Logit Model_Predictive Regression

#1
I want to know your mind about one point related to logit regression model. I am using logit model for my analyzing. My key independent variable is the lagged; hence, it is predictive regression. So, my dependent variable is 0 and 1. These 0 and 1 is related to the time of the day. To make it more clear, I have minutely time-series data for one day. In one day, we have 24 hours * 60 minutes = 1440 rows as my dependent variable. The dependent variable is "0" from 1st to 600th rows and from 900th to 1440th rows - it is "normal period". However, the dependent variable is "1" from 600th to 900th rows - let's say it is "abnormal period". In its simplest from, my dependent and independent variables are:

Number of rows Dependent variable Independent variable
1 0 0.1
2 0 0.15
. . .
. . .
600 0 0.17
601 1 0.13
. . .
. . .
900 1 0.22
901 0 0.19
. . .
. . .
1440 0 0.21

I am interested the examine the predictive power of my key independent variable. Now I use the first lag of my independent variable as my KEY VARIABLE. Actually, I am confusing about the result of my regression. The issue is, I guess that the majority part of the predictive power of lagged variable will come from the "abnormal period" rather than "normal period". What do you think about that?