ABSTRACT
CONTENTS 6.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
6.1.1 Computational Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 6.2 The Data Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 6.3 Reading the Financial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 6.4 Visualizing the Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 6.5 Finding Opening and Closing Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
6.5.1 Identifying a Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 6.5.2 Displaying Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 6.5.3 Finding All Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 6.5.4 Computing the Profit for a Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 6.5.5 Finding the Optimal Value for k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
6.6 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 6.6.1 Simulating the Stock Price Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 6.6.2 Making stockSim() Faster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
6.1 The Problem Finance and financial trading are important elements of all economies. Historically, people used various strategies and hunches to choose when to buy and sell stock and which stocks to trade. Increasingly, people try to use data, algorithms and, importantly, statistical methods to develop more automated strategies for determining what and when to trade in order to increase profits. Over the years, there have been many different approaches and algorithms in this direction, and recent developments illustrate computer trading is increasing rapidly. Some people are even developing statistical/machine learning algorithms that run on network routers to make sub-millisecond trades to exploit time delays other people experience.
