Error: TSError: ⨯ Unable to compile TypeScript

I had met same issue. First I remove ts-node and typescript from package.json. then,

npm install ts-node --save-dev
npm install typescript -g 
npm install typescript --save-dev

I came here looking for a solution for a similar error when I updated my typescript version, Mine was not a new project, I am running an angular2 project with "@angular/cli": "1.2.0". I updated my typescript version from 2.0.3 to 2.7.2 and then I was getting similar issues like below while running ng e2e.

Error: TSError: ⨯ Unable to compile TypeScript
Cannot find type definition file for 'core-js'. (2688)
Cannot find type definition file for 'grecaptcha'. (2688)
Cannot find type definition file for 'jasmine'. (2688)
Cannot find type definition file for 'moment-timezone'. (2688)
Cannot find type definition file for 'node'. (2688)
Cannot find type definition file for 'q'. (2688)

The proposed solutions in this post didn't work for me.

I fixed it by updating ts-node to 5.0.1. Versions above this were giving errors like the one below while running ng e2e even though I had experimentalDecorators set to true in tsconfig.json:

error TS1219: Experimental support for decorators is a feature that is subject to change in a future release. Set the 'experimentalDecorators' option to remove this warning

Apart from the above change, I also changed few lines in protractor.conf.js

Changed:

beforeLaunch: function () {
    require('ts-node').register({
        project: 'e2e'
    });
},

to

beforeLaunch: function () {
   require('ts-node/register')
}

This is for people who may stumble into this post and the proposed solution doesn't work for them.