Concept
The conventional approach to analyzing financial markets relies on time-based bars, where price data is sampled at fixed intervals like minutes, hours, or days. This method, while simple, introduces a fundamental distortion. It assumes that information arrives in the market at a constant, clock-driven rate. The reality of market dynamics is far different.
Periods of intense activity, where significant information is processed, are interspersed with quiet intervals where very little of consequence occurs. A one-minute bar at market open, teeming with order flow and price discovery, is treated with the same weight as a one-minute bar in the middle of a placid trading session. This temporal rigidity masks the true rhythm of the market, leading to statistical anomalies that can impair the effectiveness of forecasting models.
Information-driven bars offer a superior alternative by synchronizing data sampling with the flow of market activity itself. Instead of sampling at fixed time intervals, this technique creates bars based on accumulated changes in market variables like the number of trades (tick bars), the total volume traded (volume bars), or the total dollar value exchanged (dollar bars). The core principle is to sample data when something meaningful happens. This approach produces a time series that is more attuned to the underlying economic process.
When a flurry of trades occurs, signaling the arrival of new information and the participation of informed traders, the data is sampled more frequently. During lulls, the sampling rate naturally decreases. This adaptive sampling aligns the data structure with the very events that drive price changes and, consequently, volatility.
By sampling data based on market activity rather than the clock, information-driven bars produce a time series that better reflects the economic process of price discovery.
The implications for volatility forecasting are profound. Standard time-series models often struggle with the statistical properties of time-based financial data. Returns sampled in calendar time are typically not independent and identically distributed (i.i.d.), exhibiting characteristics like volatility clustering and heavy tails. Information-driven bars help mitigate these issues.
By construction, each bar represents a similar quantum of market activity, leading to returns that are closer to being i.i.d. and more closely approximate a normal distribution. This improved statistical character makes the data more suitable for traditional econometric models like GARCH, leading to more reliable parameter estimates and, ultimately, more accurate volatility forecasts. The purpose is to sample more frequently when new information arrives, allowing for analysis before prices reach a new equilibrium.
Strategy
Implementing information-driven bars is a strategic decision to align a model’s data input with the mechanics of market microstructure. The choice of which type of bar to use depends on the specific market and the analytical objective. Each bar type captures a different dimension of market activity, offering a distinct lens through which to view information flow.
A Taxonomy of Activity-Based Sampling
The primary types of information-driven bars provide a flexible toolkit for the quantitative analyst. Understanding their construction and the economic rationale behind each is key to their effective deployment.
- Tick Bars ▴ These are the most direct measure of activity. A new bar is formed after a fixed number of trades (e.g. every 1,000 ticks). Tick bars are sensitive to the fragmentation of large orders, as one large institutional order might be broken into hundreds of small trades, each counted as a single tick. This makes them a granular, albeit sometimes noisy, measure of market participation.
- Volume Bars ▴ These bars are formed when a predetermined amount of the asset has been traded (e.g. every 500,000 shares). Volume bars provide a more robust measure of activity than tick bars because they are less affected by order-splitting algorithms. A large volume of shares traded, regardless of the number of individual transactions, signals significant capital commitment and is a strong indicator of information flow.
- Dollar Bars ▴ A dollar bar is completed when a certain amount of notional value has been traded (e.g. every $10 million). Dollar bars have a distinct advantage, particularly in assets that experience large price fluctuations. A bar based on a fixed number of shares (a volume bar) will represent a much larger capital commitment when the price is high than when it is low. Dollar bars standardize the economic significance of each bar, ensuring that each sample represents a consistent level of market value being reallocated.
Imbalance Bars a Deeper Informational Signal
Beyond simple activity measures, more sophisticated bars, known as imbalance bars, attempt to sample data specifically when there is evidence of informed trading. The premise is that informed traders, acting on private information, create directional pressure in the market. By tracking this pressure, one can sample data precisely when new information is being impounded into prices.
- Tick Imbalance Bars (TIBs) ▴ These bars are formed by tracking the sequence of buyer-initiated and seller-initiated trades. Using the tick rule (a trade at a higher price is a buy, a trade at a lower price is a sell), one can maintain a running tally of the “tick imbalance.” A new bar is sampled when the absolute value of this imbalance exceeds a dynamically updated expectation. This method is designed to capture moments when a directional consensus emerges among traders.
- Volume and Dollar Imbalance Bars (VIBs and DIBs) ▴ These extend the concept of imbalance to volume and dollar value. Instead of just counting the number of up-ticks versus down-ticks, they accumulate the volume or dollar value associated with those ticks. This gives more weight to larger trades, on the assumption that they are more likely to be initiated by informed institutions. A bar is sampled when the cumulative signed volume or dollar value surpasses a threshold, signaling a significant, directional shift in capital flow.
Strategic Comparison of Bar Types
The choice between these bar types is a strategic one, dependent on the specific characteristics of the asset and the goals of the volatility model.
| Bar Type | Sampling Trigger | Primary Advantage | Potential Weakness | Best Suited For |
|---|---|---|---|---|
| Time Bars | Fixed time interval (e.g. 1 minute) | Simplicity and ease of use. | Ignores market activity, leading to statistical issues. | Low-frequency analysis, simple models. |
| Tick Bars | Fixed number of trades | Direct measure of market participation. | Sensitive to order splitting and high-frequency noise. | Markets with relatively uniform trade sizes. |
| Volume Bars | Fixed number of shares/contracts traded | Robust to order splitting; measures capital commitment. | Can be distorted by large price changes. | Most equity and futures markets. |
| Dollar Bars | Fixed notional value traded | Standardizes economic significance across price levels. | Requires price and volume data for construction. | Assets with high price volatility. |
| Imbalance Bars | Excess accumulation of directional trades | Designed to sample upon arrival of new information. | More complex to implement; requires trade-side classification. | Sophisticated algorithmic trading and high-frequency volatility forecasting. |
The strategic selection of a bar type allows a model to listen more closely to the specific type of market information that is most relevant for its forecasting objective.
Alignment with Market Microstructure Theory
The effectiveness of information-driven bars is grounded in the Mixture of Distributions Hypothesis (MDH). This theory posits that the number of trades, or volume, in a given time interval serves as a proxy for the rate of information flow. When more information is arriving, trading activity increases, which in turn leads to higher price volatility. By sampling in “activity time” (e.g. volume or ticks) rather than calendar time, we are effectively controlling for the rate of information flow.
This process helps to restore the desirable statistical properties that are assumed by many volatility models. The result is a time series where the variance of returns per bar is more stable, making the underlying volatility process easier to model and forecast.
Execution
The transition from the theoretical appeal of information-driven bars to their practical execution requires a rigorous data processing pipeline and a clear understanding of their impact on volatility model parameters. The execution phase is where the structural advantages of these bars are realized, translating into tangible improvements in forecast accuracy.
Constructing Information-Driven Bars from Tick Data
The foundational input for constructing these bars is high-frequency tick-by-tick trade data. This data typically includes a timestamp, price, and volume for every transaction. The process involves accumulating these ticks until a predefined threshold for a chosen metric (ticks, volume, or dollar value) is met.
At that point, a bar is “closed,” and its summary statistics ▴ such as the open, high, low, close (OHLC) prices, total volume, and timestamp ▴ are recorded. A new bar then begins to form.
Consider the following example of processing raw tick data into different bar types. The threshold for each bar is set for illustrative purposes.
| Timestamp | Price | Volume | Cumulative Ticks (Threshold ▴ 4) | Cumulative Volume (Threshold ▴ 1000) | Cumulative Dollars (Threshold ▴ 100,000) |
|---|---|---|---|---|---|
| 09:30:01.123 | 150.01 | 200 | 1 | 200 | 30,002.00 |
| 09:30:01.456 | 150.02 | 300 | 2 | 500 | 75,008.00 |
| 09:30:01.789 | 150.00 | 100 | 3 | 600 | 90,008.00 |
| 09:30:02.112 | 150.03 | 500 | 4 (New Tick Bar) | 1100 (New Volume Bar) | 165,023.00 (New Dollar Bar) |
| 09:30:02.345 | 150.05 | 100 | 1 | 100 | 15,005.00 |
In this simplified example, a tick bar is formed after the fourth trade. A volume bar is formed at the same time, as the cumulative volume exceeded 1000 shares. A dollar bar also closed on that trade, as the cumulative dollar value surpassed $100,000. This demonstrates how different bar types can sample the same underlying data at different frequencies, dictated by their respective activity metrics.
Impact on Volatility Model Inputs and Outputs
Once the new bar series is constructed, it can be used as the input for a volatility forecasting model, such as a GARCH(1,1) model. The GARCH model estimates future volatility based on past squared returns and past conditional volatilities. The key benefit of using information-driven bars is the improvement in the statistical quality of these inputs.
The returns calculated from information-driven bars, let’s call them activity-based returns, tend to exhibit lower autocorrelation and are closer to being normally distributed compared to time-based returns. When these cleaner returns are fed into a GARCH model, the estimation of the model’s parameters (α, β, and ω) becomes more stable and statistically significant. The α parameter captures the reaction to market shocks (past squared returns), while the β parameter captures the persistence of volatility (past conditional volatility). With information-driven bars, the model can more accurately discern the true persistence of volatility from the noise introduced by inactive periods in time-based sampling.
Utilizing information-driven bars transforms the input data for GARCH models, leading to more reliable parameter estimates and a clearer signal of the underlying volatility process.
A Case Study in GARCH Modeling
Imagine forecasting volatility for a highly active technology stock. During the first and last hours of the trading day, activity is immense, while midday trading is often subdued. A time-based GARCH model would be forced to process low-volatility returns during the midday lull, potentially underestimating the persistence (β) of volatility from the morning session and overreacting to small price changes. An information-driven model, such as one using dollar bars, would generate fewer bars during the quiet midday period.
The bars it does generate would represent significant capital flows, providing a clearer signal. The resulting GARCH model would likely estimate a higher β, correctly identifying the persistent nature of volatility on active days, and a more appropriately calibrated α, preventing overreaction to noise. This leads to more accurate out-of-sample forecasts, particularly in predicting the volatility of the next high-activity period.
System Integration and Technological Architecture
The operational deployment of models based on information-driven bars requires a robust technological infrastructure. The system must be capable of:
- Ingesting and Storing High-Frequency Data ▴ This requires a high-throughput messaging system to capture every tick from a data feed and a time-series database optimized for storing and querying massive datasets.
- Real-Time Bar Construction ▴ For live trading applications, the process of aggregating ticks and forming bars must occur in real-time with minimal latency. This is typically handled by a dedicated processing engine written in a high-performance language like C++ or Java.
- Model Estimation and Forecasting ▴ A statistical engine, often using libraries in Python or R, must be able to access the newly constructed bar data, re-estimate model parameters periodically, and generate forecasts.
- Signal Generation and Execution ▴ The volatility forecasts are then fed into downstream systems, such as options pricing models or algorithmic execution strategies. This integration requires well-defined APIs and a low-latency connection to an Order Management System (OMS) or Execution Management System (EMS).
The entire architecture must be designed for resilience and accuracy, as errors in data processing or bar construction can lead to flawed forecasts and poor trading decisions. The computational cost is non-trivial, but the potential improvement in forecasting accuracy often justifies the investment for sophisticated market participants.
References
- De Prado, M. L. (2018). Advances in financial machine learning. John Wiley & Sons.
- Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41(1), 135-155.
- Easley, D. Lopez de Prado, M. & O’Hara, M. (2012). Flow toxicity and liquidity in a high-frequency world. The Review of Financial Studies, 25(5), 1457-1493.
- Ghysels, E. & Jasiak, J. (1998). GARCH for irregularly spaced data ▴ The ACD-GARCH model. Studies in Nonlinear Dynamics & Econometrics, 2(4).
- Andersen, T. G. Bollerslev, T. Diebold, F. X. & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579-625.
- Engle, R. F. (2000). The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives, 14(4), 157-168.
- Hansen, P. R. & Lunde, A. (2005). A forecast comparison of volatility models ▴ does anything beat a GARCH(1,1)?. Journal of applied econometrics, 20(7), 873-889.
- Corsi, F. (2009). A simple approximate long-memory model of volatility. Journal of Financial Econometrics, 7(2), 174-196.
Reflection
Beyond the Clockwork Market
Adopting information-driven bars is more than a technical upgrade to a forecasting model; it represents a fundamental shift in perspective. It is an acknowledgment that the market operates on its own time, driven by the ebb and flow of human decisions, capital allocation, and the arrival of new information. By moving away from the arbitrary grid of calendar time, we build systems that listen to the market’s internal rhythm. The resulting clarity is not just a statistical artifact; it is a source of analytical edge.
The knowledge gained from these more refined models becomes a component in a larger system of intelligence, where superior forecasts inform better risk management, more precise options pricing, and more effective execution strategies. The ultimate potential lies in using this deeper understanding of market dynamics to construct a more robust and responsive operational framework.
Glossary
Information-Driven Bars
Market Activity
Volatility Forecasting
Market Microstructure
Information Flow
Fixed Number
Tick Bars
Volume Bars
Dollar Bars
Dollar Value
Garch Model
