I modeled a directional prediction of a time series. In every step, I predict next direction of that series (up or down). Currently I have a lag in predicted outputs compared to real outputs.
For example, in above outputs, first figure is real direction and second figure is predicted direction (red star: next up trend, blue star: next down trend). So we can see that in prediction outputs we have 1-step lag. Totally, I have better results If I don't have this lag in prediction. I saw this link which mentions that this is a problem related to "naive predictor". We have same behavior in this problem (inputs: different lags of time series, output: 1 or 0)? How can I resolve that? Currently, I'm using logistic regression in this model.
- I checked my input data using unit root test. The input data was non-stationary so I transformed it to stationary using different methods (difference,detrend, etc.) but I have same problem. Is this same problem mentioned HERE?