moment.js

var momento = moment(556095600000); // 1987-08-16T07:00:00.000Z
var day   = momento.date();         // 16
var month = momento.month() + 1;    // 8
var year  = momento.year();         // 1987

var timeperiods = {
    year  : moment(year, "YYYY").toISOString(),                                // 1987-01-01T08:00:00.000Z
    month : moment(month + "-" + year, "MM-YYYY").toISOString(),               // 1987-08-01T07:00:00.000Z
    day   : moment(day + "-" + month + "-" + year, "DD-MM-YYYY").toISOString() // 1987-08-16T07:00:00.000Z
}

native.js

var timestamp = new Date(556095600000); // 1987-08-16T07:00:00.000Z
var day   = timestamp.getUTCDate();     // 16
var month = timestamp.getMonth() + 1;   // 8
var year  = timestamp.getFullYear();    // 1987

var timeperiods = {
    year  : new Date(year).toISOString(),            // 1970-01-01T00:00:01.987Z Off by 17 years
    month : new Date(year, month).toISOString(),     // 1987-09-01T07:00:00.000Z Off by 1 month
    day   : new Date(year, month, day).toISOString() // 1987-09-16T07:00:00.000Z Off by 1 month
}

Oooops... here's a fixed version for native

var timestamp = new Date(556095600000); // Sun Aug 16 1987 00:00:00 GMT-0700 (PDT)
var day   = timestamp.getUTCDate();     // 16
var month = timestamp.getMonth() + 1;   // 8
var year  = timestamp.getFullYear();    // 1987

var timeperiods = {
    year  : new Date(year, 0, 1).toISOString(),         // 1987-01-01T08:00:00.000Z
    month : new Date(year, month-1).toISOString(),      // 1987-08-01T07:00:00.000Z
    day   : new Date(year, month-1, day).toISOString()  // 1987-08-16T07:00:00.000Z
}

Updated JSperf to run more optimized versions of the code above while still getting the same final output: http://jsperf.com/moment-js-vs-native-date

Optimized moment.js version:

var momento = moment(556095600444)

var timeperiods = {
  "year": momento.clone().startOf('year').toISOString(),
  "month": momento.clone().startOf('month').toISOString(),
  "week": momento.clone().startOf('week').toISOString(),
  "day": momento.clone().startOf('day').toISOString()
}

Optimized native version:

Date.prototype.getStartOfDay = function() {
  this.setHours(0, 0, 0, 0)
  return this
}

Date.prototype.getStartOfWeek = function() {
  if (this.getDay()) {
    this.setHours(-Math.abs(this.getDay() - 1) * 24, 0, 0, 0)
  } else {
    this.setHours(-6 * 24, 0, 0, 0)
  }
  return this
}

Date.prototype.getStartOfMonth = function() {
  if (this.getDate()) {
    this.setHours(-Math.abs(this.getDate() - 1) * 24, 0, 0, 0)
  } else {
    this.setHours(0, 0, 0, 0)
  }
  return this
}

Date.prototype.getStartOfYear = function() {
  if (this.getDayOfYear()) {
    this.setHours(-Math.abs(this.getDayOfYear() - 1) * 24, 0, 0, 0)
  } else {
    this.setHours(0, 0, 0, 0)
  }
  return this
}

Date.prototype.getDayOfYear = function() {
  var date = this.clone(this)
  date.setMonth(0, 0)
  return Math.round((this - date) / 8.64e7)
}

Date.prototype.clone = function() {
  return new Date(this.getTime())
}

var date = new Date(556095600444)

var timeperiods = {
  "year": date.clone().getStartOfYear().toISOString(),
  "month": date.clone().getStartOfMonth().toISOString(),
  "week": date.clone().getStartOfWeek().toISOString(),
  "day": date.clone().getStartOfDay().toISOString()
}