Apologies as I can\'t think of a better way of including all the information... When I run this, I get an error saying the following. I\'ve followed the Ionic Docs to the T,
The updated version to use firebase would be in app.module.ts
import { AngularFireModule } from '@angular/fire';
import { AngularFirestoreModule } from '@angular/fire/firestore';
import { AngularFireAuthModule } from '@angular/fire/auth';
import { AngularFireDatabaseModule } from '@angular/fire/database';
imports: [
AngularFireModule.initializeApp(environment.firebase),
AngularFirestoreModule,
AngularFireAuthModule,
AngularFireDatabaseModule,
....
]
AngularDatabase(same for AngularAuth) is separated to its own module AngularFireDatabaseModule(AngularFireAuthModule for AngularAuth) from 
 version angularFire2@4.0.0, see documentation here.
you should import AngularFireDatabaseModule(AngularFireAuthModule for Authentication) in your RootModule.
import { AngularFireModule } from 'angularfire2';
// for AngularFireDatabase
import { AngularFireDatabaseModule } from 'angularfire2/database';
import { AngularFireDatabase, FirebaseObjectObservable } from 'angularfire2/database';
// for AngularFireAuth
import { AngularFireAuthModule } from 'angularfire2/auth';
import { AngularFireAuth } from 'angularfire2/auth';
@NgModule({
  imports: [
    AngularFireModule.initializeApp({         <---- main module
      apiKey: ...,
      authDomain: '...',
      databaseURL: '...',
      storageBucket: '...',
      messagingSenderId: '...'
    }),                                       
    AngularFireDatabaseModule,                <---- for database 
    AngularFireAuthModule                     <---- for auth
  ]
})
Add it in providers array in app.module.ts -
  imports: [
    BrowserModule,
    FormsModule,
    HttpModule,
    RouterModule.forRoot(appRoutes),
    AngularFireModule.initializeApp(firebaseConfig)
  ],
  providers: [AuthService,**AngularFireAuth, AngularFireDatabase**, AuthGuard, InventoryService]
Inside app.module.ts add below:
import { AngularFireModule } from 'angularfire2';
import { AngularFireDatabaseModule } from 'angularfire2/database';
Then import as below:
@NgModule({
  declarations: [
    MyApp,
    HomePage
  ],
  imports: [
    BrowserModule,
    IonicModule.forRoot(MyApp),
    AngularFireModule.initializeApp(firebaseConfig),
    AngularFireDatabaseModule
  ],
Inside home.ts use as below:
import { AngularFireDatabase, FirebaseListObservable } from 'angularfire2/database';
items: FirebaseListObservable<any[]>;
  constructor(public navCtrl: NavController, db: AngularFireDatabase) {
        this.items = db.list('/items');
  }
My Ionic info:
Ionic Framework: 3.1.1
Ionic App Scripts: 1.3.7
Angular Core: 4.0.2
Angular Compiler CLI: 4.0.2
Node: 6.10.1
OS Platform: macOS Sierra
Make sure FireBaseDatabaseModule is imported from angularfire2/database-deprecated if youre using FireBaseDatabase from angularfire2/database-deprecated
and vice-versa. The only problem is the mismatch of import statements because they need to belong to the same package either
angularfire2/database or angularfire2/database-deprecated
if you would try to import the database from the first and the module from the second package or vice-versa. It wont recognize it as a DatabaseModule or Database.
------------ ROOT MODULE -------------
    import { AngularFireDatabaseModule } from "angularfire2/database-deprecated"
    imports: [
        BrowserModule,
        RouterModule.forRoot(appRoutes),
        FormsModule,
        AngularFireModule,
        AngularFireDatabaseModule,
        AngularFireAuthModule,
        AngularFireModule.initializeApp(environment.firebase)    
]
------- SERVICE CLASS ------------
import { AngularFireDatabase, FirebaseListObservable } from "angularfire2/database-deprecated";
I had this error in my Angular application. It turns out my auto-import imported AngularFirebase from 'angularfire2/database-deprecated'. Clearing the -deprecated solved my issue. You might want to check your imports too.