Quantitative Return Forecasting
6. Neural networks
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6.1 Mathematicians first realised the fundamental
limitations of traditional time series analysis two or three decades ago. This
coincided with a time when computer scientists were particularly enthusiastic
about the prospects of developing artificial intelligence. The combination led
to the development of neural networks.
6.2 A neural network is a mathematical algorithm
that takes a series of inputs and produces some output dependent on these
inputs. The inputs cascade through a series of steps that are conceptually
modelled on the apparent behaviour of neurons in the brain. Each step
(‘neuron’) takes as its input signals one or more of the input feeds (and
potentially one or more of the output signals generated by other steps), and
generates an output signal that would normally involve a non-linear function of
the inputs (e.g. a logistic function). Typically some of the steps are
intermediate.
6.3 Essentially any function of the input data
can be replicated by a sufficiently complicated neural network. So it is not
enough merely to devise a single neural network. What you actually need to do
is to create lots of potential alternative neural networks and then develop
some evolutionary or genetic algorithm that is used to work out
which is the best one to use for a particular problem. Or, more usually, you
define a much narrower class of neural networks that are suitably parameterised
(maybe even just one class, with a fixed number of neurons and predefined
linkages between these neurons, but where the non-linear functions within each
neuron are parameterised in a suitable fashion). You then train the
neural network, by giving it some historic data, adopting a training
algorithm that you hope will home in on an appropriate choice of parameters
that are likely to work well when attempting to predict the future.
6.4 There was an initial flurry of interest
within the financial community in neural networks, but this interest seemed
over time to subside. It is not that the brain doesn’t in some respects seem to
work in the way that neural networks postulate. Rather, earlier computerised
neural networks generally proved rather poor at the sorts of tasks they were
being asked to perform in this space.
6.5 More recently, with the advent of ‘Big Data’
and more powerful computers, there seems to have been a resurgence of interest in
the topic of ‘machine learning’ and artificial intelligence. We can expect this
to percolate into the financial community, if some firms identify approaches
that seem successful with investment orientated problems. However, there is no
guarantee that this will be easy. As Ghahramani
(2015) notes, machine learning involves uncertainty, i.e. there is no
certainty that investment orientated problems are easily amenable to such
techniques, although possibly there are ways of modelling this uncertainty
using the probabilistic framework to machine learning and therefore using probabilistic
approaches to work out which types of investment problems are most amenable to machine
learning techniques. He writes:
“The
key idea behind the probabilistic framework to machine learning is that learning
can be thought of as inferring plausible models to explain observed data. A
machine can use such models to make predictions about future data, and take
decisions that are rational given these predictions. Uncertainty plays a
fundamental part in all of this. Observed data can be consistent with many
models, and therefore which model is appropriate, given the data, is uncertain.
Similarly, predictions about future data and the future consequences of actions
are uncertain. Probability theory provides a framework for modelling
uncertainty.”
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