My component with to way data bind is in error

I have my component responsible for search input and stuff.

import { Component, Output, Input, EventEmitter } from '@angular/core';

@Component({
    selector: 'header-lista',
    templateUrl: './header-lista.component.html',
})
export class HeaderListaComponent {

    @Input() pesquisar: string;
    @Output() pesquisarChanged = new EventEmitter<string>();

    public onPesquisarChanged() {
        console.log('chamou');
        this.pesquisarChanged.emit(this.pesquisar);
    }
}

Each time something is typed my onPesquisarChanged is activated.

I have my other component that is responsible for the list and for mounting the table.

import { Component, OnInit } from '@angular/core';

import { CidadeService } from './cidade.service';

@Component({
    selector: 'ngx-lista-cidades',
    templateUrl: './cidade.component.html',
    providers: [ CidadeService ],
})

export class ListaCidadesComponent implements OnInit {

    private cidades: object[];
    private coluna: string;
    private critererioBusca: string = '';

    constructor(private cidadeService: CidadeService) {}

    teste() {
        console.log('aqui', this.critererioBusca);
    }

    ngOnInit() {
        this.ListaTodasCidades();
    }

    private ListaTodasCidades() {

        this.cidadeService.TodasCidades().then((response: object[]) => {
            this.cidades = response.sort(function(a: any, b: any) {
                return a.NOME < b.NOME ? -1 : a.NOME > b.NOME ? 1 : 0;
            });
        }, (error) => {
            console.log(error);
        });
    }

    private ordena(coluna) {

        if (this.coluna === coluna) {
            this.cidades.reverse();
        } else {
            this.cidades.sort((a, b) => {
                return a[coluna] < b[coluna] ? -1 : a[coluna] > b[coluna] ? 1 : 0;
            });
        }
        this.coluna = coluna;
    }
}

The expected behavior would be to receive the value of @Input() pesquisar: string; and with this value carry out the criterion pipe. It turns out that in the test method I have my critererioBusca is always empty.

If I assign something to critererioBusca it will be received by @Input() pesquisar: string; , but the opposite path does not happen.

<header-lista [(pesquisar)]="critererioBusca"></header-lista>

What am I doing wrong?