NOTE: IF you have not set up your workspace yet or have not started with Vue.js, you always can refer to these Tutorials to get started

1. An introduction to Vue Framework?
2. Getting Started with Vue using Fiddle
3. Learn Fast Handling User Inputs & form bindings using Vue
4. Easily Bind Select and Multi-select using Vue
5. Learn to make a ToDo List – Vue Component Creation
6. Vue ToDo list with Delete Option & Global Event Bus – Part II
7. How to Create Global Event Bus using Vue.js?
8. Learn how to work with Computed Properties in VueJS
9. How to Use Vue.js watchers for Async Updates?
10. Make a Basic HTML Editor using Vuejs v-html directive
11. Prevent XSS in Vue.js using Google Caja
12. How does Event Handling work in Vue.js?
13. Namespacing the Filters for Better Maintainability 

var vue = new Vue({
data:{},
filters:{
customFilter:function(){
}
}
});

<span>{{data | customFilter}}</span>

<div id="app">
  <table border=1>
    <tr>
      <th class="invalid">Format</th>
      <th>Result</th>
    </tr>
    <tbody>
      <tr>
        <td>MMM Do YYYY</td>
        <td>{{date | MMMMDoYYYY}}</td>
      </tr>
      <tr>
        <td>YYYY-MM-DD HH:mm</td>
        <td>{{date | YYYY_MM_DD_HH_mm}}</td>
      </tr>
      <tr>
        <td>dddd, MMMM Do YYYY, h:mm:ss a</td>
        <td>{{date | dddd_MMMM_Do_YYYY_h_mm_ss_a}}</td>
      </tr>
    </tbody>
  </table>
</div>

var vue = new Vue({
  el: '#app',
  data: {
    date: 1501283339
  },
  filters: {
    MMMMDoYYYY: function(value) {
      return moment.unix(value).format('MMM Do YYYY');
    },
    YYYY_MM_DD_HH_mm: function(value) {
      return moment.unix(value).format('YYYY-MM-DD HH:mm');
    },
    dddd_MMMM_Do_YYYY_h_mm_ss_a: function(value) {
      return moment.unix(value).format('dddd, MMMM Do YYYY, h:mm:ss a');
    }
  }
});

JSFiddle implementation

NOTE: If you have a complicated Data Manipulation then it’s always better to use Computed property rather than filters. Filters are designed for Text Transformation purpose only and must not be abused.