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On the basis of previous research, this study assembled trading data from January 2004 to October 2014 to verify the overreaction in Shanghai stock market. The influence of overreaction decreases with time from 2007 onwards and turns to disappear from 2011. The neuron model with dendritic nonlinearity (NMDN) proposed in this paper fits and predicts the variability of abnormal returns of ill-preforming and well-preforming stocks in the test period. This experiment demonstrates that NMDN possesses high computational ability and succeeds to predict trends in the influence of overreaction.

One way used to predict the extent of stock-market weak-form efficiency is through testing for the effect of overreaction, i.e. the degree to which investors overreact to good or bad news causing share prices to deviate from their equilibrium level. In particular, securities suffering abnormally-low returns in the past (losers) will experience relatively higher returns, whereas shares performing well in the past (winners) will do less well in the future.

De Bondt and Thaler are the forerunners in the study of the effect of overreaction on the stock markets. They have used the data of stock mark in the US between 1926 and 1982 to analyze whether investors overreact, and identified a long-term reversion in stock prices due to the investors’ irrational behavior (De Bondt & Thaler, 1985) . Lehmann (1990) has used data from the US stock market between 1965 and 1989 to identify the factors that have reversed the market in a short time-interval but could not correlate short-term profitability with overreaction, suggesting that market reversal was a result of short-term pressures on prices in short term or the lack of liquidity (Lehmann, 1990) .

To build the stock market value, one of the best ways is to use expert systems with Artificial Neural Networks (ANN), which can easily adapt the changes of the stock market. It is observed that in most of the cases ANN models give better result than other methods. However, there have been a few studies on using the ANN for stock market: Generalized version of ARCH model, Generalized ARCH (GARCH) model (Bollerslev, 1986) , Exponential GARCH (EGARCH) model (Nelson, 1991) , Dynamic Architecture for Artificial Neural Networks (DAN2) and so on. Since the late 1990s, Chinese scholars have studied overreaction on stock mark in China. Zhang Renji, Zhu Pingfang, and Wang Huaifang (1998) have found a decreasing trend in winner portfolio. Zhu Shaoxing (2000) has conducted that overreaction did not affect the Shenzhen stock market. Song Xianzhong and Tang Sheng (2006) have conducted an empirical study on overreaction and scale effect on the corporations listed in A-share market in Shanghai. In our previous study, Shanghai stock market trading data from January 2007 to June 2011 have suggested an overreaction on the stock market (Hu Lin, Sha Zijun, Liu Xiuyi, & Chen Wenjun, 2013) . In recent years, there have been a growing number of studies about movements of various kinds on stock market. Both academic researchers and practitioners have made tremendous efforts to predict the future movements of the stock markets. Zhang Yanqing and Wan Xuhui (2007) have developed a new ANN based on Fuzzy Interval Neural Network. Zhu Xiaotian, Wang Hong, Xu Li, and Li Huaizu (2008) have found trading volume can improve the prediction performance of neural networks by using basic and augmented neural network models. Liao Zhe and Wang Jun (2010) have identified some results on the global stock indices, using stochastic time effective neural network model.

In this paper, stock market data from 2004 to 2014 are analyzed to verify the overreaction in Shanghai stock market once again, and the neuron model with dendritic nonlinearity, for the first time, is used to fit and predict the trends of overreaction. This new approach aims to provide a novel solution for future research, as well as a valuable tool for business implementation.

The remaining sections of this paper are organized as follows: Section 2 gives the sample selection and test methods; Section 3 introduces the models in this paper and Section 4 shows the experiments and results. The final section gives the conclusion and recommendations for future researches. This study will make contribution not only to the ANN research but also to the business implementations of stock market.

This paper extracts 200 stocks, at random, from the Shanghai stock market, covering the time-interval from January 2004 to October 2014 including the daily closing prices. Considering stock dividends and rights offerings, the returns of each stock is calculated on the price excluding rights. The stock’s closing price remains the same for stocks pending suspension. Based on the sequence of the level of cumulative abnormal returns in formation period, the top 20 stocks constitute the winner portfolio, and the loser portfolio is composed of the lowest 20 stocks.

The formation period in the paper is divided into 3 months, 6 months, 12 months, 18 months and 24 months; the corresponding test period is separated by 1 month, 3 months, 6 months, 12 months, 24 months and 36 months. If the reference time, the length of formation period and the length of test period are set to T_{0}, T_{1} and T_{2}, respectively, (T_{0} − T_{1}, T_{0}) is the formation period, and (T_{0}, T_{0} + T_{2}) is the test period. If the reference time is constant, more combinations between the formation period and the test period may be attained. The formations period and the test period, in these combinations, do not overlap, but the current test period and the next formation period may overlap.

The calculation of excess returns uses incorporates a marketing adjustment, as proposed by De Bondt, Richard Thaler and Paul Zarowin. The formula is

R_{i}_{,k} is yield of stock I in k month.

R_{m}_{,k} is yield of market in k month.

Cumulative excess return for stock I in the formation period is

On the basis of the data sequence of the cumulative abnormal returns levels in the formation period, the top 20 stocks make the winner portfolio and the lowest 20 stocks make the loser portfolio. Thus, the calculated average abnormal monthly returns for each combination are given by:

Here, AR_{w}_{,k} is the average abnormal monthly returns of the winner portfolio, AR_{l}_{,k} is the average abnormal monthly returns of the loser portfolio, CAR_{w}_{,k} is the average cumulative abnormal returns of the winner portfolio, and CAR_{l}_{,k} is the average cumulative abnormal returns of the loser portfolio.

In 1943, McCulloch and Pitts have proposed a neuron model, which is recognized as the basic computation units for neural network (McCulloch & Pitts, 1943) . However, in this model, the dendrites are only taken as mere weight, thus an independent McCulloch-Pitts model (

However, with the gradual in-depth study, it has been proved that the dendrites participate into the computation of neuron instead of mere transmitting signals (Kitajima & Hara, 1987; Koch, Poggio, & Torre, 1982 ; London & Häusser, 2005) .

In 2000, Tang et al. have proposed a neuron model based on dendritic mechanism ( Tang, Tamura, Kuratu, Ishizuka, & Tanno, 2000 ; Tang, Tamura, Ishizuka, & Tanno, 2000 ). Moreover, it also holds the movement direction selection function based on time difference (Tamura, Tang, & Ishii, 2001) . The computational ability of this model can be expressed as logical operation of AND, OR and NOT. Moreover, in order to reduce computational time and generalize the neuron model into a continuum of values between 1 and 0, Tang et al. have proposed a novel neuron model, called Neuron Model with Dendritic Nonlinearity (NMDN), which uses the multiplication and addition to replace the logical AND and OR, respectively (Todo, Tang, Todo, Ji, & Yamashita, 2014 ). As shown in

In NMDN, the synaptic function is expressed by the sigmoid function. The output of the synapse whose address is from i-th

where

The synaptic output on the branch performs a simple multiplication. The output of j-th branch is given by

Moreover, as mentioned above, the summation on signals sent from the dendrites is expressed by

Finally, the function of soma is also described through a sigmoid function as following

where the

NMDN is a feed-forward network with continuous functions, all differential. Therefore, the gradient descent learning algorithm is used as the learning procedure. Learning is aimed to reduce the difference between the output and the target vector by modifying

The error between the target vector and the output vector can be expressed by following

where the T is taken as the target, and the O is taken as the output.

During the learning procedure, these parameters are modified to decrease the error, and the connection parameters should be corrected according to the following formulas:

where

where

The applied method, in this study, provides substantial results in

However, the data listed in

As mentioned in Section 3, there are some parameters in NMDN need to be set up. Altering these parameters have distinct influence on the training and predicting. However, there has been no clear criterion to determine which values of parameters can maximize the ability of NMDN.

However, in order to train NMDN for prediction, the input data of NMDN is defined in

Formation period | Test period CAR | ||||||
---|---|---|---|---|---|---|---|

One month | Three months | Six months | Twelve months | Twenty four months | Thirty six months | ||

Eighteen months | Winner portfolio (W) | 0.1969 | 0.2918 | 0.3854 | 0.5064 | 0.7110 | 0.9838 |

Loser portfolio (L) | 0.2495 | 0.4350 | 0.5590 | 0.6667 | 0.7864 | 0.9674 | |

L-W | 0.0526 | 0.1433 | 0.1736 | 0.1603 | 0.0754 | −0.0164 |

k | ksoma | Branch | γ | η | Epochs | MSE |
---|---|---|---|---|---|---|

3 | 3 | 25 | 0.5 | 0.01 | 10000 | 0.0001 |

Step | ||||
---|---|---|---|---|

3 | 4 | 5 | 6 | |

Train data | 40 |

Combining

In this paper, the overreaction effect on the Shanghai stock market is confirmed once again by using more recent data. The influence of overreaction occurring since 2007 can be found to turn to gradually diminish and finally becomes obsolete.

Step | ||||
---|---|---|---|---|

3 | 4 | 5 | 6 | |

Rnew | −0.2548 | 0.6601 | 0.6763 | 0.6797 |

A neuron model with dendritic nonlinearity (NMDN) is used here, for the first time, to predict the tendency of overreaction. The first n-months’ data are treated as input data to predict the following month’s data. The result indicates that the neuron model possesses huge computational ability and succeeds in predicting the overreaction tendency. Moreover, with the increase of steps, the correlation between the data of the first n-month and the following month turns to be improved. Moreover, NMDN provides another new approach for the researchers.

For the future work, the research will be focused on the accuracy of prediction by using NMDN.