-1). Autoregressive models are a form of time series models, but not all time series are autoregressives.
Alrite so in other words “If the time-series variable is x, then xt = b0 + b1 xt” is a correct statement. It is a time series model because the variables are units of time, but not an AR model. Therefore, C is a true statement. Correct?
Show, Correct me if I am wrong, but you are thinking that if your mean reverting level is below the value today, the value today should pull up the mean reverting level - like a grade above the class average pulls up the class average. Try and think of it like this…if our current observation is above the level we expect to prevail in the long run, than we can expect subsequent observations to be lower (closer to the mean reverting level, or they can even be below). C is a false statement because it says that we would expect the next value to be higher, when we want it to be closer to the mean reverting level (lower). We observe mean reversion and because B is simply a statement that the variable x in time t is equal to some intercept number + a slope coefficient, it says nothing to contradict the idea of mean reversion.
tdigz, that’s exactly how i see it. thanks for the good explanation. B is just a theoretical, kind of random statement in my opinion put there to throw you off. it is a time series equation that is not AR (because the independent variable is not a lag of the dependent variable).