# Time Series Terminal Whitepaper

Brief Solutions Ltd, May 2022

### The Problem

*Is time series A predictive of time series B?*

i.e. given all information about A's value up to time $t$, is it predictive of the conditional distribution of B's value at a future time $t+p$, with $p$ being the prediction horizon?

*Is this relationship causal?*

i.e. the presence of A makes the prediction of the future of B better, its absence makes it worse.

### The Solution

Given a pre-configured collection of time series data, we designed a computational engine to compute the predictive power of any series A for any series B, for a given prediction horizon. When we collate the results we obtain a causal graph that represents the strengths of predictive power between them.

For example, following the close of Mon 23 May 2022, the computational engine updates all causal relations (for 2 day ahead prediction). The vicinity around the Invesco Nasdaq-100 ETF would read like

The engine employs a group of trained models to make prediction for any target time series. Each model eventually produces a single output: "up", "down" or "undecided" for the direction of movement for a given horizon. When grouped together, with the Invesco Nasdaq-100 ETF as the forecast target,

- For Tue 24th, 20% predict up, 70% predict down, 10% undecided;
- For Wed 25th, 40% predict up, 60% predict down, 0% undecided.

The *net* predictions, in terms of the percentage of models predicting up minus that predicting down are thus

- For Tue 24th, 50% predict down;
- For Wed 25th, 20% predict down.

### Backtest

As one exercise, if we use the above net prediction as size for hypothetical trading, under ideal condition of no trading cost, the performances would be:

For Invesco Nasdaq-100 ETF,

For SPDR S&P 500 ETF,

For SPDR Dow Jones Industrial Average ETF,

For US 10-Year Interest Rate,