Vue components can have a watch property which is an object. The object keys need to be the name of the prop or data that needs to be watched, and the value is a function that is invoked when the data changes.

https://v2.vuejs.org/v2/guide/computed.html#Computed-vs-Watched-Property

Vue.component('component', {

  template: '#component',

  data: function () {

    return {

      dataToBeWatched: ''

    }

  },

  methods: {

    change: function (e) {

      var that = this;

      setTimeOut(function() {

        that.dataToBeWatched = 'data changed';

      }, 2000);

    },

    makeSmthWhenDataChanged: function () {

      // ajax request when dataToBeWatched changed or when dataToBeWatched isn't empty

    }

  },

  watch: {

      dataToBeWatched: function(val) {

          //do something when the data changes.

          if (val) {

              this.makeSmthWhenDataChanged();

          }

      }

  }

});