This document describes a financial time series analysis application called Quant Machine. It aims to forecast stock returns and determine bullish or bearish market conditions using historical return data. The application would analyze data on adjusted closing prices and returns for a universe of stocks, and use machine learning tools like regression, classification, PCA and feature selection to find patterns and make predictions. It discusses validating models on training and test data to select the most predictive model, and provides examples of using techniques like ARIMA, GARCH and Hidden Markov Models. The goal is to provide insights to algorithmic traders on directional stock moves and improve trading performance.

1. Quant Machine
Application for Analyzing Financial Time Series
quantmachine.xyz

2. Problem Statement
Knowing the performance of foreign markets, determine if the US
stock market will be bullish or bearish (up/down)
Forecast the return of a given stock in S&P500 in terms of
historical returns of all stocks in the same set
How much profit can we make trading based on this forecast?

3. Problem Statement
Universe of stocks: {𝑠𝑖}𝑖=1
𝑁
 Adjusted Close price of stock 𝑠𝑖 at time 𝑡 : 𝑃(𝑠𝑖, 𝑡)
 Return of stock 𝑠𝑖 at time 𝑡: 𝑅 𝑠𝑖, 𝑡 =
𝑃 𝑠 𝑖, 𝑡 − 𝑃(𝑠 𝑖, 𝑡−1)
𝑃(𝑠 𝑖, 𝑡−1)
 Assume 𝑟 is either 𝑅 (continuous) or 𝑠𝑖𝑔𝑛 𝑅 (discrete)
 We want to find 𝐹 (regressor/classifier) if it exists, such that:
𝑟(𝑠𝑖, 𝑡) = 𝐹[ 𝑟 𝑠1, 𝑡 − 1 , 𝑟 𝑠1, 𝑡 − 2 , … , 𝑟(𝑠 𝑛, , 𝑡 − 𝑛𝑙𝑎𝑔𝑠) ]

4. Motivation
In many trading strategies, additional insight about the
directional moves of stock returns can significantly improve
performance
This application will provide useful analytics for retail
algorithmic traders and day-traders in general

5. Data
Dates IBM_lag1 IBM_lag2 MSFT_lag1 MSFT_lag2 … IBM_vol_lag1
6/25/2016 - 5.65% +0.03% - 3.99% +1.02% +5.5%
6/24/2016 +0.03% +1.55% +1.02% - 0.52% +2.5%
Samples are
trading days
Table of daily returns (including % change of volume)
IBM is the stock of interest
Number of Lags is 2
Features
Dates IBM_lag1 IBM_lag2 MSFT_lag1 MSFT_lag2 … IBM_vol_lag1
6/25/2016 - 1 +1 - 1 +1 +1
6/24/2016 +1 +1 +1 - 1 +1
Table of daily directional moves
# Features ≤ # Samples

6. FEATURE EXTRACTION
DATA
MACHINE LEARNING TOOLS
PREDICTIONS
ECONOMETRIC TOOLS
• NYSE, Asian Markets
+ lags
• PCA
• VIF
• Lasso
• ARIMA(p, r, q), GARCH(1, 1) • Regressors
• Classifiers
• Returns
• Pairs

7. Feature Selection
For Classifiers
• Select features according to k highest scores
• Recursive Feature Elimination
For Regressors
• Lasso
• Multicollinearity Reduction

8. Game of Markets
Hours Open Nasdaq Frankfurt London Hong Kong Shanghai Japan (Nikkei) Australia
UTC times 14:30-21:00 07:00-19:00 08:00-16:30 01:30-08:00 01:30-07:00 00:00-06:00 00:00-6:00

9. Validation
Model Validation (get the best hyper parameters)
Time Series require specific type of validation to preserve causality
Moving or cascading window technique is used
Model Selection (get the most predictive model)
Model that performed the best on a validation set is used as a
predictor on a test set

10. ROC
Example of ROC and AUC for one of the classifiers

11. ARIMA Model
Forecasting returns using ARIMA(p, r, q) model

12. ARIMA Model
Checking (partial) autocorrelation and normality of residues

13. Hidden Markov Model
Simple application of Gaussian HMM