Pattern error in React JS traffic light simulator

I am trying to build a traffic light using ReactJS. I need the traffic light to go in the order red, yellow, green, red, yellow, green, etc. My current code gives me a different pattern. I don't know quite how to work with setInterval on this one and I could really use some help. I looked at a solution to the same problem by CarterTsai on CodePen, but I was neither able to understand most of his code, nor convert it into a stackblitz-friendly format to adapt it to my code. Does anyone have any answers? Any help is appreciated! It would also be great if anyone could provide a solution with two components - one that changes the traffic light state, and another that utilizes that state shows the actual traffic light(that was the requirement for my homework).

Here is a link to view my project on stackblitz: https://stackblitz.com/edit/react-eqkhd7?file=src/style.css

my code in App.js :

import React from 'react';
import './style.css';

export default class App extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      color1: '',
      color2: '',
      color3: ''
    };

    setInterval(this.changeColor1.bind(this), 2000);
    setInterval(this.changeColor2.bind(this), 4000);
    setInterval(this.changeColor3.bind(this), 6000);
  }

  changeColor1 = () => {
    this.setState({ color1: 'red', color2: '', color3: '' });
  };

  changeColor2 = () => {
    this.setState({ color1: '', color2: 'yellow', color3: '' });
  };

  changeColor3 = () => {
    this.setState({ color1: '', color2: '', color3: 'green' });
  };

  render() {
    return (
      <div>
        <span style={{ backgroundColor: this.state.color1 }} class="circle" />
        <p />
        <span style={{ backgroundColor: this.state.color2 }} class="circle" />
        <p />
        <span style={{ backgroundColor: this.state.color3 }} class="circle" />
      </div>
    );
  }
}

style.css :

h1,
p {
  font-family: Lato;
}

.circle {
  margin: auto;
  height: 100px;
  width: 100px;
  border: 5px black solid;
  border-radius: 50%;
  display: block;
}

index.js :

import React from "react";
import ReactDOM from "react-dom";

import App from "./App";

ReactDOM.render(<App />, document.getElementById("root"));

You can do this using setTimeout and call the other traffic light function after the current traffic light execution.

export default class App extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      color1: '',
      color2: '',
      color3: ''
    };

    setTimeout(this.changeColor1, 2000);
  }

  changeColor1 = () => {
    this.setState({ color1: 'red', color2: '', color3: '' });
    setTimeout(this.changeColor2, 2000);
  };

  changeColor2 = () => {
    this.setState({ color1: '', color2: 'yellow', color3: '' });
    setTimeout(this.changeColor3, 2000);
  };

  changeColor3 = () => {
    this.setState({ color1: '', color2: '', color3: 'green' });
    setTimeout(this.changeColor1, 2000);
  };

Here is the working fiddle