Why Using the Current Price in a Next-Period Return Target Is Not Leakage
Summary
The document considers whether a one-step-ahead log return, defined using the current and next binned prices, leaks information when forecasting from tick data. It describes forming midpoint prices, aggregating them into bins, calculating log returns, and fitting a rolling ARIMA model to predict the next return. The key reply is that the current bin’s price is already observable at the forecast origin, so its appearance in the realized next-period return does not by itself introduce future information into the training target.
The question reports different directional accuracies when bins use average midpoints versus their last tick, but these figures do not establish leakage. The answer is brief and does not assess the full experiment, including bin timing, preprocessing, rolling-window design, or evaluation procedure. A valid forecast must use only information available at the forecast time, and the reported comparison alone cannot diagnose other sources of look-ahead bias or validate predictive performance.
Key ideas
- The next-period log return uses the current price, which is known at the end of the current interval.
- Including an already observable current price in a forecast target does not alone create information leakage.
- The question compares average midpoint prices with the last midpoint in each bin.
- Differences in reported directional accuracy do not by themselves prove leakage or predictive skill.
- Leakage assessment depends on whether all data processing and model inputs respect the forecast-time information set.
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Full text
# Does Computing Log Returns as $\log(x_t / x_{t-1})$ Introduce Information Leakage in Time Series Forecasting?
# Does Computing Log Returns as $\log(x_t / x_{t-1})$ Introduce Information Leakage in Time Series Forecasting?
I have tick-level data for a single trading day of a specific contract and aim to conduct time series analysis on it. The mid-price at each tick is computed as $MidPrice=0.5×(Ask_1 +Bid_1)$. The data is then segmented into fixed-length time intervals (hereafter referred to as bins), within which I calculate the average mid-price, denoted as $x_t$. Subsequently, I compute the log returns as $r_t =\log(x_t /x_{t−1})$, and apply a rolling window to the series $\{r_t ,r_{t−1} ,…,r_1\}$ to fit an ARIMA model for forecasting the next interval's return, $r_{t+1}$. While I initially considered this methodology sound, my supervisor pointed out a possible issue of information leakage—specifically, the computation of $r_t$ involves $x_t$, while the predicted value $r_{t+1} = \log(x_{t+1}/ x_t)$ also contains the value $x_t$, thereby contaminating the training process with future information.
I set a benchmark to compare the ARIMA model result. i.e. the mid-price of next bin, $t+1$, is calculated by $x_{t+1} = x_t + (x_t - x_{t-1})$, and the log return of time $t+1$ is still computed by $r_t = \log(x_{t+1} / x_t)$. Then, I computed the accuracy by comparing the signs of the actural log return and the benchmark log return, where $x_{t+1} = x_t + (x_t - x_{t-1})$.
My supervisor suggested that instead of using the average mid-price of each bin, i.e. $x_t = \frac{1}{\text{#ticks in a bin}}\sum_{i \in \text{ticks in a bin}} \text{mid-price}_i$ I should use the last tick’s mid-price, i.e. $x_t = \text{mid-price}_\text{last tick of the bin}$. I implemented both approaches to compare the results.
For the average mid-price of each bin, the benchmark accuracy is 57.63%, while the ARIMA forescasting accuracy is 60.21%. The 2.58% difference between these two results seems to verify my supervisor's concern.
For the last tick's mid-price of each bin, the benchmark accuracy is 48.51%, while the ARIMA forecasting accuracy is 48.96%.
The difference of acuracy is big. Does my method have the problem of information leakage?
## Answer by Hans-Peter Schrei (score 2)
https://quant.stackexchange.com/a/83700
Although the target that will eventually be realised, $$ r_{t+1} = \log\!\left(\frac{x_{t+1}}{x_t}\right), $$ also contains $x_t$, this does not contaminate training because $x_t$ is already part of the information set $\mathcal{F}_t$ available to any real-world trader at the end of interval $t$.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.