Example solution to the StackOverflow question: http://stackoverflow.com/questions/26703211/android-autocomplete-matching-options

DemoActivity.java

public class DemoActivity extends Activity {

    private String[] values = {
            "Saudi Arabia",
            "Aruba",
            "Argentina",
            "Something Else"
    };

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_demo);

        AutoCompleteTextView autoCompleteTextView = (AutoCompleteTextView) findViewById(R.id.autoCompleteTextView);
        SpecialAdapter adapter = new SpecialAdapter(this, android.R.layout.simple_dropdown_item_1line, values);
        autoCompleteTextView.setAdapter(adapter);
    }

    public class SpecialAdapter extends BaseAdapter implements Filterable {

        private List<String> originalItems;
        private List<String> filteredItems;
        private int layoutResource;
        private Context context;

        public SpecialAdapter(Context context, int resource, String[] items) {
            this.context = context;
            this.layoutResource = resource;
            this.originalItems = Arrays.asList(items);
            this.filteredItems = new ArrayList<String>(originalItems);
        }

        @Override
        public int getCount() {
            return filteredItems.size();
        }

        @Override
        public String getItem(int position) {
            return filteredItems.get(position);
        }

        @Override
        public long getItemId(int position) {
            return position;
        }

        @Override
        public View getView(int position, View convertView, ViewGroup parent) {
            LayoutInflater inflater = (LayoutInflater) context.getSystemService(Context.LAYOUT_INFLATER_SERVICE);
            String item = getItem(position);
            if(convertView == null) {
                convertView = inflater.inflate(layoutResource, parent, false);
            }
            ((TextView) convertView).setText(item);
            return convertView;
        }

        @Override
        public Filter getFilter() {
            return new SpecialFilter();
        }

        private class SpecialFilter extends Filter {

            @Override
            protected FilterResults performFiltering(CharSequence constraint) {
                FilterResults results = new FilterResults();

                // If there is no constraint, just return the original list of items
                if (constraint == null || constraint.length() == 0) {
                    ArrayList<String> list = new ArrayList<String>(originalItems);
                    results.values = list;
                    results.count = list.size();
                }
                // Else, only return the strings that start with the constraint
                else {
                    String prefixString = constraint.toString().toLowerCase();
                    ArrayList<String> values = new ArrayList<String>(originalItems);
                    final ArrayList<String> newValues = new ArrayList<String>();

                    for (String value : values) {
                        final String valueText = value.toLowerCase();
                        if (valueText.startsWith(prefixString)) {
                            newValues.add(value);
                        }
                    }

                    results.values = newValues;
                    results.count = newValues.size();
                }

                return results;
            }

            @Override
            protected void publishResults(CharSequence constraint, FilterResults results) {
                filteredItems = (List<String>) results.values;
                if (results.count > 0) {
                    notifyDataSetChanged();
                } else {
                    notifyDataSetInvalidated();
                }
            }
        }
    }
}