Creating line charts with irregular time intervals

The main difference between line charts with irregular time intervals and those with regular time intervals is that the latter has a fixed point interval. The problem with the charts with irregular intervals is that we can't define a single point interval, hence we have to manually provide the date/time against each data point in the series.

Consider the example of conversion rates of USD to Euros at the end of each month. Months fall in the category of irregular time intervals because each month can be 28 (leap year), 29, 30, or 31 days.

In the following example, we will create a line chart with irregular time intervals (months) to analyze the conversion rate of Euros to US Dollars for a period of 7 months starting from September 2013 to March 2014:

(function() {
  $( '#chart_container' ).highcharts({
    chart: {
      type: 'line'
    },
    title: {
      text: 'Historical Conversion Rates of Euro to USD'
    },
    subtitle: {
      text...