That string is in Json format. Use the Json.NET library to deserialize it:
string str = "[[1502942400000,"4261.48000000","4261.48000000","4261.48000000","4261.48000000","1.77518300",1502942459999,"7564.90685084",3,"0.07518300","320.39085084","7960.54017996"],[1502942460000,"4261.48000000","4261.48000000","4261.48000000","4261.48000000","0.00000000",1502942519999,"0.00000000",0,"0.00000000","0.00000000","7960.45262989"]]";
double[][] res = JsonConvert.DeserializeObject<double[][]>(str);
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…