PHP PDO connection with static variable in class

Question

I did a research on connections using Singleton in PDO, in most people use a private or protected Construct so that if there is no connection the same is created when instantiating a new Class(), but I wrote the code snippet using static functions and a static variable (that receives the connection) in the class presented below, and by my tests works smoothly without recreating multiple connections, however I’m not entirely sure if the code does the same effect as a Singleton, if someone can give a feedback on the code thank you!

class Conexao {

    private static $conexao = NULL;
    const DB_HOST = "localhost";
    const DB_NAME = "test";
    const DB_USER = "root";
    const DB_PASS = "12345678";

    private static function conectar(){

        if(empty(self::$conexao)){

            try {

                self::$conexao = new PDO('mysql:host='.self::DB_HOST.';dbname='.self::DB_NAME.';charset=utf8', self::DB_USER, self::DB_PASS);
                self::$conexao->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
                if(!self::$conexao){

                    echo "Houve um erro ao efetuar a conexão!";
                    return null;
                }

            } catch(PDOException $e){

                echo "Não foi possível efetuar a conexão ao banco de dados! ".$e->getMessage();
            }

        } else if(isset(self::$conexao)){

            //Conexao já existe
        }

        var_dump(self::$conexao);

        echo "<br>";

        return self::$conexao instanceof PDO ? self::$conexao : null;
    }

    public static function QFA($q, $i){

        return self::conectar()->query($q)->fetchAll(!$i ? PDO::FETCH_ASSOC : NULL);
    }
}

try {

    $x = Conexao::QFA("SELECT * FROM nomes");
    //print_r($x);

    $y = Conexao::QFA("SELECT * FROM nomes");
    //print_r($y);

} catch(PDOException $e){

    print_r($e->getMessage());
}