深度学习驱动的金融时间序列预测：超越传统方法

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"《深度学习在多变量金融时间序列中的应用》（DeepLearningforMultivariateFinancialTimeSeries）是一篇由Gilberto Batres-Estrada于2015年6月撰写的文章，探讨了深度学习在金融行业的实际应用。随着深度学习框架在图像和语音识别等任务中取得显著突破，作者将其引入金融领域，特别是预测金融市场数据。该研究主要聚焦于使用深度学习算法构建深度神经网络（Deep Neural Network, DNN），其中深度信念网络（Deep Belief Networks, DBN）与多层感知器（Multilayer Perceptron, MLP）相结合。这种方法的应用目标是形成投资组合，通过选择股票来实现收益。研究结果显示，这些由深度学习构建的组合能够超越组成标普500指数的股票平均回报，显示出其优越性。与传统的机器学习方法，如逻辑回归网络（Logistic Regression Network）和朴素基准进行对比，深度学习模型的表现更佳且稳定性更高。这表明深度学习方法因其可靠性和优秀性能，有望在金融领域占据一席之地，预示着深度学习技术在金融决策中的潜力和未来发展方向。关键词：反向传播算法（Back-Propagation Algorithm）、神经网络、深度信念网络、多层感知器以及深度学习，都成为本文探讨的核心概念，展示了深度学习如何通过复杂的学习能力，对金融市场的动态和趋势进行精准预测，为投资者提供有价值的信息和策略指导。"

The biases have diﬀerent ﬁxed oﬀsets which are −0.5, −1.5, −2.5, . . . .

Then the sum of the probabilities is given by

i=1

ϕ(v −i + 0.5) ≈ log(1 + e

), (2.7)

where v = w

x + b. A drawback of this model is that the sigmoid

function has to be used many times to get the probabilities required

for sampling an integer value correctly. A fast approximation is

ϕ(v) = max



0, v + N



0, ϕ(v)





, (2.8)

where N(0, σ) is a Gaussian noise with zero mean and variance σ.

−5 0 5 10

Figure 2.5: Rectiﬁed linear units. The ﬁgure shows log(1 + e

4. Odd Activation Functions. It is worth noting in these examples of

activation functions, that they range from 0 to +1. In some situations

it is preferable to have an activation function whose range is from −1

to +1 in which case the activation function is an odd function of the

local ﬁeld. The threshold function ranging from −1 to +1 which is

known as the signum function is:

ϕ(v) =







1 if : v ≥ 0

0 if : v = 0

−1 if : v < 0

2.1.4 The Perceptron

The Perceptron was the ﬁrst model of a neural network. Rosenblatt, a psy-

chologist, published his paper (Rosenblatt, 1957) on the perceptron. This

paper was the starting point in the area of supervised learning. Engineers,

physicists and mathematicians got interested in neural networks and be-

gan to use those theories in their respective ﬁelds in the 1960s and 1970s,

(Haykin, 2009). McCulloch and Pitts (1943) introduced the idea of neural

networks as computing machines, Hebb (1949) postulated the ﬁrst rule for

self-organised learning. Rosenblatt’s perceptron is built around a nonlinear

neuron, that of the McCulloch-Pitts model, Figure 2.1.

2.1.5 The Perceptron As a Classiﬁer

The perceptron consists of a linear combiner followed by a hard limiter, ϕ(·),

performing the signum function. The summing node in the neural network

computes a linear combination of the inputs applied to its synapses, and it

incorporates a bias. The resulting sum is applied to the hard limiter. The

neuron then produces an output equal to +1 if the hard limiter input is

positive, and −1 if it is negative.

In the neuron model of Figure 2.1 we have m input signals, x

, x

, . . . , x

and m weights, w

, w

, . . . , w

. Calling the externally applied bias b we see

that the hard limiter input or induced local ﬁeld of the neuron is

v =

i=1

+ b. (2.11)

A perceptron can correctly classify the set of externally applied input signals

, x

, . . . , x

into one of two classes C

or C

. The decision for the classiﬁ-

cation is based on the resulting value of y corresponding the to input signal

, x

, . . . , x

where y = 1 belongs to C

and y = −1 belongs to C

To gather insight in the behaviour of a pattern classiﬁer, it is customary

to plot a map of the decision regions in a m-dimensional signal space spanned

by the input variables x

, x

, . . . , x

. The simplest case of a perceptron

network consists of two decision regions separated by a hyperplane which is

deﬁned by

i=1

+ b = 0. (2.12)

This is illustrated in Figure 2.7 for the case of two variables x

, x

for which

the decision line is a straight line. A point (x

, x

) lying in the region above

the boundary line is classiﬁed as belonging to class one, C

, and a point

, x

) lying below the boundary to class two, C

. We can see from the

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