jquery combobox with cakephp 2x

Question

With the code similar to what jquery ui provides, I am testing this combobox in my cakephp, the problem is that in no way it shows the arrow to enable the dropdown menu, already downloaded jquery ui with the image folder, and it still didn’t work. Code below:

the entire code in my cakephp is like this:

<?php $this->start('script'); ?>
<script src="/js/jquery.currency.js"></script>
 <script>
        var current = new Date();
        var aux = new Date(current.getFullYear(), current.getMonth(), current.getDate() + 7);
        if (aux.getDay() != 1) {
var nextMonth = new Date(aux.getFullYear(), aux.getMonth() + 1, 1);
        var days = Math.floor((nextMonth - aux) / (1000 * 60 * 60 * 24))

        if (days < 7)
        current = new Date(aux.getFullYear(), aux.getMonth(), aux.getDate() + days);
        else
        current = aux;
} else {
current = aux;
}
$("#data-inicio").datepicker({
minDate: current,
        dateFormat: 'dd/mm/yy',
        dayNames: ['Domingo', 'Segunda', 'Terça', 'Quarta', 'Quinta', 'Sexta', 'Sábado', 'Domingo'],
        dayNamesMin: ['D', 'S', 'T', 'Q', 'Q', 'S', 'S', 'D'],
        dayNamesShort: ['Dom', 'Seg', 'Ter', 'Qua', 'Qui', 'Sex', 'Sáb', 'Dom'],
        monthNames: ['Janeiro', 'Fevereiro', 'Março', 'Abril', 'Maio', 'Junho', 'Julho', 'Agosto', 'Setembro', 'Outubro', 'Novembro', 'Dezembro'],
        monthNamesShort: ['Jan', 'Fev', 'Mar', 'Abr', 'Mai', 'Jun', 'Jul', 'Ago', 'Set', 'Out', 'Nov', 'Dez'],
        beforeShowDay: function (date) {
        return [date.getDay() == 1, ""]
        },
});       
 </script>
    <?php $this->end(); ?>
     <?php $this->start('script'); ?>
     <script>
  (function( $ ) {
$.widget( "custom.combobox", {
  _create: function() {
    this.wrapper = $( "<span>" )
      .addClass( "custom-combobox" )
      .insertAfter( this.element );

    this.element.hide();
    this._createAutocomplete();
    this._createShowAllButton();
  },

  _createAutocomplete: function() {
    var selected = this.element.children( ":selected" ),
      value = selected.val() ? selected.text() : "";

    this.input = $( "<input>" )
      .appendTo( this.wrapper )
      .val( value )
      .attr( "title", "" )
      .addClass( "custom-combobox-input ui-widget ui-widget-content ui-state-default ui-corner-left" )
      .autocomplete({
        delay: 0,
        minLength: 0,
        source: $.proxy( this, "_source" )
      })
      .tooltip({
        tooltipClass: "ui-state-highlight"
      });

    this._on( this.input, {
      autocompleteselect: function( event, ui ) {
        ui.item.option.selected = true;
        this._trigger( "select", event, {
          item: ui.item.option
        });
      },

      autocompletechange: "_removeIfInvalid"
    });
  },

  _createShowAllButton: function() {
    var input = this.input,
      wasOpen = false;

    $( "<a>" )
      .attr( "tabIndex", -1 )
      .attr( "title", "Show All Items" )
      .attr("role","button")
      .tooltip()
      .appendTo( this.wrapper )
      .button({
        icons: {
          primary: "ui-icon-triangle-1-s"
        },
        text: false
      })
      .removeClass( "ui-corner-all" )
      .addClass( "ui-button ui-widget ui-state-default ui-button-icon-only custom-combobox-toggle ui-corner-right")
      .mousedown(function() {
        wasOpen = input.autocomplete( "widget" ).is( ":visible" );
      })
      .click(function() {
        input.focus();

        // Close if already visible
        if ( wasOpen ) {
          return;
        }

        // Pass empty string as value to search for, displaying all results
        input.autocomplete( "search", "" );
      });
  },

  _source: function( request, response ) {
    var matcher = new RegExp( $.ui.autocomplete.escapeRegex(request.term), "i" );
    response( this.element.children( "option" ).map(function() {
      var text = $( this ).text();
      if ( this.value && ( !request.term || matcher.test(text) ) )
        return {
          label: text,
          value: text,
          option: this
        };
    }) );
  },

  _removeIfInvalid: function( event, ui ) {

    // Selected an item, nothing to do
    if ( ui.item ) {
      return;
    }

    // Search for a match (case-insensitive)
    var value = this.input.val(),
      valueLowerCase = value.toLowerCase(),
      valid = false;
    this.element.children( "option" ).each(function() {
      if ( $( this ).text().toLowerCase() === valueLowerCase ) {
        this.selected = valid = true;
        return false;
      }
    });

    // Found a match, nothing to do
    if ( valid ) {
      return;
    }

    // Remove invalid value
    this.input
      .val( "" )
      .attr( "title", value + " didn't match any item" )
      .tooltip( "open" );
    this.element.val( "" );
    this._delay(function() {
      this.input.tooltip( "close" ).attr( "title", "" );
    }, 2500 );
    this.input.autocomplete( "instance" ).term = "";
  },

  _destroy: function() {
    this.wrapper.remove();
    this.element.show();
  }
});
 })( jQuery );
 $( "#combobox" ).combobox();
 $( "#toggle" ).click(function() {$( "#combobox" ).toggle();});

</script>
<?php $this->end(); ?>
 <?php
 $this->TipoCurso = ClassRegistry::init('TipoCurso');
$this->Idioma = ClassRegistry::init('Idioma');
$this->Localidade = ClassRegistry::init('Localidade');
  $listaCurso = $this->TipoCurso->find('list');
 $listaIdioma =         $this->Idioma->find('list',array('conditions'=>array('ativo'=>1),'order'=>'id'));
 $listaLocalidade = $this->Localidade->find('list',array('conditions'=>array('Localidade.localidade_id is null')));
   $opcoesPaisCidade = array();
 foreach($listaLocalidade as $p_id => $p_nome){
   $cidades =    $this->Localidade->find('list',array('conditions'=>"Localidade.Localidade_id ={$p_id}", 'Localidade.programas is not null'));    
$opcoesPaisCidade[$p_id] = $p_nome;

foreach($cidades as $c_id => $c_nome){
    $opcoesPaisCidade[$c_id] = ' - '.$c_nome;
    //die(print_r($opcoesPaisCidade));
}
}
   //die(print_r($opcoesPaisCidade));
 ?>
  <section class="custom-budget-section custom-budget-section-lg">
<div class="shadow">
    <div class="container-fluid">
  <?=
    $this->Form->create('orcamento', array(
    'url' => array('controller' => 'Simulador', 'action' => 'index'),
   'type' => 'POST'
 ));
  ?>
        <h2 class="custom-budget-section-title f-white text-center f-light">
            Faça o seu Orçamento personalizado                
        </h2>

        <h3 class="f-transparent-white text-center f-light">
            A forma mais fácil de escolher o intercâmbio ideal para    você.<br/>(Faça uma simulação e veja uma estimativa de custo)
        </h3>

        <div class="content">
            <div class="col-md-6">
                <div class="form-group form-group-white">
                    <label for="">Data de nascimento</label>
                    <?= $this->Form->input('data_nascimento', array('class' => 'form-control mask_date', 'label' => false)) ?>
                </div>
                <div class="form-group form-group-white">
                    <label for="">País ou cidade</label>                        
                    <div class="ui-widget">                            
                        <select id="combobox" name="data[orcamento][localidade_id]">
                          <option value="">Select one...</option>
                          <?php
                            foreach($opcoesPaisCidade as $p_id => $p_nome){
                          ?>
                          <option value="<?=$p_id?>"><?=$p_nome?></option>
                          <?}?>
                        </select>
                      </div>
                </div>
                <div class="form-group form-group-white">
                    <label for="">Data de Início</label>
                    <input type="text" name="data[orcamento][data_inicio]" id="data-inicio" class="form-control datepicker" placeholder="Data de início" aria-describedby="data-inicio-addon">                        
                    <!--label for="tags">Tags: </label>
                    <input id="tags" class='form-control'-->
                </div>

            </div>
            <div class="col-md-6">
                <div class="form-group form-group-white">
                    <label for="">Tipo de Curso</label>
                    <?= $this->Form->input('tipoCurso', array('label' => false, 'options' => $listaCurso, 'empty' => 'Selecione um tipo de curso', 'class' => 'form-control')); ?>
                </div>
                <div class="form-group form-group-white custom-budget-s-in">
                    <label for="">Duração (semanas)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*Gênero*</label>
                    <div class="row">

                        <div class="col-xs-6">
  <?= $this->Form->input('duracao', array('class' => 'form-control', 'placeHolder' => 'Quantidade', 'label' => false)) ?>
                        </div>
                        <div class="col-xs-6">
                            <?= $this->Form->input('sexo', array('class' => 'form-control', 'empty' => 'Selecione', 'label' => false, 'options' => array('M' => 'Masculino', 'F' => 'Feminino'))) ?>                                
                        </div>
                    </div>
                </div>

                <div class="form-group form-group-white">
                    <input type="submit" value="Buscar" class="btn btn-primary">
                </div>
            </div>

            <div class="col-md-12 budget-contact text-center">
                <p>Você pode entrar em <a href="/conteudo/112">contato</a> conosco</p>
            </div>
        </div>
  <?= $this->Form->end() ?>
    </div>        
</div>

 <?=$this->element('/aereo/orcamenton')?>

And my input appears like this: