Use split on string:

var array = coolVar.split(/-/);

Here is my explanation with a jsfiddle.

//this is already a valid javascript object
//no need for you to use JSON.parse()
var obj1 = {"name":"abcd", "details":"1234"};
console.log(obj1);

//assume you want to pass a json* in your code with an ajax request
//you will receive a string formatted like a javascript object
var str1 = '{"name":"abcd", "details":"1234"}';
console.log(str1);

//in your code you probably want to treat it as an object
//so in order to do so you will use JSON.parse(), which will
//parse the string into a javascript object
var obj2 = JSON.parse(str1);
console.log(obj2);

JSON, or JavaScript Object Notation, is a minimal, readable format for structuring data. It is used primarily to transmit data between a server and web application, as an alternative to XML.

See an example below (this example uses the native JSON object). My changes are commented in CAPITALS:

function Foo(obj) // CONSTRUCTOR CAN BE OVERLOADED WITH AN OBJECT
{
    this.a = 3;
    this.b = 2;
    this.test = function() {return this.a*this.b;};

    // IF AN OBJECT WAS PASSED THEN INITIALISE PROPERTIES FROM THAT OBJECT
    for (var prop in obj) this[prop] = obj[prop];
}

var fooObj = new Foo();
alert(fooObj.test() ); //Prints 6

// INITIALISE A NEW FOO AND PASS THE PARSED JSON OBJECT TO IT
var fooJSON = new Foo(JSON.parse('{"a":4,"b":3}'));

alert(fooJSON.test() ); //Prints 12

There is no standard JSON representation of dates. You should do what @jAndy suggested and not serialize a DateTime at all; just send an RFC 1123 date string ToString("r") or a seconds-from-Unix-epoch number, or something else that you can use in the JavaScript to construct a Date.

Description

This will allow for the numerical ascii character of any character. However, if you only have quotations to remove it isn't too much to run a replace.

var str = "[["2016-11-17",771.22998],["2016-11-16",764.47998],["2016-11-15",758.48999],["2016-11-14",736.080017],["2016-11-11",754.02002],["2016-11-10",762.559998],["2016-11-09",785.309998],["2016-11-08",790.51001],["2016-11-07",782.52002],["2016-11-04",762.02002],["2016-11-03",762.130005],["2016-11-02",768.700012],["2016-11-01",783.609985],["2016-10-31",784.539978]]";
// regex to get the ascii number
var r = /\&#(\d\d);/gi;
// replaces each numerical ascii character with their character representation
str = str.replace(r, function (match, grp) {
    return String.fromCharCode(parseInt(grp)); } );

console.log(JSON.parse(str));