WPF CollectionView Filter on Property of Model?

//Model
class Y {
  string Name;
  List<X> ListOfX;
}

class X {
  string Name;
}

//ViewModel
public ObservableCollection<Y> ObservableListOfY { get; set; }


private Y _SelectedY;
public Y SelectedY;
{
  get { return _SelectedY; }
  set
  {
    _SelectedY = value;
    OnPropertyChanged();
  }
}

private string _SearchBoxText = string.Empty;
public string SearchBoxText
{
  get { return SearchBoxText; }
  set
  {
    _SearchBoxText = value;
    FilterData();
    OnPropertyChanged();
  }
}

public ctor()
{
  ObservableListOfY = ...
}

public void FilterData()
{
  //This filter works
  CollectionViewSource.GetDefaultView(ObservableListOfY ).Filter = o => (o as Y).ListOfX.Any(x => x.Name.Contains(SearchBoxText));

  //This one doesn't, probably because ListOfZ is not an ObservableCollection
  CollectionViewSource.GetDefaultView(SelectedY.ListOfZ).Filter = o => (o as X).Name.Contains(SearchBoxText);
}

<!--View-->
<TextBox Text="{Binding SearchBoxText}" />
<ListBox ItemsSource="{Binding ObservableListOfY}" SelectedItem="{Binding SelectedY}" />
<ListBox ItemsSource="{Binding SelectedY.ListOfX}" />