You provided too little information for a sensible answer.

For many binary data sets with time dependencies, a time series probit regression model (and a time series logit model) are a sensible starting point for analysis.

Without more information, a better answer cannot be given. Is it acceptable from a theoretical point of view to make the assumptions underlying this model? Is it acceptable from a statistical scrutiny of the data to carry on with these assumptions? Etc.

 Alright Casper. Let me pose the same question in the form of an example. Lets say that in a restaurant a chair is occupied by a customer. He can sit there for as long as he wants to depending on various factors like the ambience of the surrounding, quality of food, friendliness of staff etc. The time duration would be split into blocks of 15 mins i.e. every 15 mins a researcher would observe if he is still sitting there or has he left. The customer would be assigned a dichotomous value of 0 if he leaves and 1 if he still continues to occupy the chair. 

Time          Customer Sitting         No. of servings/Food quality

7:00 pm                1                                            5/Good

7:15 pm                1                                            5/Good

7:30 pm                1                                            5/Good

7:45 pm                1                                            5/Good

8:00 pm                1                                            5/Good

8:15 pm                0

8:30 pm                1                                            3/Average

8:45 pm                1                                           3/Average

9:00 pm                0

9:15 pm                1                                         2/Poor

9:30pm                 0

In the above example a customer arrives at the restaurant and sits there at 7:00 pm and remains there till 8:00 pm. After that he leaves and another customer occupies that chair and continues till 9:00 pm. Second customer leaves after that and third one arrives at 9:15pm and so on and so forth. 

In this illustration the occupancy of the chair by a customer is the dependent variable taking values 1 or 0, and food quality/no. of servings would be  independent variables. 

I want to ask if logit and probit regression can be applied on such a problem. Is it a violation of criteria of independence of dependent variable that the value following "0" has to be "1". Can logit and probit regression be applied with some modifications, if yes what are those? Can logit/probit regression be applied on a time series data like this without any loss of generality? 

Thanks in Advance

Naseem