Time Series Analysis for Categorical Data Output

Suppose I am having dataset which consist of date as one column and fruits as second column which is categorical data having set of 4 different fruits in that column and my output column has 0's and 1's whether the particular fruit sold at that time or not.Based on this, I can able to predict for pattern like,what will be the status of particular fruit selling after some years?

How to do time series analysis for those categorical data?

Any suggestions would be really helpful.Since I am new to the time series data analysis.Please help me in this