How to interpret probit model results

Hi everyone,

I have a question concerning the interpretation of the results of a probit model. I have a timseries of a binary variable Y (nx1) and a regressor X (nx1). I have estimated several models, one 'normal' and the others are lagged, I estimated the lagged models as follows: glmfit(X(1:n-i,1),Y(1+i:n,1),'binomial','link','probit')

Now I chose my preferred model of lag i based on a manually computed pseudo R squared and made a plot. I plotted both Y and normcdf(const + X*B) on the y-axis over the entire time span. Here const, is the estimated constant and B the estimated Beta coefficient of model with lag i. Now I observe a significant spike each time before Y=1 and now my question is: should I interpret the spike as there will be an occurence of Y in i lags, or should I read this as there will be an occurance of Y in the immediate future. I'm asking this because I want to use the model also out of sample. And btw I did not lag anything for the plot.

Kind regards,

Michael