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Discussing the article: "Forecasting a Conditional Distribution Using MLP"

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Check out the new article: Forecasting a Conditional Distribution Using MLP.

In this article, we will consider an MLP-based regression model that predicts not only the conditional expectation but also the conditional variance. In other words, we will train our network to predict the entire distribution of future prices based on the input feature vector. But for this purpose we will have to implement our own loss function.

In the highly volatile and uncertain financial markets such as Forex, accurately predicting price movements remains a key challenge for traders and analysts. Traditional regression approaches based on standard loss functions such as mean squared error (MSE) or sum of squared errors (SSE) often underperform. These functions assume homoscedasticity, that is, constancy of the variance of the target variable, which rarely corresponds to the real dynamics of financial time series. To adequately model such data, an approach is required that takes into account heteroscedasticity — the variable variance of price increments that depends on the input features.

The article presents a probabilistic approach to the regression problem using a multilayer perceptron (MLP) to predict the conditional Gaussian distribution of price increments. For this purpose, we implement a custom loss function based on the Gaussian negative log-likelihood (GaussianNLLLoss).


Author: Evgeniy Chernish

That’s brilliant – this must be the first post on the forum about probabilistic MO.

I wonder if it’s possible to do something similar for other distributions (such as the Gamma or Weibull distributions)?

Aleksey Nikolayev Weibull distributions)?

Yes, of course. If the predicted value follows roughly that distribution, why not?

For the increments, you could also try the Student’s distribution instead of the normal distribution.
Evgeniy Chernish #:

Yes, of course. If the predicted value has roughly this distribution, why not?

For the increments, you could also try the Student’s distribution instead of the normal distribution.

I think I’ll have a go at it sometime for the height of the zigzag’s knee. There, for random walk, the distribution is exponential, so we need distributions on the positive half-axis that include the exponential distribution as a special case.

I could also try to incorporate a survival analysis, but I just haven’t got round to it yet.

Everything’s fine, apart from one thing. For the ‘forecast indicator’, the PLOT_SHIFT parameter (shifting the lines into the future) should have been enabled, but at the moment, instead of a forecast, only the ‘actual’ data from the historical record is being plotted. Or perhaps we have different interpretations of the term ‘forecast’.
Stanislav Korotky #:
Everything’s fine, apart from one thing. For the ‘forecast indicator’, the PLOT_SHIFT parameter (shifting the lines into the future) should have been enabled, but at the moment, instead of a forecast, only the ‘actual’ data from the historical record is being plotted. Or perhaps we have different interpretations of the term ‘forecast’.
After all, we only make forecasts one step ahead. We don’t forecast several bars ahead.

Therefore, what the indicator displays are all forecasts one step ahead, based on a feature vector constructed with a shift of one bar back.

And before the forecasts are displayed, a training sample is selected, on which we train the network.
Evgeniy Chernish #:
After all, we only make forecasts one step ahead. We don’t forecast several bars ahead.

Therefore, what the indicator displays are all forecasts one step ahead, based on a vector of features constructed with a one-bar offset to the past.

And before the forecasts are displayed, a training sample is selected, which we use to train the network.
In other words, on each test bar, are we showing the predicted closing price and its range for a bar that, as it were, does not yet exist?
Stanislav Korotky #:
In other words, are we showing on each test bar where the predicted closing price and its range lie for a bar that, as it were, does not yet exist?
Why ‘non-existent’? The zero bar is still forming, but we’ve already received the forecast for it when this bar opened, as a new vector of indicators has been formed. And this forecast does not change or get recalculated, as it depends on past prices, not on past and current prices. Or have I missed something, and does the code actually look into the future?
Evgeniy Chernish #:
Why ‘non-existent’? The zero bar is still forming, but we’ve already received the forecast for it when this bar opened, as a new vector of indicators has formed. And this forecast does not change or get recalculated, as the forecast depends on past prices, not on past and current prices. Or have I missed something, and does the code look into the future?
It’s highly unlikely that it’s looking into the future; I meant something else. It seems that the forecast is calculated right at the start of a new bar’s formation—that is, effectively only when the opening price of that ‘bar’ is known—which is why I described it, and I quote, as ‘virtually non-existent’.
Stanislav Korotky #:
It’s unlikely to be a glimpse into the future; that’s not what I meant. Apparently, the forecast is calculated right at the start of a new bar forming, i.e. effectively only when the opening price of that ‘bar’ is known, which is why I described it, and I quote, as ‘virtually non-existent’.
Yes, that’s exactly how it’s intended
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