January 6, 2024
12
min
Financial data structures
Basic financial data structures as examples
In Finance we have a wide range of data that influences the price. Here is a list of the different data types:
Forming Bars:
Information does not arrive to the market at a constant entropy rate. Sampling data in chronological intervals means that the informational content of the individual observations is far from constant. A better approach is to sample observations as a subordinated process of the amount of information exchanged:
- Trade bars
- Volume bars
- Dollar bars
- Volatility or runs bars
- Order imbalance bars
- Entropy bars
From Line
To Bars
The Stationarity vs. Memory Dilemma
In order to perform inferential analyses, researchers need to work with invariant processes, such as
- returns on prices (or changes in log-prices)
- changes in yield
- changes in volatility
These operations make the series stationary, at the expense of removing all memory from the original series.
• Memory is the basis for the model’s predictive power.
• For example ,equilibrium (stationary) models need some memory to assess how far the price process has drifted away from the long-term expected value in order to generate a forecast.
• The dilemma is returns are stationary however memory-less and prices have memory however they are non-stationary.
Returns:
SquaredReturns:
It is clear to see that the Returns-/ Squared Returns- Charts have no more memories and the market movements can no longer be seen clearly, but the time series now has the white noise effect, i.e. it resembles a random wark.
Price-Chart:
Log-Price-Chart:
The difference between the Amazon price chart and the logarithmic chart of the Amazon price can be clearly seen. First, the log chart becomes more linear. Second, due to the exponential development of the Amazon price, the drops in 2007 and 2009 will disappear. These can still be seen in the log-chart. This is caused by the scaling from 0-2000 in the price chart from 0-8 inthe log-price-chart.
The Optimal Stationary-Memory Trade Off
Question: What is the minimum amount of differentiation that makes a price series stationary while preserving as much memory as possible?
• Answer: We would like to generalize the notion of returns to consider stationary series where not all memory is erased.
• Under this framework, returns are just one kind of (and in most cases suboptimal) price transformation among many other possible.
Green line: E-mini S&P 500 futures trade bars of size 1E4
• Blue line: Fractionally differentiated (𝑑 = .4)
• Over a short time span, it resembles returns
• Over a longer time span, it resembles price levels
