How to extend and override array methods in typescript

now i want to implement an array proxy. here is my code

class ArrayProxy<T> extends Array<T> {

    constructor(data: T[]) {
        super(...data);
    }

    push(...items: T[]): number {
        var res = super.push(...items);
        console.log("push invoked!");
        // some code to do extra operation.
        return res;
    }
}

var foo = new ArrayProxy(["aa","bb"]);
foo.push("cc");

      

        
        
        
      

    

it seems that my push override methods were not being called. and the variable foo is an Array instance other than ArrayProxy.
my typescript version: 2.3.2
tsconfig.json

{
    "compilerOptions": {
        "emitDecoratorMetadata": true,
        "experimentalDecorators": true,
        "moduleResolution": "classic",
        "target": "es5",
        "module": "system",
        "outFile": "js/test.js"
    }
}

      

        
        
        
      

    

MyTest
I was looking for some solution but couldn't.

class MyNewArray<T> extends Array<T> {
    getFirst() {
        return this[0];
    }
}

var myArray = new MyNewArray<string>();
myArray.push("First Element");
console.log(myArray.getFirst()); // "First Element"

      

        
        
        
      

    

from David Sherret
but I got the error.

Uncaught (in promise) Error: myArray.getFirst is not a function
  Evaluating http://localhost:8080/application/test/application/ts/bind_test
  Loading application/ts/bind_test
    at Object.execute (test.js:1733)
    at j (system.js:4)
    at E (system.js:4)
    at O (system.js:4)
    at system.js:5

      

        
        
        
      

    

Update it works when I add Object.setPrototypeOf(this, ArrayProxy.prototype);

after supercall in the ArrayProxy constructor. thanks to @Aluan Haddad.