Skip to content
All library documents

Choosing Between Jump Diffusion and Neural Networks for Forecasting

Article Quant Q&A · Author: Furqan Hashim
Read the original

Summary

The document compares jump diffusion models and neural networks, especially LSTMs, for forecasting time series such as stock prices or ATM cash withdrawals. It distinguishes forecasting conditional averages from modeling the distribution of future outcomes. When the objective is minimizing mean squared error, the relevant target is the conditional expected value; a jump diffusion model may add little to that task unless its jump intensity or jump sizes vary over time.

Jump models may be more useful when the goal is to describe higher moments or forecast conditional quantiles, such as prediction intervals or value-at-risk measures. Neural networks can also target quantiles by using a pinball loss objective, and simpler models such as linear regression can do so as well. The document offers conceptual guidance rather than an empirical comparison for ATM withdrawals. Model choice should follow the forecast target and evaluation metric, and the discussion does not establish that either approach will perform better for a particular dataset.

Key ideas

  • The forecast objective and loss function should guide the choice between model classes.
  • For mean squared error, the target is the conditional expected value of the time series.
  • Jump diffusion models are primarily useful here for representing distributional features such as skewness, kurtosis, and jumps.
  • Quantile forecasts can be trained with pinball loss to produce prediction intervals or risk measures.
  • The document gives no dataset-specific evidence that jump diffusion or neural networks are superior for ATM withdrawal forecasts.

Tags

Machine learningStatisticsVolatilityRisk management
Full text
# Predicting time series using Jump Diffusion model and Neural Networks


# Predicting time series using Jump Diffusion model and Neural Networks












I am trying to understand the difference between using Jump diffusion model and Neural Networks or more precisely LSTM to predict time series data regardless what that data contains for example a stock price or withdrawals from ATMs.

If I look at research papers I will find examples of Jump Diffusion model and LSTM to predict stock prices. But if I try searching literature to forecast withdrawals from an ATM I couldn't find any example pertaining to Jump diffusion model. Mostly LSTM or ANN has been used to predict withdrawals from ATM.

If I am trying to predict ATM cash withdrawals can I use Jump Diffusion model to make forecast or would that be an incorrect approach?

## Answer by Stéphane (score 2)

https://quant.stackexchange.com/a/51301

Most of the work you will find on jump diffusion models will be in derivative pricing or related work on insurance. In essence, they tend to be interesting ways to think about future distributions.

If your performance metric is the mean squared error, we can easily show that what you should be trying to estimate is the conditional expected value of the process. Jump diffusions are designed to think about higher moments. They seldom are very sophisticated ways to think about conditional expectations, unless you try to look at time-varying dynamics for jump intensities and/or sizes. It wouldn't be especially interesting, in other words.

Now, if you want measures of conditional quantiles to predict intervals, that would tap directly into the interesting properties of jump diffusion models -- people use them to force skewness and kurtosis, mostly on shorter horizons to force agreement with empirical volatility surfaces. You can set up a pinball loss type function as the objective function of your neural network and it would force it to predict quantiles from which you can build prediction intervals.

In that case, maybe your comparison would be interesting: you could get build things like value-at-risk type measures for future withdrawals, or predict things like between X_1 and X_2 number of people will make withdrawals over some period of time in the future, with a confidence of Z%. Both types of models can do this, just as could a linear regression (if you change the least square loss for a pinball loss).

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.