How to add index signature in TypeScript

The type of your accumulator in the .reduce call is almost certainly the issue. Since it is just given as {}, that's what its type is inferred as, and the type {} doesn't have an index signature. You can fix this by casting your initial value so that it does include a signature:

var counts = data.reduce((newArray, item) => {
    let time = item.time;
    if (!newArray.hasOwnProperty(time)) {
        newArray[time] = 0;
    } 
    newArray[time]++;
    return newArray;
}, {} as {[key: string]: any}); // <-- note the cast here

I gave the index signature type any, but you may want to make it something more specific for your particular case.

The correct types for your array would be:

Array<{time: string}>

or:

{time: string}[]

or:

{[key: number]: {time: string}}