global String query;

global my_ProcessPurge_Batch() {
 //initialize query string here
}

global Database.QueryLocator start(Database.BatchableContext BC) {
    return Database.getQueryLocator(query);
}

global void execute(Database.BatchableContext BC, List<sObject> scope) {
    //some DML statements here
}

global void finish(Database.BatchableContext BC) {
   //send email of the result
  //schedule next batch
  my_ProcessPurge_Batch nextBatch = new my_ProcessPurge_Batch();
  //job should start executing after 24 hrs
  //scope is 1000
  System.scheduleBatch(nextBatch, 'my_ProcessPurge_Batch', 1440, 1000);
}

@isTest static void testProcessPurge() {
    Test.startTest();
    //populate test data
    //start batch
    my_ProcessPurge_Batch purgeBatch = new my_ProcessPurge_Batch();
    database.executeBatch(purgeBatch);
    Test.stopTest();
}