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High frequency data

High frequency data is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand High frequency data rather than just read about it. In short: High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at an efficient rate for analysis.

High frequency data — main illustration
High frequency data — illustration

Key takeaways

  • High frequency data belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect High frequency data to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of High frequency data from memory before moving on to harder problems.

Reference excerpt

High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at an efficient rate for analysis. Largely used in the financial field, high frequency data provides observations at very frequent intervals that can be used to understand market behaviors, dynamics, and micro-structures. High frequency data collections were originally formulated by massing tick-by-tick market data, by which each single 'event' (transaction, quote, price movement, etc.) is characterized by a 'tick', or one logical unit of information. Due to the large amounts of ticks in a single day, high frequency data collections generally contain a large amount of data, allowing high statistical precision. High frequency observations across one day of a liquid market can equal the amount of daily data collected in 30 years.

Use

Due to the introduction of electronic forms of trading and internet-based data providers, high frequency data has become much more accessible and can allow one to follow price formation in real time. This has resulted in a large new area of research in the high frequency data field, where academics and researchers use the characteristics of high frequency data to develop adequate models for predicting future market movements and risks. Model predictions cover a wide range of market behaviors including volume, volatility, price movement, and placement optimization. There is an ongoing interest in both regulatory agencies and academia surrounding transaction data and limit order book data, of which greater implications of trade and market behaviors as well as market outcomes and dynamics can be assessed using high frequency data models. Regulatory agencies take a large interest in these models due to the fact that liquidity and price risks are not fully understood in terms of newer forms of automated trading applications. High frequency data studies contain value in their ability to trace irregular market activities over a period of time. This information allows a better understanding of price and trading activity and behavior. Due to the importance of timing in market events, high frequency data requires analysis using point processes, which depend on observations and history to characterize random occurrences of events. This understanding was first developed by 2003 Nobel Prize in Economics winner Robert Fry Engle III, who specializes in developing financial econometric analysis methods using financial data and point processes.

High frequency data forms High frequency data are primarily used in financial research and stock market analysis. Whenever a trade, quote, or electronic order is processed, the relating data are collected and entered in a time-series format. As such, high frequency data are often referred to as transaction data. There are five broad levels of high frequency data that are obtained and used in market research and analysis:

Trade data Individual trade data collected at a certain interval within a time series. There are two main variables to describe a single point of trade data: the time of the transaction, and a vector known as a 'mark', which characterizes the details of the transaction event.

Trade and quote data Data collected details both trades and quotes, including price changes and direction, time stamps, and volume. Such information can be found at the TAQ (Trade and Quote) database operated by the NYSE. Where trade data details the exchange of a transaction itself, quote data details the optimal trading conditions for a given exchange. This information can indicate halts in exchanges and both opening and closing quotes.

Fixed level order book data Using systems that have been completely computerized, the depth of the market can be assessed using limit order activities that occur in the background of a given market.

Messages on all limit order activities This data level displays the full information surrounding limit order activities, and can create a reproduction of the trade flow at any given time using information on time stamps, cancellations, and buyer/seller identification.

Data on order book snapshots Snapshots of the order book activities can be recorded on equi-distant based grids to limit the need to reproduce the order book. This however limits trade analysis ability, and is therefore more useful in understanding dynamics rather than book and trading interaction.

Properties in financial analysis In financial analysis, high frequency data can be organized in differing time scales from minutes to years. As high frequency data comes in a largely dis-aggregated form over a time-series compared to lower frequency methods of data collection, it contains various unique characteristics that alter the way the data are understood and analyzed. Robert Fry Engle III categorizes these distinct characteristics as irregular temporal spacing, discreteness, diurnal patterns, and temporal dependence.

Irregular temporal spacing High frequency data employs the collection of a large sum of data over a time series, and as such the frequency of single data collection tends to be spaced out in irregular patterns over time. This is especially clear in financial market analysis, where transactions may occur in sequence, or after a prolonged period of inactivity.

Discreteness High frequency data largely incorporates pricing and transactions, of which institutional rules prevent from drastically rising or falling within a short period of time. This results in data changes based on the measure of one tick. This lessened ability to fluctuate makes the data more discrete in its use, such as in stock market exchange, where popular stocks tend to stay within 5 ticks of movement. Due to the level of discreteness of high frequency data, there tends to be high level of kurtosis present in the set.

Diurnal patterns Analysis first made by Engle and Russel in 1998 notes that high frequency data follows a diurnal pattern, with the duration between trades being smallest at the open and the close of the market. Some foreign markets, which operate 24 hours a day, still display a diurnal pattern based on the time of the day.

… excerpt ends here. Continue reading the full article.

Illustrations

High frequency data: High frequency data plotted over time on the FTSE 100 index chart
High frequency data plotted over time on the FTSE 100 index chart

Worked examples

Example 1 — a first encounter with High frequency data

Start with the simplest possible case. Write down what High frequency data claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to High frequency data before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about High frequency data ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of High frequency data

In research
High frequency data appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses High frequency data in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
High frequency data is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data, Mathematical finance, Time series, so understanding it makes those chapters shorter.
In everyday life
Look for High frequency data outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study High frequency data in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what High frequency data means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain High frequency data out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is High frequency data in simple terms?

High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at an efficient rate for analysis.

Why does High frequency data matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study High frequency data?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on High frequency data.

Tags

  • Data
  • Mathematical finance
  • Time series

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