# Lag between forecast and actual value without lagged dependent variable as features

I'm trying to predict a time series using a model-tree (Cubist) and I'm getting a strange behavior, I think. This is a stock market data but I'm not using the raw level of the stock price but change in the trend of the stock price. I did expect the prediction accuracy to be poor but I didn't expect the forecast to be the actual values lagged. The reason I didn't expect this is that I'm not using lagged values of the dependent variable as features.

There are lot of questions here regarding the forecast just being a lag of the actual values and the remedy seems to be to not include lagged values of the dependent variable in your regression.

So my question is if it is normal to get a forecast that is just the actual values lagged even though I'm not using lags of the dependent variable as features?

• If the stock market is efficient, the best forecast for $x_t$ might just be $x_{t-1}$. So perhaps you are discovering that the price is unpredictable beyond its last observed value? That would not be too bad, actually. A forecast not equal to the last observed value is quite likely to be more wrong than the last observed value. Nov 6 '18 at 20:40
• Thank you for a quick answer. What I don't get is that the regression doesn't include x_t-1 so how does the model know what x_t-1 is in the first place? I get it that if I have x_t-1 as an input to the model, then this forcast would make sense to me. Nov 6 '18 at 20:54
• Perhaps your other variables manage to approximate $x_{t-1}$ well enough? In any case, $x_{t-1}$ seems like valuable information to me, so not including it in the model might be wasting it. Nov 6 '18 at 20:58

If the stock market is efficient, the best forecast for $$x_{t}$$ might just be $$x_{t-1}$$. So perhaps you are discovering market efficiency, i.e. that the price is unpredictable beyond its last observed value? That would not be too bad, actually. A forecast not equal to the last observed value is quite likely to be more wrong than the last observed value, unless the market is grossly inefficient.
the regression doesn't include $$x_{t-1}$$ so how does the model know what $$x_{t-1}$$ is in the first place?
Perhaps your other variables manage to approximate $$x_{t-1}$$ well enough?
In any case, $$x_{t-1}$$ seems like valuable information to me, so not including it in the model might be wasting it.