trading volume volatilities via a series of disturbance experiments. Furthermore, we .... changing rate of financial trading volumes on a daily basis also exhibits ...
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
Mining associations between trading volume volatilities and financial information volumes based on GARCH model and neural networks Nan Li, Jian Yang, Xun Liang Institute of Computer Science and Technology, Peking University, China E-mail: {linan, yangjian, liangxun}@icst.pku.edu.cn Abstract: There has been an increasing attention on the influences online financial information has on the financial markets. In the meanwhile, the volatility of trading volumes, just as the volatility of stock returns, has an inseparable association with financial risks. It has been considered that there might exist some direct or indirect correlations between online financial information volumes and financial volatilities, though corresponding quantitative analyses or empirical studies are still absent. In this paper, we introduce a mathematical model utilizing artificial neural networks (ANNs) and GARCH (Bollerslev, 1986) model, in order to mine the associations in between. The rudimentary mathematical basis is the GARCH model, while we introduce the volume of financial information from the Internet as an exogenous input, in conjunction with artificial neural networks as the prediction tool. Since combining ANN and GARCH to probe into the correlations between the aforementioned two is somewhat left untouched, it’s worth mentioning that not only have we realized the prediction of the trading volume volatilities to an acceptable extent; we also have quantitatively analyzed the model’s forecasting ability for the volatility trends. Besides, we further substantiate the impact online financial information has on financial trading volume volatilities via a series of disturbance experiments. Furthermore, we have presented a basic forecasting measure relying on the volatility-clustering feature, and proved that our model significantly outplays this measure in forecasting volatility trend. Keywords: Internet financial information; financial volatility; GARCH model; neural network; financial forecasting; time series.
1
Peramunetilleke and Raymond, 2001), whose commonality, however, lies in that they based their researching on the natural language processing (NLP) techniques to mine the correlations between financial markets and the frequencies of financial keywords occurred in financial news online. On the other hand, we take an approach mainly focused on the volume of online financial information, and particularly try to dig into the associations between it and the financial volatilities for the purpose of forecasting. In the first place, within the financial field, prediction of the financial volatilities has always been appealing to academicians, investors as well as practitioners. Since above all, forecasting volatilities serves as the fundamental basis for pricing financial assets and derivatives exemplified by that financial volatility constitutes an important parameter in the Black-Scholes model (Black and Scholes, 1973). It can also be illustrated by the trading of straddle options, which requires the buyers to accurately predict the underlying asset’s volatility if they want to gain a profit. Besides, it has also been acknowledged that there is a close correlation between financial volatilities and risks, with usually the former as a representative of the latter, resulting in that to effectively predict the financial volatilities becomes a main measure taken by portfolio holders to evade risks. What’s more, an accurate prediction
INTRODUCTION
Due to its real-time interaction, exuberance and a wide coverage, Internet has gradually superseded some traditional media to become one of the primary channels people acquire information. Consequently, financial information attained from the Internet plays an important role within the financial markets. Liang (2005) pointed out that compared to other media, Internet enables people to get the most up-to-date and comprehensive financial information. Nonetheless, from the current literature, already-adopted exogenous inputs for forecasting financial volatilities include consumable prices, interest rates, foreign exchange rates, etc. (Catfolis, 1996), whereas nobody has ever taken online financial information volume into consideration yet. Thus does online financial information really have an impact on financial volatility? Will the introduction of online financial information volume help improve the accuracy of forecasting? In this paper, we will give our answers to such questions by presenting a mathematical mining model based on GARCH and ANN. It’s worth mentioning that there have already existed some research works regarding the associations between financial markets and Internet financial news (Wuthrich et al., 1998; Chuttur and Bhurtun, 2005; Costantino, 1997;
ISBN 978-0-9783350-0-7
388
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
of financial volatilities will definitely serve as an effective obstacle of financial crimes. Secondly, we base our mathematical model on GARCH theory mainly due to the fact that financial data is a typical time series exhibiting its own features, which entails a more suitable theoretical basis for mathematical modelling. Within the current literature, several traditional time series models and statistical methods have been adopted to forecast financial volatilities (Pang, 2004), including autoregressive model, moving average model (Dickey et al., 1986), logical model, long-run moving model, randomwalking, etc. Nonetheless, GARCH model apparently outplays these approaches in modelling financial time series since it’s more capable to catch those features as fat tail, volatility-clustering, asymmetry, time-varying variance, leverage effect, etc, therefore has been widely applied into financial time series investigation (Garcia et al., 2005; Zheng et al., 2005; Liu, 2005). In the meanwhile, ANN has been adopted in this paper as the prediction tool. Before the application of ANN into the financial markets, people mainly relied on some linear tools to establish the prediction model, such as linear regression (Lai et al., 1996). However, due to its superiority in nonlinear learning and modelling, ANN has progressively been applied into financial forecasting by an increasing number of researchers (Freisleben and Ripper, 1997). Up till now, investigation into the correlations between financial volatilities and online financial information based on a combination of GARCH and ANN is still absent. Our approach is just aimed at promoting the accuracy of financial forecasting with the aid of these two methodologies. As a matter of fact, the empirical studies have substantiated that our model is sufficient to provide a satisfying prediction of the volatility trend and is scalable enough to be applied into different stocks or indices by appropriately modifying the parameters. The rest part of this paper is organized as follows. Section 2 briefly explains the characteristics and architecture of our model, while section 3 details the underlying theoretical and mathematical bases. How to utilize the ANN to implement a dynamic training and prediction is presented in section 4 and empirical studies are covered in section 5. In section 6, an eventual conclusion is reached. 2
The primary subject in this paper is the correlation between Internet financial information and the trading volume volatilities, which is for the purpose of improving the predicting performance of the latter. In order to achieve this goal, we introduce the GARCH model as our theoretical basis, whose application has spanned a wide range into risk management, portfolio management, asset allocation, option pricing, etc. The primary reasons that have contributed to GARCH’s superiority over the other methodologies are in the first place, it is built on advances in the understandings and modeling of volatilities of the past; and in the second hand, it takes into account some specific characteristics of financial time series, such as excess kurtosis, volatility clustering and time-varying conditional variances. It can be concluded that GARCH is a preferable alternative to capture effects exhibited by financial time series. In addition, GARCH model can be applied on any time series that has significantly exhibited GARCH effects. There are examples such as Garcia et al. (2005) and Zheng et al. (2005) who applied GARCH theory into the prediction for electricity prices, and Liu (2005) otherwise into the Japanese foreign exchange markets. In our approach, we have substantiated that the changing rate of financial trading volumes on a daily basis also exhibits GARCH effects such as fat tail and the volatility thereof is persistent. Furthermore, we have proved that the online financial information volume time series also exhibits GARCH effects using the GARCH toolbox provided by MATLAB. Besides, ANN has been adopted into our approach as the self-learning and prediction tool. So far, ANN has been widely studied and implemented into the financial domains (Catfolis, 1996; Freisleben and Ripper, 1997; Lai et al., 1996; Kuan and White, 1994; Tino et al., 2001; Gencay and Min, 2001). Nonetheless, the current literature is still lack of applying ANN into forecasting the volatility of stock market trading volumes. In the meanwhile, there have existed some research workings that conduct a comparison between the prediction performances of ANN and GARCH (Freisleben and Ripper, 1997; Tino et al., 2001) or combine these two to predict the financial volatilities (Donaldson and Kamstra, 1997). However, as mentioned previously, we are still in lack of works that take the investigation into the associations between financial trading volume volatilities and online information volumes based on a conjunction of these two techniques. In this paper, we regard the online financial information volume as an important element that influences the financial trading volumes, and take the endeavor to forecast the volatility of the latter one with the aid of GARCH and ANN. The basic architecture of our methodology can be visualized in Figure 1.
OUR APPROACH
In this paper, we haven’t taken the approach, as the other previous researchers did, to investigate into the volatility of financial assets’ values; on the other hand, we probe into the volatility of financial trading volumes. This is mainly because we consider that the fluctuation of trading volumes, just like that of the asset values, vividly reflects the alterations of markets’ and investors’ behaviours. Therefore, effectively forecasting the trading volume’s volatility will be beneficial and advisory to those who are exposed to financial risks and wish to somewhat master the developing trend of trading volumes. ISBN 978-0-9783350-0-7
389
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007 Figure 2 Changing rates of the trading volumes of NASDAQ index on a daily basis within the period from Oct 11th, 1984 to Oct 16th, 2006
It can be apparently observed, from Figure 2, that the changing rates on a daily basis of the trading volumes as well exhibit volatility-clustering feature. Besides, a Kurtosis value as 11.53 calculated from this specific time series also illustrates that there exists a fat tail effect of this time series. To make it more tenable, we’ve also discovered obvious GARCH effects exhibited by online financial information volume time series via test experiments conducted on more than 100 stocks in the U.S. stock markets. As aforementioned, the principal subject being investigated in our approach is the volatility of the daily changing rates of stock trading volumes, which entails a sound expression for the volatility. Corresponding to this, we define the variance of the trading volumes’ daily changing rates within a certain period as the volatility. In particular, for a specific stock, let vt denote its trading volume on day t, thus the daily changing rate y t of the trading volumes can be denoted as v (1) y t ln t . vt 1 If we define D as the width of the calculating window for the volatility, the volatility can be calculated by computing the variance of the y t within the (t-D+1)th and the tth day, as indicated in
Figure 1 Architecture and functional parts of our approach
3 GARCH METHODOLOGY AND MATHEMATICAL MODEL
That we base our approach on the GARCH model in this paper, as previously mentioned, is primarily because the specific features exhibited by financial time series (Freisleben and Ripper, 1997; Zhang and Fan, 2005; Liu, 2005), which can be illustrated by fat tail, volatility clustering, time-varying variance (Engle, 1982), asymmetry, non-linearity, etc. All these features determine that traditional time series models might not be capable enough to accurately model financial time series. In the meanwhile, GARCH model takes into account the timevarying variance and auto-regression (Engle, 1982; Bollerslev, 1986) as well as bases its mathematical equations on the information set derived from the immediate past, which constitutes the superiority of GARCH in modeling financial time series. We suppose that the volatility of financial trading volumes exhibits similar characteristics as that of stock prices, and we further substantiate this supposition via the tools provided by MATLAB. Figure 2 visualizes the time series of the changing rates of the trading volumes of NASDAQ index on a daily basis within the period from Oct 11th, 1984 to Oct 16th, 2006.
D 1
t2
(y i 0
t i
yt ) 2
,
D 1
(2)
where D 1
yt
y i 0
D
t i
.
(3)
Thus we achieve t as the volatility of the trading volume’s changing rates in this paper. Before we further probe into the GARCH methodology implemented in our approach, we first take a look at the original version of the GARCH model, which is composed of the mathematical equations as (4) yt t t , 2
t | t 1 ~ N (0, t2 ) , p
q
i 1
j 1
(5)
t2 0 i t2i j t2 j ,
(6)
0 >0, i , j ≥0, yt represents the daily stock return, t 1 represents the information set available at time t and t denotes the disturbance, also known as the shock, where
forecast error, residual, innovation, etc. (Freisleben and Ripper, 1997; Engle, 1982; Bollerslev, 1986; Zhang and Fan, 2005), which to some extent reflects the difference between the actual return and the expected one; t , i.e. 2
ISBN 978-0-9783350-0-7
390
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
the volatility, serves as the time-varying variance of both y t and t . According to the analyses covered in the
t | t 1 ~ N (0, t2 ) , q
r
i 1
j 1
k 1
,(11) where p, q, r in (11) represent the three time lags in this model respectively; the three unknown functions, namely the t i , t j and t k represent the undetermined non-
rates of the trading volumes, in order to mine the associations between the trading volume volatilities and the online financial information volumes. A close correlation between the financial volatilities and the innovation can be illustrated from equations (4) to (6). As a matter of fact, how to appropriately and correctly model the innovation term t has a significant effect on the
linear correlations between the volatility and itself, the daily changing rate yt and the exogenous input Wt , which is the online financial information volume. Equations (9) to (11) constitute the primary theoretical basis relied upon which we decide the input and output vectors of the ANN in our approach. Miller (1979) pointed out that the residuals within the auto-regressive moving-average model do not exhibit significant auto-correlations or persistence, whereas the squared values of them do. What’s more, GARCH model, expressed in (4) to (6), as well takes the squared residual as one of its inputs. Consequently, we make all the inputs in (11) their squared values.
accuracy of the volatility forecasting. What GARCH has disclosed is that t , in all probability, is an undetermined function of those exogenous inputs which might have an impact on the financial volatilities. Undeniably, financial information has been attracting researchers’ and practitioners’ attention as being an important exogenous input for predicting financial volatility. What adds to rationality to regard financial information as one exogenous input is that GARCH model bases its conditional distribution on the information set available at time t. Additionally, Freisleben and Ripper (1997) pointed out that the parameter j in equation (6) determines the
4 ESTABLISHMENT OF THE NON-LINEAR PREDICTION MODEL USING NEURAL NETWORKS
extent of the immediate reaction on new events in the market, mostly in the form of financial news, of the stock return. Nonetheless, due to the feasibility of the available technologies, previous academicians were not able to conduct an in-depth and comprehensive analysis of the financial information, due to the dependence upon manual selection from a limited amount of financial news. Fortunately, the fast development of Internet has enabled us to acquire the financial information that we’re interested from online in a most real-time and exhaustive fashion and afterwards conduct a quantitative analysis between it and the financial volatility. Considering these facts, to designate the financial information volume as one variate of t is justifiable. Empirical studies to further confirm this
Currently, ANN has been pervasively as well as successfully applied into the financial fields. Good illustrations include the work done by Freisleben and Ripper (1997), who utilized ANN to realize the estimation of the parameters for the GARCH model, that by Zhang, Liang and Yang (2006), who capitalized ANN to implement the pricing for options, and that by Tino, Schittenkopf and Dorffner (2001), who predicted the stock return volatilities based upon a recurrent neural network as well as implemented a comparison to the GARCH model’s performance. In our approach, we can not get to know the exact expressions of the three functions contained in (11), however the only conclusion we are capable to obtain is that there might come along some non-linear correlations between the volatilities, the daily changing rates and the online financial information volumes. On the other hand, the advent of ANN has provided an effective tool for people to investigate into the non-linear associations between different data sets. Via appropriate configurations of the parameters and hidden nodes’ number, ANN is sufficient to approximate almost all forms of functions (Cai and Shi, 2003; Huang et al., 2006; Wu et al., 2006; Kuan and White, 1994). In addition, the works done by Cybenko (1989), Funahashi (1989), Hornik (1991) and Hornik et al. (1989) also indicate that ANNs with sufficiently many hidden nodes and properly configured parameters can approximate an arbitrary function arbitrarily well. Due to the fact that financial data is inherently characteristic of being noisy, stochastic and non-stationary (Tino et al., 2001), we adopt a special training process, namely an “online” or a “dynamic” training process, in order to prevent the phenomenon of over-fitting, which seriously impedes the generality of the model. Because of
conclusion will be presented in section 5. According to what we have achieved so far, there is a good reason to formulize t using the following two equations, (7) t yt , (8)
where (7) is derived from (4), is supposed to be a constant (under the premise that we assign a constant as the expected value for the daily changing rate of trading volumes), and Wt is the Internet financial information volume on day t. Combining these two equations (7) and (8), we can come to a conclusion that the innovation term t is a certain function of both the online financial information volume and the daily changing rate of the trading volumes. Therefore we make a modification on the original GARCH model and thus achieve a new time series model expressed as (9) yt t t , ISBN 978-0-9783350-0-7
p
t2 0 i t i ( t2i ) j t j ( y t2 j ) k t k (Wt 2 k )
former parts of this paper, it is reasonable to replace the y t contained in these equations with the daily changing
t f t (Wt , t' ) g t (Wt ) t t' ,
(10)
391
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
the stochastic nature of financial time series, we select the data acquired within the period which is the closest to the current time point as the training patterns for every training epoch. In addition, data acquired within a time which is too remote from the current time point might contain potentially misleading information. In particular, if we want to realize the prediction for the volatility on day t, provided that the size of the training patterns amounts to C, we first train a neural network via conducting supervised predictions for the volatilities from day t-C to day t-1. A well-trained neural network is then used to forecast the volatility of the day t afterwards. In a nutshell, during the process of “online” or “dynamic” training, the forecasting for the volatility on a certain day is always based on a newly-trained neural network using data attained within the most immediate past. The ANN adopted in our approach is a three-layer feedforward neural network using different variations of back-propagation as the training algorithms, whose architecture can be visualized in Figure 3. The non-linear correlations between the input and the output vectors are reflected via the non-linear transfer function of the hidden layer, in particular the logsig function. The specific algorithms used in our approach contain the bayesian regularization back-propagation (Chan et al., 2002; Gancay and Min, 2001), BFGS quasi-Newton backpropagation (Hu et al., 2006) and the LevenbergMarquardt back-propagation (Kanzow et al., 2004). The former two are able to effectively impede the over-fitting effect while the third is characteristic of fast convergence.
those ranged from
average part. The size of the input vector amounts to p+q+r, and each of the input vectors represents the volatilities, squared daily changing rates and squared online information volumes within the most immediate past. Besides, there are H units in the hidden layer and the size of the output vector is 1. Let C denote the size of the training patterns for one training epoch, i.e. the neural network for each training epoch is trained based on the data acquired from the past C days. In addition, suppose that we use a matrix tuple to demonstrate the training patterns for one training epoch, thus we have
t2C 1 2 t C 2 ... t2C p 2 y t C 1 2 y P t C 2 ... 2 y t C q 2 Wt C 1 W 2 t C 2 ... 2 Wt C r
1
2 t 1
and
t2p
y
^
2 t
2 t q
y
Wt 21 H-1
Wt 2r H output layer
Figure 3 Architecture of the ANN in our approach The p, q, r indicated in Figure 3 correspond to the time lags of the volatility, the daily changing rate and the online financial ^
information
volume,
respectively,
while
the t represents the forecasting value for the volatility on 2
day t. The input elements ranged
T t2C
2 t 1
hidden layer
2 t p represent
from
t21
to
the auto-regressive part of the model while
ISBN 978-0-9783350-0-7
t2C
t2C 1
... t2 2
t2C 1
t2C
... t23
t2C p 1 t2C p 2 ... t21 p y t2C
y t2C 1
... y t2 2
y t2C 1
y t2C
... y t23
y t2C q 1 y t2C q 2 ... y t21 q Wt 2C
Wt 2C 1 ... Wt 22
Wt 2 C 1
Wt 2 C
... Wt 23
Wt 2C r 1 Wt 2 C r 2 ... Wt 21 r
(1 2)
2
input layer
y t21 to Wt 2 r represent the moving
392
t2C1
t2C2 ... t21 .
(13)
The trained neural network is then used to forecast the volatility on the day t and a comparison between the forecast value and the real value is also carried out thereafter. What’s worth mentioning is that we name this forecasting process as the testing process. Likewise, we denote the testing patterns by another matrix tuple as
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
t21 2 t 2 ... t2 p 2 y t 1 2 y P' t 2 , ... 2 yt q 2 Wt 1 W 2 t 2 ... 2 Wt r and
T ' t2 ,
experiments on the financial information acquired from Google Finance (http://finance.google.com), which collects its financial news and reports from more than 500 financial portals online. Moreover, we acquire our trading data in the financial markets from Yahoo Finance (http://finance.yahoo.com). 5.1 Using ANN to forecast the daily trading volume volatility
(14)
In the first place, all our experiment data are acquired from the finance sections of two predominant portals, Google and Yahoo. Specifically, the link for the financial information entry is http://finance.google.com, where we can attain the financial news within the past several months collected from more than 500 websites online. The entry for the trading data is http://finance.yahoo.com, where we can download the historical prices and trading volumes of almost every stock or index in the U.S. financial markets. Secondly, we introduce a comparative criterion to serve as a so called benchmark for our own approach. As has been mentioned previously, this criterion resembles the one used by Catfolis (1996), both of which rely on the basic rationale of volatility clustering. If we
(15)
where T’ stands for the real volatility on the day t, which is also the comparative target for the testing process.
use 5
EMPIRICAL STUDIES AND DISCUSSIONS
^
and t to represent the actual and the forecast 2
volatility on the day t, respectively, we are able to obtain ^
t2 t21 ,
The empirical studies covered in this paper can primarily be divided into two phases. During the first phase, we utilize the ANN to carry out the forecasting for the volatilities while recording the mean forecast errors and the accuracies for the volatility trend forecasting. Catfolis (1996) introduced a criterion using the previous day’s volatility to forecast that of the current one, which is based on the volatility-clustering feature, in order to establish a comparative benchmark for his own predictive model. In this paper, we adopt a similar approach to implement a comparison. Considering that currently there is no acknowledged standard to rely on when it comes to the prediction of volatility trend, we again utilize the volatility-clustering feature to implement the comparison regarding this. Specifically, we suppose that the volatility trend of the day t-1 can be used to forecast that of the day t, and thereafter substantiate, via empirical studies, that our model can considerably outplay such kind of approach in volatility trend forecasting. In the second phase, we conduct disturbance experiments on those well-trained neural networks for the purpose of observing to what extent the change of each element in the input vector can cause a corresponding change on the output. Via this way, we’re able to perceive qualitatively whether the exogenous input of the online financial information volume really has an effect on the trading volume volatility. The widths of the calculating windows, namely the D, in both phases are set to 20 days. In the work done by Wuthrich et al. (1998), only 15 webpages are downloaded from indicated news sources in the morning on the current day for the purpose of investigation, whereas in our approach, we based our ISBN 978-0-9783350-0-7
2 t
(16)
which is based on the hypothesis that we can use the volatility on the day t-1 to forecast that on the day t. ^
Similarly, if we let and t denote the actual and 2 t
2
the forecast volatility trend on the day t, respectively, first we assume that
1, 2 t 0, 1,
t2 t21 t2 t21 ,
(17)
t2 t21
and then we can also obtain that ^
t2 t21 ,
(18)
which is based on the hypothesis that we can use the volatility trend on the day t-1 to forecast that on the day t. As aforementioned, we have introduced two ways to measure the forecasting performance, namely the average
e and the volatility trend forecasting accuracy ratio. If we define et as the forecast error for the forecast error day t, we have ^
| 2 2 | et t 2 t , t
(19)
and
e
393
t1 1 et , t1 t 0 1 t t 0
(20)
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
where t 0 and
t1 represent the beginning and ending day for
ANN
the forecasting, respectively. In addition, we define the ratio as the percentage of the days on which the forecast volatility trend is equivalent to the real one. When we conduct our experiments, we actually take into consideration a lot of factors that might impose an influence on the ultimate forecasting performance, including the width of the calculating window for the volatility, the specific stock, the values of the time lags, the size of the training patterns, etc., and we therefore conduct a series of experiments with different configurations for these factors. Conclusively, we conduct our experiments on two indices, NASDAQ and DOW, and two stocks, MSFT and INTC, with the time span as from Jun 30th, 2006 to Sept 28th, 2006, from Jun 29th, 2006 to Sept 26th, 2006, from Jun 28th, 2006 to Sept 26th, 2006 and from Jul 3rd, 2006 to Sept 28th, 2006, respectively. The results of these experiments are shown in Table 1.
benchmark ANN I
C
H
p
q
r
e (%) ratio (%)
ANN
20
5
4
9
1
11.08
83.33
6.32
30.77
9.33
73.91
4.95
41.67
7.67
69.57
4.95
41.67
11.49
76.47
5.73
44.44
benchmark N
ANN benchmark ANN benchmark ANN benchmark ANN benchmark
D
ANN benchmark ANN benchmark ANN benchmark ANN
M
benchmark ANN benchmark
-----------------10
5
5
8
2
-----------------10
4
3
8
3
-----------------20
6
4
4
4
-----------------10
8
6
6
1
-----------------15
6
9
9
3
-----------------15
5
9
4
2
-----------------20
5
4
9
1
-----------------10
8
5
8
2
-----------------10
6
5
5
------------------
ISBN 978-0-9783350-0-7
3
10.17
benchmark
4
9
1
-----------------6
5
5
3
-----------------15
benchmark
6
9
9
3
------------------
15.57
75.00
7.76
61.54
14.31
61.54
7.59
51.85
16.72
64.71
8.76
55.56
5.2 Disturbance experiments conducted upon trained neural networks
Within this phase of experiments, we further justify the correlation between online financial information volumes and the financial trading volume volatilities by conducting disturbance experiments on the trained neural networks
The forecasting results for the daily volatilities using neural networks. s/i in the first row stands for stock/index, while N, D, M, I stand for NASDAQ, DOW, MSFT, INTC, respectively. ANN here represents the approach we take while benchmark represents the comparative criterion we introduce based on volatility clustering. As aforementioned, C represents the size of the patterns, H the number of the hidden nodes and p, q, r the three time lags in equation (11).
model
5
10
ANN
Table 1
s/i
20
during the testing process. To accomplish this, we consecutively adjust each element of the input vector [
t21 ,... t2 p , yt21,... yt2q ,Wt 21 ,...Wt 2r
] from 75% to
125% of the original value based on a predetermined steplength,
and
thereafter
observe
and
record
the
corresponding changing rates of the output incurred by the adjustment of the input vector. Let
it , j denote the
changing rate of the forecast volatility on day t caused by adjusting j step-lengths on the value of the ith element in
i , j the average changing rate of the output caused by the above action within the day t0 and the day t1 (refer to 5.1), and we have the input vector,
i, j
t1 1 ti , j , t1 t0 1 t t0
(21)
where ^ i, j
68.00
i, j t
^
2 t2 . t
(22)
^
2 t
4.82
53.85
9.24
64.71
The t
5.73
44.44
12.96
64.71
when the ith element of the input vector has been modified by j step-lengths.
5.73
44.44
9.72
83.33
6.23
46.15
9.39
82.61
5.47
54.17
11.04
69.23
6.86
51.85
^ i, j 2
in (22) represents the changed forecast volatility
Table 2 demonstrates the values of we have acquired when conducting the experiments on the index NASDAQ within the period from Jun 30th, 2006 to Sept 28th, 2006. The specific configurations regarding the parameters are p=3, q=8, r=3, C=10 and H=4. i, j
Table 2 The disturbance experiment results for the NASDAQ within the period from Jun 30th, 2006 to Sept 2006 with the configuration as p=3, q=8, r=3, C=10 and The rows in grey indicate the changing rates of the elements.
394
index 28th, H=4. input
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007
y y y y y y y y W W W
2 t 1 2 t 2 2 t 3 2 t 1 2 t 2 2 t 3 2 t 4 2 t 5 2 t 6 2 t 7 2 t 8 2 t 1 2 t 2 2 t 3
t21 t2 2 t23 yt21 yt2 2 yt23 yt2 4 yt25 yt2 6 yt2 7 yt28 Wt 21 Wt 2 2 Wt 23
0.75
0.8
0.85
0.9
0.95
-0.0479
-0.0356
-0.0250
-0.0153
-0.0069
0.0019
0.0051
0.0068
0.0059
0.0035
-0.0228
-0.0155
-0.0104
-0.0058
-0.0018
0.0007
0.0006
0.0005
0.0003
0.0002
0.0064
0.0052
0.0040
0.0027
0.0014
0.0019
0.0015
0.0011
0.0007
0.0003
-0.0043
-0.0034
-0.0026
-0.0017
-0.0009
-0.0010
-0.0007
-0.0004
-0.0002
-0.0001
-0.0021
-0.0017
-0.0013
-0.0008
-0.0004
0.0036
0.0029
0.0022
0.0014
0.0007
0.0024
0.0020
0.0015
0.0010
0.0005
-0.0019
-0.0016
-0.0012
-0.0009
-0.0005
-0.0007
-0.0005
-0.0004
-0.0003
-0.0001
-0.0015
-0.0012
-0.0009
-0.0006
-0.0003
1.05
1.1
1.15
1.2
1.25
0.0064
0.0128
0.0194
0.0264
0.0342
-0.0039
-0.0070
-0.0102
-0.0131
-0.0151
0.0010
0.0027
0.0061
0.0116
0.0183
-0.0002
-0.0004
-0.0006
-0.0007
-0.0009
-0.0014
-0.0027
-0.0040
-0.0053
-0.0065
-0.0003
-0.0006
-0.0009
-0.0012
-0.0014
0.0008
0.0017
0.0025
0.0033
0.0041
0.0000
-0.0001
-0.0001
-0.0001
-0.0002
0.0004
0.0009
0.0013
0.0017
0.0022
-0.0007
-0.0014
-0.0021
-0.0029
-0.0036
-0.0005
-0.0011
-0.0016
-0.0022
-0.0028
0.0005
0.0011
0.0018
0.0024
0.0031
0.0001
0.0003
0.0004
0.0005
0.0007
0.0003
0.0006
0.0008
0.0011
0.0014
stock return volatility. Nonetheless, we’ve discovered that the forecasting performance for the trading volume volatility considerably outplays that for the price return volatility, if we take online information volume as an exogenous input. Therefore, we deem that trading volume is more inclined to be affected by online financial information. In addition, we’ve found out that the greater the value of D is, the smaller the average forecast error becomes, which further proves the volatility clustering feature of financial time series. Furthermore, an apparently better forecast performance can be achieved if we square the moving average part of the input vector, which constitutes a proof for one of the GARCH theory’s conclusions, i.e. there might exist a significant correlation between the squared residuals of financial time series.
6
In this paper, we have introduced a mathematical model based upon GARCH and ANN used for the investigation of the correlations between financial trading volume volatility and online information volume, in order to forecast the former. According to the experimental results, our model is capable to achieve an acceptable forecasting performance for the daily trading volume volatility and an excellent one for the volatility trend compared to the approach based on the volatility clustering. Regarding future works, we intend to make further improvements on the training algorithms adopted in our approach. Since the three algorithms adopted in our paper all have its own deficiencies such as the former two suffer from the drawback of slow convergence while the third an inclination of over-fitting. In addition, we wish, in the future, to base our model on a more comprehensive set of online financial information, which might span several years in time.
ACKNOWLEDGEMENT
This research was supported by the National Natural Science Foundation of China under Grant 70571003.
According to the results shown in Table 2, it is clearly demonstrated that compared to the other input factors, such as the volatilities and the daily changing rates during the immediate past, online financial information volume does have a certain influence on the output, which can be considered as of the same magnitude of significance with the others. 5.3
REFERENCES Catfolis, T. (1996) ‘Neural networks models for the prediction of stock return volatility’, IEEE International Conference on Neural Networks ’96, 3-6 June, Vol.4, pp. 2118–2123. Freisleben, B. and Ripper, K. (1997) ‘Volatility estimation with a neural network’, Proceedings of the IEEE/IAFE on Computational Intelligence for Financial Engineering (CIFEr) ’97, 24-25 March, pp. 177–181. Lai, H.Z.H., Cheung, Y.M. and Xu L. (1996) ‘Trading mechanisms and return volatility empirical investigation on shang hai stock exchange based on a neural network model’, Proceedings of the IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering ’96, NYC, USA, 24-26 March, pp. 259-263.
Discussions
Within the process of conducting different experiments, we also have established our model upon the stock price returns, for the purpose of investigating the correlation between the online financial information volume and the ISBN 978-0-9783350-0-7
CONCLUSION AND FUTURE WORKS
395
Proceedings of the 2007 International Conference on Management Innovation, Shanghai, China, June 4-6, 2007 Cybenko, G. (1989) ‘Approximation by superposition of a sigmoidal function’, Math. Control, Signals, Syst., Vol. 2, pp. 303–314. Funahashi, K. (1989) ‘On the approximate realization of continuous mappings by neural networks’, Neural Networks, Vol. 2, pp. 183–192. Hornik, K. (1991) ‘Approximation capabilities of multilayer feedforward networks’, Neural Networks, Vol. 4, pp. 251– 257. Hornik, K., Stinchcombe, M. and White, H. (1989) ‘Multilayer feedforward networks are universal approximators’, Neural Networks, Vol. 2, pp. 359–366. Wuthrich, B., Cho, V., Leung, S., Permunetilleke, D., Sankaran, K. and Zhang, J. (1998) ‘Daily stock market forecast from textual web data’, IEEE International Conference on Systems, Man, and Cybernetics, 11-14 Oct. 1998, Vol. 3, pp. 27202725. Chuttur, M.Y. and Bhurtun, C. (2005) ‘Monitoring financial market using French written textual data’, IEEE 3rd International Conference on Computational Cybernetics, 1316 April 2005, pp. 239-242. Costantino, M., Morgan, R.G., Collingham, R.J. and Carigliano, R. (1997) ‘Natural language processing and information extraction: qualitative analysis of financial articles’, Proceedings of the IEEE/IAFE, NYC, USA, 23-25 March 1997, pp. 116-122. Donaldson, R.G., Kamstra, M. (1997) ‘An artificial neural network-GARCH model for international stock return volatility’, Journal of Empirical Finance, Vol. 4, Issue 1, pp. 17-46. Peramunetilleke, D. and Raymond K.W. (2002) ‘Currency exchange rate forecasting from news headlines’, Proceedings of the 13th Australasian Database Conference, Melbourne, Victoria, Australia, Vol. 5, pp. 131-139.
Engle, R.F. (1982) ‘Autoregressive conditional Heteroscedasticity with estimation of the variance of united kingdom inflation’, Econometrica Vol. 50, No. 4, pp. 9871007. Bollerslev, T. (1986) ‘Generalized autoregressive conditional heteroskedasticity’, Journal of Econometrics, Vol. 31, No. 3, pp. 307-327. Dickey, D.A., Bell, W.R. and Miller, R.B. (1986) ‘Unit roots in time series models,tests and implications’, The American Statistician, Vol. 40, No. 1, pp. 12-26. Pang, S.L. (2004) ‘An application of logistic model in stock forecasting’, The 8th Control, Automation, Robotics and Vision Conference 2004, Vol. 2, pp. 1491-1496. Cai, C.L. and Shi, Z.Z. (2003) ‘A modular neural network architecture with approximation capability and its applications’, Proceedings of the Second IEEE International Conference on Cognitive Informatics 2003, pp. 60-64. Huang, G.B., Chen L. and Siew C.K. (2006) ‘Universal approximation using incremental constructive feedforward networks with random hidden nodes’, IEEE Transactions on Neural Networks, Vol. 17, Issue 4, pp. 879-892. Wu, J.M., Lin, Z.H. and Hsu, P.-H. (2006) ‘Function IEEE approximation using generalized adalines’, Transactions on Neural Networks, May, Vol. 17, Issue 3, pp. 541-558. Kuan, C. and White, H. (1994) ‘Artificial neural networks: an econometric perspective’, Econometric Review, Vol. 13, pp. 1–91. Tino, P., Schittenkopf, C. and Dorffner, G. (2001) ‘Financial volatility trading using recurrent neural networks’, IEEE Transactions on Neural Networks, July, Vol. 12, Issue 4, pp. 865-874. Zhang, S.Y. and Fan, Z. (2005) ‘Cointegration theory and volatility models: financial time series analysis and applications’, Tsinghua University Press, April. Liang, X., Zhang, H.S., and Yang J. ‘Pricing options in Hong Kong market based on neural networks’, ICONIP 2006, Part III, LNCS 4234, pp. 410-419. Chan, Z.S.H., Ngan, H.W., Rad, A.B. and Ho, T.K. (2002) ‘Alleviating 'overfitting' via genetically regularised neural network’, Electronics Letters, Vol. 38, Issue 15, pp. 809-810. Gencay, R. and Min Q. (2001) ‘Pricing and hedging derivative securities with neural networks: bayesian regularization,early stopping,and bagging’, IEEE Transactions on Neural Networks, Vol. 12, Issue 4, pp. 726-734. Hu, J.L., Wu, Z., McCann, H., Davis, L.E. and Xie, C.G. (2006) ‘BFGS quasi-Newton method for solving electromagnetic inverse problems’, Microwaves, Antennas and Propagation, IEE Proceedings, April 2006,, Vol. 153, Issue 2, pp. 199204. Garcia, R.C., Contreras, J., Van Akkeren, M. and Garcia, J.B.C. (2005) ‘A GARCH forecasting model to predict day-ahead electricity prices’, IEEE Transactions on Power Systems, Vol. 20, Issue 2, pp. 867-874. Zheng, H., Xie, L. and Zhang, L.Z. (2005) ‘Electricity price forecasting based on GARCH model in deregulated market’, The 7th International Power Engineering Conference, 29 Nov.-2 Dec. 2005. Liu, J.Y. (2005) ‘An analysis of daily volatility in the Japanese foreign exchange market’, Proceedings of International Conference on Services Systems and Services Management 2005, Vol. 2, pp. 1222-1227. Black F. and Scholes, M. (1973) ‘The pricing of options and corporate liabilities’, Political Economy, Vol. 81, Issue 3, pp. 637-654. Kanzow, C., Yamashita, N. and Fukushima M. (2004) ‘Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints’, Journal of Computational and Applied Mathematics, Vol. 172, No. 2, pp. 375-397.
ISBN 978-0-9783350-0-7
WEBSITES The online financial news volumes are gathered and calculated at http://finance.google.com. The historical trading prices and volumes are downloaded at http://finance.yahoo.com.
396
