dateonclicknextprevious.html

<script>
var picker = $('#test').pickadate({
  format: 'dd/mm/yyyy'
}).pickadate('picker');

$('#previous_day, #next_day').click(function(e) {
  e.preventDefault();
  setDate($(this).data('diff'));
})

function setDate(diff) {
  var date = new Date(picker.get('select').pick);
  var newDate = date.setDate(date.getDate() + diff);
  picker.set('select', newDate)
}
</script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/picker.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/picker.date.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/picker.time.js"></script>

<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/themes/default.css" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/themes/default.date.css" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/pickadate.js/3.5.6/compressed/themes/default.time.css" />

<form method="post">
  <a href="#" id="previous_day" data-diff="-1">previous day</a>
  <input type="text" id="test" data-value="01/11/2017">
  <a href="#" id="next_day" data-diff="1">next day</a>
  <button type="submit">Submit</button>
</form>