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首页深度学习网络在股市分析与高频预测中的应用比较
本文主要探讨了深度学习网络在股票市场分析与预测中的应用潜力。深度学习由于其独特的特性,如能够从大量未经处理的数据中自动提取特征,而无需预先设定预测因子,使其在高频股票市场预测中展现出吸引力。研究的焦点在于深度学习算法在不同结构(如网络架构)、激活函数以及模型参数选择上的多样性,以及这些因素如何影响其性能,特别是数据表示方法对结果的影响。 文章深入探讨了三种无监督特征提取方法在深度学习网络中的应用:主成分分析(PCA)、自编码器(Autoencoder)和受限玻尔兹曼机(RBM)。通过以高频日交易回报作为输入数据,作者考察了这些方法对预测未来市场行为能力的影响。实验结果显示,深度神经网络可以从自回归模型的残差中提取额外信息,从而提高预测精度,反之,若先应用自回归模型再处理网络的残差,效果则不明显。此外,研究还发现,当将预测网络应用于基于协方差的市场结构分析时,协方差估计有显著提升。 本文的实证研究提供了宝贵的实践指导,对于深度学习网络在股票市场分析中的有效利用提供了客观评估,并指出了潜在的研究方向。尽管深度学习在某些情况下显示出了优势,但同时也揭示了挑战和局限性,这为投资者、金融分析师以及机器学习研究人员提供了关于如何优化和进一步探索深度学习技术在金融市场中的应用的重要启示。未来的研究可以继续探索不同的网络架构、优化算法以及结合其他数据源以提升股票市场预测的准确性。
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AE is a neural network model characterized by a structure in which the model parameters are
calibrated by minimizing the reconstruction error. Let h
l
= δ
l
(W
l
h
l−1
+ b
l
) be the network
function of the lth layer with input h
l−1
and output h
l
. Although δ
l
can differ across layers, a
sigmoid function, δ(z) = 1/(1 + exp (−z)), is typically used for all layers, which we also adopt
in our research.
2
Regarding h
l
as a function of the input, the representation of x can be written as
u = φ(x) = h
L
◦ ··· ◦ h
1
(x) for an L-layer AE (h
0
= x). Then the reconstruction of the data
can be similarly defined: x
rec
= ψ(u) = h
2L
◦ ··· ◦ h
L+1
(u), and the model can be calibrated
by minimizing the reconstruction error over a training dataset, {x
n
}
N
n=1
. We adopt the following
learning criterion:
min
θ
1
N
N
X
n=1
||x
n
− ψ ◦ φ(x
n
)||
2
, (8)
where θ = {W
i
, b
i
}, i = 1, ..., 2L. W
L+i
is often set as the transpose of W
L+1−i
, in which case
only W
i
, i = 1, ··· , L, need to be estimated. In this paper, we consider a single-layer AE and
estimate both W
1
and W
2
.
(iii) Restricted Boltzmann Machine, RBM
RBM (Hinton, 2002) has the same network structure as a single-layer autoencoder, but it uses
a different learning method. RBM treats the input and output variables, x and u, random, and
defines an energy function, E(x, u), from which the joint probability density function of x and u
is determined from the formula
p(x, u) =
exp(−E(x, u))
Z
, (9)
where Z =
P
x,u
exp(−E(x, u)) is the partition function. In most cases, u is assumed to be a d-
dimensional binary variable, i.e., u ∈ {0, 1}
d
, and x is assumed to be either binary or real-valued.
When x is a real-valued variable, the energy function has the following form (Cho, Ilin, & Raiko,
2011):
E(x, u) =
1
2
(x − b)
T
Σ
−1
(x − b) − c
T
u − u
T
W Σ
−1/2
x , (10)
where Σ, W , b, c are model parameters. We set Σ to be the identity matrix; this makes learning
simpler with little performance sacrifice (Taylor, Hinton, & Roweis, 2006). From Equations (9)
and (10), the conditional distributions are obtained as follows:
p(u
j
= 1|x) = δ(c
j
+ W
(j,:)
x), j = 1, ··· , d, (11)
p(x
i
|u) = N(b
i
+ u
T
i
W
(:,i)
, 1), i = 1, ··· , D, (12)
where δ(·) is the sigmoid function, and W
(j,:)
and W
(:,i)
are the jth row and the ith column of W ,
respectively. This type of RBM is denoted the Gaussian-Bernoulli RBM. The input data is then
represented and reconstructed in a probabilistic way using the conditional distributions. Given an
input dataset {x
n
}
N
n=1
, maximum log-likelihood learning is formulated as the following optimiza-
tion:
max
θ
"
L =
N
X
n=1
log p(x
n
; θ)
#
, (13)
2
exp (z) is applied to each element of z.
7
where θ = {W, b, c} are the model parameters, and u is marginalized out (i.e., integrated out
via expectation). This problem can be solved via standard gradient descent. However, due to
the computationally intractable partition function Z, an analytic formula for the gradient is usu-
ally unavailable. The model parameters are instead estimated using a learning method called the
contrastive divergence (CD) method (Carreira-Perpinan & Hinton, 2005); we refer the reader to
Hinton (2002) for details on learning with RBM.
3 Data Specification
We construct a deep neural network using stock returns from the KOSPI market, the major stock market
in South Korea. We first choose the fifty largest stocks in terms of market capitalization at the beginning
of the sample period, and keep only the stocks which have a price record over the entire sample period.
This leaves 38 stocks in the sample, which are listed in Table II. The stock prices are collected every five
minutes during the trading hours of the sample period (04-Jan-2010 to 30-Dec-2014), and five-minute
logarithmic returns are calculated using the formula r
t
= ln(S
t
/S
t−∆t
), where S
t
is the stock price at
time t, and ∆t is five minutes. We only consider intraday prediction, i.e., the first ten five-minute returns
(i.e., lagged returns with g = 10) each day are used only to construct the raw level input R
t
, and not
included in the target data. The sample contains a total of 1,239 trading days and 73,041 five-minute
returns (excluding the first ten returns each day) for each stock.
The training set consists of the first 80% of the sample (from 04-Jan-2010 to 24-Dec-2013) which
contains 58,421 (N
1
) stock returns, while the remaining 20% (from 26-Dec-2013 to 30-Dec-2014) with
14,620 (N
2
) returns is used as the test set:
Training set: {R
n
t
, r
n
i,t+1
}
N
1
n=1
, Test set: {R
n
t
, r
n
i,t+1
}
N
2
n=1
, i = 1, ··· , M.
To avoid over-fitting during training, the last 20% of the training set is further separated as a validation
set.
All stock returns are normalized using the training set mean and standard deviation, i.e., for the
mean µ
i
and the standard deviation σ
i
of r
i,t
over the training set, the normalized return is defined as
(r
i,t
− µ
i
)/σ
i
. Henceforth, for notational convenience we will use r
i,t
to denote the normalized return.
At each time t, we use ten lagged returns of the stocks in the sample to construct the raw level input:
R
t
= [r
1,t
, ··· , r
1,t−9
, ··· , r
38,t
, ··· , r
38,t−9
]
T
.
3.1 Evidence of Predictability in the Korean Stock Market
As a motivating example, we carry out a simple experiment to see whether past returns have predictable
power for future returns. We first divide the returns of each stock into two groups according to the
mean or variance of ten lagged returns: If the mean of the lagged returns, M(10), is greater than some
threshold η, the return is assigned to one group; otherwise, it is assigned to the other group. Similarly,
by comparing the variance of the lagged returns, V (10), with a threshold , the returns are divided into
two groups.
8
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