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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?

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  • $\begingroup$ This is quite broad. What is the exact problem you’re trying to solve? $\endgroup$ – Bob Jansen May 25 '19 at 14:23
  • $\begingroup$ I've made changes. $\endgroup$ – Furqan Hashim May 25 '19 at 14:35
  • $\begingroup$ I don't know much about ATM withdrawals, but they probably follow a rather different process than stock prices. In particular ATM withdrawals have important seasonaliity (day of the week and holidays matter) and I do not think they 'jump' from one level to another like stock prices sometimes do (on a takeover or bankrupcty etc.). I doubt jump diffusion would model ATM w/d well $\endgroup$ – Alex C May 25 '19 at 17:48
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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).

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