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I am a newcomer using GEE and now I want to do a NDVI time series. The condition is that it must be based on the result of the pixel, and it need to displayed on the map. I just made the NDVI time series, but there is no ideas as a pixel based.

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maybe this will help you

    var l8 = ee.ImageCollection("COPERNICUS/S2")
        .filterDate('2018-06-01', '2019-06-01');
    var ndvi = l8.map(function(image) {
      return image.select().addBands(image.normalizedDifference(['B8','B4']));});
    var panel = ui.Panel();
    panel.style().set('width', '400px');
    var intro = ui.Panel([
      ui.Label({value: 'NDVI Chart Inspector',
        style: {fontSize: '20px', fontWeight: 'bold'}  }),
      ui.Label('Click a point on the map to inspect.')]);
    panel.add(intro);
    var lon = ui.Label();
    var lat = ui.Label();
    panel.add(ui.Panel([lon, lat], ui.Panel.Layout.flow('horizontal')));
    Map.onClick(function(coords) {
      lon.setValue('lon: ' + coords.lon.toFixed(5)),
      lat.setValue('lat: ' + coords.lat.toFixed(5));
      var point = ee.Geometry.Point(coords.lon, coords.lat);
      var dot = ui.Map.Layer(point, {color: 'FF0000'});
      Map.layers().set(1, dot);
      var ndviChart = ui.Chart.image.series(ndvi, point, ee.Reducer.mean(), 500);
      ndviChart.setOptions({
        title: 'NDVI Over Time',vAxis: {title: 'NDVI'},
        hAxis: {title: 'date', format: 'MM-yy', gridlines: {count: 7}},
      });  panel.widgets().set(2, ndviChart);});
    Map.style().set('cursor', 'crosshair');
    ui.root.insert(0, panel);
    Map.setOptions('SATELLITE')
    Map.setCenter(35.84497, 32.01918, 3);

or change in the first line to other satellite like "LANDSAT/LE07/C01/T1_SR" if you change satellite don't forget to change the bands accordingly

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