How do I filter an array with TypeScript in Angular 2?

You need to put your code into ngOnInit and use the this keyword:

ngOnInit() {
  this.booksByStoreID = this.books.filter(
          book => book.store_id === this.store.id);
}

You need ngOnInit because the input store wouldn't be set into the constructor:

ngOnInit is called right after the directive's data-bound properties have been checked for the first time, and before any of its children have been checked. It is invoked only once when the directive is instantiated.

(https://angular.io/docs/ts/latest/api/core/index/OnInit-interface.html)

In your code, the books filtering is directly defined into the class content...