0. Many people think that the dynamics of the stock market is not even pre- dictable. However, after closely looking at a chart, you would agree that the trend of a stock should be predictable; at least, the price movement isnt as ran- dom as we thought (see an example chart on page 3). Nowdays, extremely short term price predication is a mature technology, pioneered by mathematician Jim Simons who successfully developed an algorithm in 1980s in predicting stock prices. Nowadays, 70% of stock trades in the United States are done by algo- rithms and hence, as a computer science graduate student, you shall understand how algorithms are, profitably, applied in the real world.
1. There is a theory called Efficient Market Hypothesis which says that all market information available is already factored into the price of a stock. In other words, stock charts themselves are already enough in predicating market's movements, nothing else needed. Therefore, your predicting algorithms shall only be based on stock charts.
2. Surprisingly, a stock chart a has a very simple data structure: an array
a[1...k],
for some large k. Each element a[i] is the market data for the stock of day i, which is represented by a tuple of five numbers:
open price of the day;
close price of the day;
⚫ highest price of the day;
⚫ lowest price of the day; and
number of shares traded in the day (called volume).
Notice that when i = k, day i refers to today. For major stocks traded in the United States, the charts are publically available for download; most of them are with a history of more than 2000 trading days (10 years); i.e., with the k≥ 2000.
3. In this exam, you are going to write a mini paper to address the following two problems:
A. (30%) Given a stock chart a with k≥ 2000, design one or more al- gorithms to predict the price for the next day. I will grade on efficiency, depth and correctness of your ideas.
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