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Journal of Business & Financial Affairs
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Validity of Weak Form Efficiency in European Stock Market

Rekha Gupta*

Assistant Professor, Department of Commerce, Maharana Partap Govt. College Amb, H.P, India

*Corresponding Author:
Rekha Gupta
Assistant Professor
Department of Commerce
Maharana Partap Govt. College Amb
H.P, India
Tel: 9418593231
E-mail: rekhaguptauna@gmail.com

Received Date: January 28, 2016; Accepted Date: February 18, 2017; Published Date: February 28, 2017

Citation: Gupta R (2017) Validity of Weak Form Efficiency in European Stock Market. J Bus Fin Aff 6: 250. doi: 10.4172/2167-0234.1000250

Copyright: © 2017 Gupta R. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

In this paper weak form efficiency is tested in ten European country indices. For this purpose Run test and Autocorrelation test are used. Run test clearly supported the dependent behavior of majority of countries. Run test has inherent weakness as only sign are conceded not how much amount of increase or decrease. The coefficients are obtained for 1-16 time lags to examine results for varying periodicity. Serial correlation coefficient statistics indicates the majority of indices are not in weak form efficiency. This study also shows that significant auto correlations are converted into insignificant with increases time lags.

Keywords

Run test; Serial correlation coefficient; Weak form efficiency

Introduction

In an efficient market, a set of information in fully and immediately reflected in market prices so that no investor is able to make excess profits based on any existing information. An efficient market is one where market price is an unbiased estimate of the true value of investment. All it require is that errors in the market price be unbiased, i.e., prices can be greater than or less than true value, as long as these deviation are random. The fact that the deviation from true value are random implies that there is an equal chance that stocks are under or over valued at any point of time, and that these deviations are uncorrelated with any observable variable. If the deviations of market prices from true values are random, it follows that no group of investors should be able to consistently earn excess return using any investment strategy. Inefficient market on the other hand offers opportunities for abnormal return to the investors. In such markets, stock which had outperformed the market in the past should continue to outperform the market in the future. Similarly, stock that has done poorly should continue to perform poorly. Rao K noted that markets could be efficient at three levels based on what information was reflected in prices [1]. A market would be described as being weak-form efficient if it is impossible to make abnormal profits by using past prices to formulate buying and selling decision. Similarly, a market would be described as being semi strong-form efficient if it is impossible to make abnormal profits by using publicly available information to formulate buying and selling decisions. Last, a market would be described as being strongform efficient if it is impossible to make abnormal profits by using any information whatsoever to make buying and selling decisions.

A large majority of studies favor prevalence of weak form stock market efficiency. They observe that prices in the Indian stock market do not follow random walk model. They support the market efficiency preposition in its weak form both in India and abroad. Bodla has tested the weak form of efficiency with two tests, namely the runs test and serial correlation test using daily data for three year period commencing January 2001 through December 2003 [2]. The sample size consisted of 47 scrip’s of S&P CNX of nifty. In order to test the null hypothesis that share prices follow the random walk behavior, the random walk model has been applied in the study. This is a suitable data transformation procedure, which is used to make the original series stationary. The results of the runs test have given a clear cut inking of the existence of weak form market efficiency in the Indian securities market. Similarly, the serial correlation analysis based on its coefficients confirms the weak form hypothesis of efficient market. This finding, thus, reduces the probability of continuously making extra profit by forecasting the security prices. Mahapatra and Biswasroy are an attempt in this direction [3]. The study is based on weekend share price data of BSE 30 scrip’s covering a time period of two years i.e. from 1st April 2000 to 31st march 2002. Rank correlation analysis has been extensively used in the study to examine the rank of performance of the above 30 stocks at different time intervals. They reveals that the Indian stock market is more efficient in the weak form in the longer run but inefficient in the short run. Mishra AK has made an attempt to study documents extensive on price behavior in the Indian stock markets [4]. One of the striking features of the results is that runs analysis too exuberate weak form efficiency further and the instances of return drift noted earlier have disappeared. On the whole, the results signify that trading strategies based on historic prices cannot be relied for abnormal gains consistently, except when these coincide with underlying drifts in the stock price movements. Satish and Sonal have analyzed the weak form of efficiency and the efficient market hypothesis on Indian stock market in the form of random walk, during the period of 2007-08 based on closing prices and daily returns on the Indian stock market three representative indices: S&P CNX 500, CNX 100 and BSE 200 [5]. Serial correlation and run test support the Random Walk theory and market efficiency hypothesis. Some studies deny its existence to keep the academic debate alive on the subject. Vandana OP have studied the weak-form efficiency in Indian stock market during a period July 1988 to Jan 1996 [6-11]. The results of autocorrelation analysis as well as run analysis carried out in respect of each of the fifty shares included in the sample were not supportive of the random walk hypotheses. Some of the observed efficient were larger than those obtained in other studies. Thus the results reported here do not lend support to the view that the Indian stock market is weak form efficiency in pricing share where market efficiency is understood as generating security prices which fully reflect information contained in their historical records. This study has aimed at re-examining the weak form efficiency proposition. In the previous studies Run and auto correlation test have been used but more emphasis is laid on Run test. But in present study more preference is given to Autocorrelation test because this test considered sign as well as absolute change.

Hypotheses

In order to examine market efficiency in weak form, historical sequences of stock prices are studied for independence and randomness to test the following null hypothesis:

Ho: Successive stock price movement are independent of past stock prices.

HA: Stock price movement are identical to that of random numbers.

Data

In order to examine the validity of null hypothesis, daily price data for a sample of ten European country indices are compiled for eight years. Data used in this study are obtained from yahoo. Finance website.

Methodology

To test independence and randomness of stock prices, Run test has been used. The number of runs is computed as a sequence of the price changes of the same sign. For testing the significance of the difference between observed and expected number of runs, standardized normal variate has been used. Since the alternative hypothesis says nothing about the direction of the deviation from a random series, a two -tailed test is applied. Accordingly, null hypothesis will be rejected at five per cent level of significance if the observed value of Z is >1.96. Expected numbers of runs of all types are computed by using the method:

equation

Where:

M = Expected number of runs;

n1 = Number of Positive signs; and

n2 = Number of Negative signs; and

n3 = Number of Zeros

Wherein, standard error (S.E.) is given as:

equation

The difference between the actual and expected number of runs is expressed by a standard normal Z variate as:

Z = [(R - M) / S.E.]

Adjusted Z variate is as follows:

Z = [(R+0.5 - M) / S.E.]

Where:

R = Actual number of runs;

M = Expected number of runs; and

SE = Standard Error

In run test, there is one limitation that is only sign is considered but not the absolute change. In order to overcome this limitation autocorrelation test is used in which raw values and direction are considered. Hence the inferences are also drawn through autocorrelation. Serial correlation is a measure of relationship between a random variable in time (Pt) and its value (Pt-n) periods earlier. It indicates whether price changes at time (t) are influenced by the price changes occurring (t-n) periods earlier. In order to hold weak form stock market efficiency, observed serial correlation should be statistically insignificant. Serial correlation coefficients are computed for a 1-16 periods lag(s). If the autocorrelations are close to zero or insignificant at a given significant level, the price changes are said to be serially independent. A significant positive correlation indicates the presence of a trend while the negative correlated depicts the existence of random reversals in the stock prices. The serial correlation coefficient is estimated by:

equation

Where:

equation

K = 0,1,2,….n

equation is mean of the whole series;

Co is variance of Pt; and

n is number of observations.

Statistical testing of the serial correlation coefficient requires the standard error of estimated coefficient, which is explained below:

equation

Results

Statistics from medium related to run test are presented in Table 1. It shows that AEX general Index correlation coefficients are insignificant up to six years. Thereafter, correlation coefficients are showing significance significant. It can also be cited that four European countries such as Athex Composite Share Price Index, ATX, Stockholm General and OSE All Share Z value are found to be insignificant with few exception. It indicates the weak form efficiency does not present in these market. Rests of the European country indices correlation coefficient are significant at one and five per cent for different years. These country indices not strongly support randomness in the stock prices. It reveal that weak form efficiency not exist in majority European countries according to run test.

YEARS NAME OF COUNTRY INDICES AEX General Athex Composite Share Price Index ATX BEL-20 CAC 40 DAX FTSE 100 Stockholm General OSE All Share Swiss Market
First Test Value 0.001 0.001 0.002 0.000 0.001 0.001 0.001 0.001 0.002 0.000
Number of Runs 125 100 90 13 129 109 113 105 102 115
Z -0.501 -2.893 -4.399 -1.567 0.000 -2.447 -1.648 -3.175 -2.517 -1.515
Sig. (2-tailed) 0.616 0.004 0.000 0.117 1.000 0.014 0.099 0.001 0.012 0.130
Second Test Value 0.001 0.002 0.002 0.001 0.002 0.002 0.001 0.002 0.003 0.001
Number of Runs 117 96 92 121 123 121 110 109 106 124
Z -1.740 -3.913 -4.418 -1.243 -0.994 -1.243 -2.380 -2.734 -1.002 -0.749
Sig. (2-tailed) 0.082 0.000 0.000 0.214 0.320 0.214 0.017 0.006 0.316 0.454
Third Test Value 0.001 0.002 0.002 0.002 0.001 0.002 0.001 0.001 0.001 0.001
Number of Runs 122 96 105 112 122 122 103 104 100 124
Z -0.815 -3.634 -2.486 -2.361 -0.815 -0.815 -3.087 -3.355 -3.124 -0.316
Sig. (2-tailed) 0.415 0.000 0.013 0.018 0.415 0.415 0.002 0.001 0.002 0.752
Fourth Test Value 0.000 0.000 0.001 0.000 0.000 0.001 0.000 0.000 0.001 0.000
Number of Runs 117 102 105 131 123 121 109 107 97 115
Z -1.323 -2.927 -2.368 0.377 -0.567 -0.634 -2.213 -2.641 -3.393 -1.211
Sig. (2-tailed) 0.186 0.003 0.018 0.706 0.571 0.526 0.027 0.008 0.001 0.226
Fifth Test Value -0.003 -0.003 -0.001 -0.003 -0.003 -0.003 -0.001 -0.001 -0.001 -0.002
Number of Runs 119 102 97 109 113 109 113 105 97 105
Z -1.372 -3.042 -3.731 -2.620 -2.121 -2.562 -2.004 -2.777 -3.953 -3.006
Sig. (2-tailed) 0.170 0.002 0.000 0.009 0.034 0.010 0.045 0.005 0.000 0.003
Sixth Test Value 0.002 0.001 0.003 0.003 0.002 0.002 0.002 0.003 0.003 0.002
Number of Runs 115 96 94 43 113 108 107 101 94 129
Z -1.871 -3.802 -4.056 -2.147 -2.121 -2.745 -2.698 -3.339 -4.220 -0.249
Sig. (2-tailed) 0.061 0.000 0.000 0.032 0.034 0.006 0.007 0.001 0.000 0.804
Seventh Test Value 0.001 -0.001 0.001 0.000 0.001 0.001 0.001 0.001 0.001 0.000
Number of Runs 109 101 103 98 116 120 119 113 101 111
Z -2.734 -3.451 -3.030 -2.858 -1.864 -1.367 -1.192 -2.004 -3.282 -2.485
Sig. (2-tailed) 0.006 0.001 0.002 0.004 0.062 0.172 0.233 0.045 0.001 0.013
Eighth Test Value 0.000 -0.005 0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.001
Number of Runs 114 114 95 114 118 124 115 113 96 112
Z -2.113 -1.819 -4.040 -2.113 -1.616 -0.870 -1.694 -2.004 -4.133 -2.246
Sig. (2-tailed) 0.035 0.069 0.000 0.035 0.106 0.384 0.090 0.045 0.000 0.025

Table 1: Run test stastics from medium.

Run test Statistics from mean are reported in Table 2. It can be seen that similar trend prevailed in this Statistics. Statistics from mode gives different result as compared to mean and medium Statistics which is presented in Table 3.

YEARS NAME OF COUNTRY INDICES AEX General Athex Composite Share Price Index ATX BEL-20 CAC 40 DAX FTSE 100 Stockholm General OSE All Share Swiss Market
First Test Value 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.000
Number of Runs 121 104 89 11 131 109 111 103 99 119
Z -0.979 -2.367 -4.429 -2.149 0.259 -2.445 -1.887 -3.419 -2.719 -0.950
Sig. (2-tailed) 0.328 0.018 0.000 0.032 0.795 0.014 0.059 0.001 0.007 0.342
Second Test Value 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.001 0.002 0.001
Number of Runs 117 96 96 103 121 113 108 107 100 122
Z -1.594 -3.886 -3.895 -3.331 -1.154 -2.154 -2.564 -2.850 -1.581 -0.994
Sig. (2-tailed) 0.111 0.000 0.000 0.001 0.248 0.031 0.010 0.004 0.114 0.320
Third Test Value 0.000 0.000 0.000 0.001 0.000 0.001 0.000 0.001 0.001 0.000
Number of Runs 120 94 100 115 120 117 101 104 100 116
Z -0.922 -3.617 -2.835 -1.712 -0.871 -1.130 -3.305 -3.307 -3.049 -1.244
Sig. (2-tailed) 0.357 0.000 0.005 0.087 0.384 0.258 0.001 0.001 0.002 0.213
Fourth Test Value -0.001 -0.001 -0.001 -0.001 -0.001 0.000 0.000 -0.001 0.000 -0.001
Number of Runs 117 102 97 133 117 119 109 103 95 113
Z -1.271 -2.806 -3.106 0.654 -1.295 -0.879 -2.213 -3.124 -3.453 -1.414
Sig. (2-tailed) 0.204 0.005 0.002 0.513 0.195 0.380 0.027 0.002 0.001 0.157
Fifth Test Value -0.003 -0.004 -0.003 -0.003 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002
Number of Runs 119 102 99 109 111 107 115 109 93 107
Z -1.372 -3.035 -3.434 -2.620 -2.357 -2.803 -1.732 -2.269 -4.404 -2.752
Sig. (2-tailed) 0.170 0.002 0.001 0.009 0.018 0.005 0.083 0.023 0.000 0.006
Sixth Test Value 0.002 0.001 0.002 0.004 0.001 0.002 0.001 0.002 0.002 0.001
Number of Runs 115 96 98 43 113 103 107 103 92 127
Z -1.871 -3.799 -3.536 -2.147 -2.091 -3.306 -2.673 -3.062 -4.442 -0.474
Sig. (2-tailed) 0.061 0.000 0.000 0.032 0.037 0.001 0.008 0.002 0.000 0.636
Seventh Test Value 0.000 -0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000
Number of Runs 111 105 99 100 114 119 115 109 99 109
Z -2.446 -2.944 -3.496 -2.595 -1.838 -1.460 -1.657 -2.404 -3.507 -2.599
Sig. (2-tailed) 0.014 0.003 0.000 0.009 0.066 0.144 0.098 0.016 0.000 0.009
Eighth Test Value 0.000 -0.003 -0.001 -0.001 -0.001 0.000 0.000 0.000 0.000 0.000
Number of Runs 114 113 101 112 118 114 115 109 93 109
Z -2.092 -1.882 -3.125 -2.358 -1.546 -1.948 -1.630 -2.464 -4.349 -2.521
Sig. (2-tailed) 0.036 0.060 0.002 0.018 0.122 0.051 0.103 0.014 0.000 0.012

Table 2: Run test statistics from mean.

YEARS NAME OF COUNTRY INDICES AEX General Athex Composite Share Price Index ATX BEL-20 CAC 40 DAX FTSE 100 Stockholm General OSE All Share Swiss Market
First Test Value 0.019 0.026 0.021 0.011 0.019 0.022 0.014 0.000 0.690 0.016
Number of Runs 3 3 3 3 3 3 3 105 3 3
Z 0.089 0.091 0.090 0.000 0.089 0.089 0.090 -2.962 0.091 0.089
Sig. (2-tailed) 0.929 0.927 0.928 1.000 0.929 0.929 0.928 0.003 0.927 0.929
Second Test Value 0.018 0.021 0.024 0.014 0.023 0.024 0.014 0.028 0.035 0.016
Number of Runs 3 3 3 3 3 3 3 3 3 3
Z 0.088 0.089 0.089 0.088 0.088 0.088 0.089 0.088 0.095 0.088
Sig. (2-tailed) 0.930 0.929 0.929 0.930 0.930 0.930 0.929 0.930 0.925 0.930
Third Test Value 0.021 0.062 0.048 0.000 0.023 0.022 0.020 0.000 0.053 0.017
Number of Runs 3 3 3 119 3 3 3 104 3 3
Z 0.089 0.090 0.090 -0.880 0.089 0.089 0.089 -3.013 0.090 0.090
Sig. (2-tailed) 0.929 0.928 0.928 0.379 0.929 0.929 0.929 0.003 0.928 0.929
Fourth Test Value 0.028 0.050 0.039 0.030 0.038 0.028 0.029 0.025 0.000 0.032
Number of Runs 3 3 3 3 3 3 3 3 97 3
Z 0.089 0.090 0.091 0.089 0.089 0.090 0.090 0.089 -3.319 0.090
Sig. (2-tailed) 0.929 0.928 0.928 0.929 0.929 0.928 0.929 0.929 0.001 0.928
Fifth Test Value 0.064 0.095 0.118 0.078 0.078 0.080 0.071 0.075 0.077 0.000
Number of Runs 3 3 3 3 3 3 3 3 3 111
Z 0.088 0.090 0.090 0.088 0.088 0.089 0.089 0.089 0.089 -2.063
Sig. (2-tailed) 0.930 0.928 0.929 0.930 0.930 0.929 0.929 0.929 0.929 0.039
Sixth Test Value 0.056 0.051 0.037 0.096 0.055 0.052 0.036 0.049 0.035 0.042
Number of Runs 2 3 2 3 2 2 2 2 2 2
Z -11.314 0.090 -11.136 0.139 -11.314 -11.314 -11.247 -11.203 -11.203 -11.358
Sig. (2-tailed) 0.000 0.928 0.000 0.890 0.000 0.000 0.000 0.000 0.000 0.000
Seventh Test Value 0.041 0.048 0.033 0.052 0.042 0.024 0.023 0.040 0.030 0.019
Number of Runs 3 3 3 3 3 3 3 3 3 3
Z 0.088 0.089 0.089 0.092 0.088 0.088 0.089 0.089 0.089 0.088
Sig. (2-tailed) 0.930 0.929 0.929 0.927 0.930 0.930 0.929 0.929 0.929 0.930
Eighth Test Value 0.044 0.083 0.056 0.046 0.045 0.054 0.032 0.038 0.038 0.049
Number of Runs 3 3 3 3 3 3 3 3 3 3
Z 0.088 0.089 0.089 0.088 0.088 0.088 0.089 0.089 0.089 0.088
Sig. (2-tailed) 0.930 0.929 0.929 0.930 0.930 0.930 0.929 0.929 0.929 0.930

Table 3: Run test statistics from mode.

Results of correlation coefficient of price changes are also used to examine the validity of null hypothesis to test the independence of successive stock prices. The coefficients are obtained for 1-16 time lags to examine results for varying periodicity. A significant interdependence in stock returns invalidates weak form market efficiency. Autocorrelation obtained for stock returns for ten countries are tabulated in Tables 4-11 for varied time lags.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.1 -0.03 0.09 0 0 0.02 0.01 -0.03 -0.03 0.01 0.06 -0.02 -0.06 -0.01 -0.05 -0.05
Value 2.46 2.69 4.77 4.78 4.78 4.87 4.9 5.12 5.36 5.41 6.44 6.58 7.71 7.73 8.35 9
P Value 0.12 0.26 0.19 0.31 0.44 0.56 0.67 0.74 0.8 0.86 0.84 0.88 0.86 0.9 0.91 0.91
Athex Composite Share Price Index   Autocorrelation 0.3 -0.06 -0.02 -0.01 -0.05 0.03 0.08 0.04 0.02 0.12 0.04 -0.03 0 0.03 -0.04 0
Value 22.19 23.14 23.25 23.3 23.98 24.18 25.65 26.04 26.19 29.85 30.27 30.57 30.57 30.85 31.3 31.31
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01
ATX   Autocorrelation 0.45 -0.05 -0.19 -0.06 0.17 0.14 -0.04 -0.11 -0.01 0.1 0.12 0 -0.09 -0.04 0 0.08
Value 50.84 51.39 60 60.9 68.45 73.33 73.75 77.08 77.1 79.87 83.6 83.6 85.59 86.01 86.01 87.51
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
BEL-20   Autocorrelation 0.33 -0.21 -0.29 -0.01 0.09 -0.1 -0.14 -0.22 -0.09 -0.17 -0.13 -0.01 0.23 0.34 0.01 -0.13
Value 4.13 5.75 9.08 9.08 9.43 9.82 10.71 13.06 13.45 14.9 15.75 15.75 18.73 25.91 25.91 27.01
P Value 0.04 0.06 0.03 0.06 0.09 0.13 0.15 0.11 0.14 0.14 0.15 0.2 0.13 0.03 0.04 0.04
CAC 40 Autocorrelation 0.04 -0.1 -0.02 -0.04 0.03 -0.02 0 -0.02 -0.04 0.04 0.03 -0.01 -0.06 0 -0.05 -0.03
Value 0.4 3.22 3.35 3.7 3.98 4.13 4.13 4.2 4.72 5.19 5.41 5.42 6.52 6.52 7.18 7.35
P Value 0.53 0.2 0.34 0.45 0.55 0.66 0.77 0.84 0.86 0.88 0.91 0.94 0.93 0.95 0.95 0.97
DAX   Autocorrelation 0.18 -0.01 0.03 -0.01 -0.03 0.01 0.03 -0.11 -0.12 -0.02 0.02 -0.03 -0.01 0.02 -0.07 0
Value 8.56 8.58 8.82 8.83 9.02 9.06 9.33 12.36 15.89 15.94 16.06 16.26 16.29 16.38 17.87 17.87
P Value 0 0.01 0.03 0.07 0.11 0.17 0.23 0.14 0.07 0.1 0.14 0.18 0.23 0.29 0.27 0.33
FTSE 100   Autocorrelation 0.23 0.04 0 0.04 0.02 0.04 0.01 -0.02 -0.06 0.04 0.04 0 -0.04 -0.11 -0.13 -0.03
Value 12.83 13.16 13.16 13.47 13.55 14 14.04 14.15 15.02 15.43 15.75 15.75 16.15 19.37 23.54 23.84
P Value 0 0 0 0.01 0.02 0.03 0.05 0.08 0.09 0.12 0.15 0.2 0.24 0.15 0.07 0.09
Stockholm General   Autocorrelation 0.27 0.01 -0.01 -0.01 0.05 0.02 0.01 -0.09 -0.07 -0.01 0.01 -0.02 -0.02 0 -0.17 -0.06
Value 19.28 19.33 19.38 19.38 20.06 20.18 20.22 22.21 23.46 23.5 23.55 23.66 23.72 23.73 31.56 32.53
P Value 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.02 0.02 0.03 0.05 0.01 0.01
OSE All Share   Autocorrelation -0.49 0 0 -0.01 0.01 0 0.01 -0.02 -0.01 0.01 0.01 -0.02 0 0.01 0 0.01
Value 60.28 60.28 60.28 60.32 60.34 60.34 60.34 60.41 60.42 60.46 60.49 60.55 60.55 60.57 60.57 60.58
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Swiss Market   Autocorrelation 0.1 -0.09 -0.05 -0.01 0.1 0.03 0 -0.1 -0.04 0.12 0.05 -0.14 -0.11 -0.07 -0.08 0.01
Value 2.61 4.86 5.43 5.43 8.23 8.4 8.4 10.88 11.22 15.17 15.81 20.79 24.28 25.64 27.25 27.25
P Value 0.11 0.09 0.14 0.25 0.14 0.21 0.3 0.21 0.26 0.13 0.15 0.05 0.03 0.03 0.03 0.04

Table 4: Serial Auto correlation Statistic in first year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.19 -0.01 0.05 0.02 0.04 -0.06 -0.01 0.03 0.03 0.01 0.02 -0.04 -0.08 -0.03 0.06 -0.04
Value 9.26 9.3 10.02 10.12 10.45 11.38 11.42 11.71 12 12.02 12.1 12.55 14.33 14.62 15.49 15.97
P Value 0 0.01 0.02 0.04 0.06 0.08 0.12 0.16 0.21 0.28 0.36 0.4 0.35 0.41 0.42 0.46
Athex Composite Share Price Index   Autocorrelation 0.3 0 0.07 -0.04 -0.01 -0.05 -0.07 -0.13 -0.08 0.04 0.01 -0.05 -0.01 0.05 0.02 -0.02
Value 23.56 23.56 24.64 24.98 25.02 25.65 26.77 30.93 32.61 33.09 33.1 33.66 33.67 34.23 34.35 34.45
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01
ATX   Autocorrelation 0.31 -0.03 0.07 0 0.05 0.06 -0.08 -0.04 0.06 -0.07 -0.07 0.01 0.05 0.03 0.03 -0.03
Value 24.32 24.54 25.83 25.83 26.41 27.35 29.06 29.38 30.36 31.75 32.92 32.94 33.48 33.72 33.99 34.28
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01
BEL-20   Autocorrelation 0.21 -0.06 -0.02 -0.05 0.05 -0.08 -0.03 0.02 0.12 -0.01 -0.07 -0.02 -0.06 -0.01 0.03 0.02
Value 11.29 12.36 12.51 13.26 13.89 15.44 15.74 15.85 19.79 19.8 21.08 21.19 22.25 22.27 22.59 22.73
P Value 0 0 0.01 0.01 0.02 0.02 0.03 0.05 0.02 0.03 0.03 0.05 0.05 0.07 0.09 0.12
CAC 40 Autocorrelation 0.1 -0.11 0 -0.03 -0.02 -0.03 -0.02 -0.03 0.04 -0.02 -0.03 -0.07 -0.05 0.01 0.09 0.01
Value 2.8 6.11 6.12 6.42 6.49 6.74 6.83 7.08 7.54 7.61 7.89 9.07 9.8 9.85 11.94 11.98
P Value 0.09 0.05 0.11 0.17 0.26 0.35 0.45 0.53 0.58 0.67 0.72 0.7 0.71 0.77 0.68 0.75
DAX   Autocorrelation 0.18 -0.01 -0.01 -0.06 -0.06 -0.02 0.01 -0.03 -0.01 -0.06 -0.08 -0.07 -0.06 0.01 0.12 0.03
Value 8.75 8.76 8.81 9.86 10.84 10.98 11.01 11.19 11.19 12.03 13.58 14.94 15.91 15.94 19.9 20.15
P Value 0 0.01 0.03 0.04 0.06 0.09 0.14 0.19 0.26 0.28 0.26 0.25 0.25 0.32 0.18 0.21
FTSE 100   Autocorrelation 0.19 -0.08 0.05 0.01 0.04 0.01 -0.09 -0.05 0.03 0.01 -0.01 -0.14 -0.16 -0.06 0.05 -0.06
Value 9.22 11 11.69 11.7 12.07 12.09 14.09 14.83 15.01 15.07 15.09 20.33 26.95 28.01 28.81 29.72
P Value 0 0 0.01 0.02 0.03 0.06 0.05 0.06 0.09 0.13 0.18 0.06 0.01 0.01 0.02 0.02
Stockholm General   Autocorrelation 0.21 -0.04 -0.02 -0.01 0.1 0.02 -0.02 0.02 -0.03 -0.03 -0.07 -0.03 -0.07 -0.02 0.02 -0.04
Value 11.53 11.93 12.02 12.07 14.59 14.69 14.8 14.9 15.12 15.37 16.8 17.04 18.56 18.63 18.7 19.14
P Value 0 0 0.01 0.02 0.01 0.02 0.04 0.06 0.09 0.12 0.11 0.15 0.14 0.18 0.23 0.26
OSE All Share   Autocorrelation 0.19 0.04 0.11 -0.04 0 -0.02 0.09 -0.02 -0.06 -0.11 -0.13 0.02 -0.01 -0.04 0.01 -0.04
Value 7.94 8.26 11.25 11.59 11.59 11.66 13.34 13.47 14.4 17.32 21.5 21.59 21.61 21.95 21.99 22.32
P Value 0.01 0.02 0.01 0.02 0.04 0.07 0.06 0.1 0.11 0.07 0.03 0.04 0.06 0.08 0.11 0.13
Swiss Market   Autocorrelation 0.03 -0.05 -0.02 -0.02 0.09 0.04 -0.04 -0.08 0.03 -0.05 -0.02 -0.04 -0.04 -0.02 0.02 0
Value 0.28 1.02 1.11 1.22 3.22 3.54 3.97 5.72 5.98 6.65 6.81 7.21 7.55 7.63 7.71 7.72
P Value 0.6 0.6 0.77 0.88 0.67 0.74 0.78 0.68 0.74 0.76 0.81 0.84 0.87 0.91 0.94 0.96

Table 5: Serial Auto correlation Statistic in second year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.257 0.023 0.013 -0.048 -0.054 -0.036 -0.089 -0.08 0.044 0.1 0.071 -0.087 -0.055 -0.018 -0.015 -0.051
Value 17.086 17.226 17.269 17.882 18.658 19.006 21.093 22.808 23.318 25.998 27.357 29.413 30.217 30.304 30.369 31.096
P Value 0 0 0.001 0.001 0.002 0.004 0.004 0.004 0.006 0.004 0.004 0.003 0.004 0.007 0.011 0.013
Athex Composite Share Price Index   Autocorrelation 0.219 -0.001 0.126 -0.1 -0.051 -0.07 -0.065 0.016 0.055 0.03 -0.016 0.086 0.118 0.016 0.08 -0.037
Value 12.038 12.039 16.017 18.566 19.216 20.454 21.54 21.609 22.395 22.631 22.698 24.631 28.302 28.372 30.052 30.417
P Value 0.001 0.002 0.001 0.001 0.002 0.002 0.003 0.006 0.008 0.012 0.019 0.017 0.008 0.013 0.012 0.016
ATX   Autocorrelation 0.263 0.024 0.015 0.048 0.072 -0.113 -0.139 -0.068 0.038 0.059 -0.018 0.04 -0.039 0.109 0.042 -0.104
Value 17.273 17.412 17.47 18.065 19.397 22.671 27.635 28.819 29.2 30.112 30.193 30.614 31.022 34.137 34.615 37.499
P Value 0 0 0.001 0.001 0.002 0.001 0 0 0.001 0.001 0.001 0.002 0.003 0.002 0.003 0.002
BEL-20   Autocorrelation 0.245 0.018 0.025 0.021 -0.031 -0.017 -0.07 -0.132 0.032 0.057 0.023 -0.065 -0.03 -0.055 0.034 -0.006
Value 15.767 15.852 16.023 16.136 16.392 16.466 17.804 22.501 22.778 23.678 23.827 24.983 25.236 26.07 26.39 26.4
P Value 0 0 0.001 0.003 0.006 0.011 0.013 0.004 0.007 0.009 0.013 0.015 0.021 0.025 0.034 0.049
CAC 40 Autocorrelation 0.205 -0.043 -0.02 0.01 -0.025 -0.044 -0.122 -0.113 0.009 0.107 0.058 -0.13 -0.061 0.011 0.041 -0.053
Value 10.81 11.286 11.387 11.413 11.576 12.087 16.024 19.388 19.412 22.484 23.386 27.913 28.912 28.944 29.405 30.178
P Value 0.001 0.004 0.01 0.022 0.041 0.06 0.025 0.013 0.022 0.013 0.016 0.006 0.007 0.011 0.014 0.017
DAX   Autocorrelation 0.227 -0.021 0.013 -0.023 -0.036 -0.04 -0.076 -0.091 -0.016 0.06 0.068 -0.025 -0.015 0.006 0 -0.056
Value 13.346 13.46 13.506 13.645 13.978 14.406 15.928 18.145 18.21 19.165 20.405 20.567 20.63 20.64 20.64 21.506
P Value 0 0.001 0.004 0.009 0.016 0.025 0.026 0.02 0.033 0.038 0.04 0.057 0.081 0.111 0.149 0.16
FTSE 100   Autocorrelation 0.292 -0.012 0.062 -0.042 -0.097 -0.073 -0.066 -0.089 -0.006 0.064 0.004 -0.059 -0.083 -0.018 0.027 -0.029
Value 21.777 21.811 22.789 23.24 25.691 27.065 28.223 30.294 30.304 31.401 31.406 32.325 34.18 34.265 34.462 34.695
P Value 0 0 0 0 0 0 0 0 0 0.001 0.001 0.001 0.001 0.002 0.003 0.004
Stockholm General   Autocorrelation 0.283 -0.003 0.158 -0.043 -0.091 -0.013 -0.113 -0.164 -0.039 0.004 -0.01 0.031 0.025 -0.007 0.08 0.086
Value 21.039 21.042 27.661 28.159 30.378 30.422 33.847 41.155 41.568 41.572 41.599 41.861 42.033 42.046 43.816 45.863
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
OSE All Share   Autocorrelation 0.244 -0.075 0.166 -0.085 -0.14 -0.004 -0.143 -0.045 0.09 -0.069 -0.041 0.073 0.007 0.113 0.048 -0.157
Value 14.922 16.347 23.317 25.133 30.108 30.111 35.338 35.856 37.96 39.211 39.641 41.04 41.054 44.437 45.044 51.641
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Swiss Market   Autocorrelation 0.227 -0.014 -0.002 0 -0.066 -0.088 -0.088 -0.048 -0.005 0.09 0.101 0.024 0.045 0.022 -0.007 -0.066
Value 13.132 13.178 13.179 13.18 14.298 16.297 18.332 18.942 18.949 21.078 23.756 23.91 24.461 24.587 24.601 25.793
P Value 0 0.001 0.004 0.01 0.014 0.012 0.011 0.015 0.026 0.021 0.014 0.021 0.027 0.039 0.056 0.057

Table 6: Serial Auto correlation Statistic in third year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.12 -0.08 0.04 0.07 0.01 -0.09 0.07 0.08 -0.06 -0.04 0.09 0.01 0.01 0.03 -0.06 -0.03
Value 3.71 5.39 5.86 7.26 7.3 9.33 10.44 11.94 12.89 13.25 15.25 15.31 15.36 15.57 16.57 16.79
P Value 0.05 0.07 0.12 0.12 0.2 0.16 0.17 0.15 0.17 0.21 0.17 0.23 0.29 0.34 0.35 0.4
Athex Composite Share Price Index   Autocorrelation 0.15 -0.01 0.08 0.11 -0.02 -0.01 0.05 0 -0.05 -0.06 -0.02 0.02 -0.01 -0.06 -0.05 -0.04
Value 5.76 5.8 7.28 10.26 10.38 10.41 11.05 11.05 11.71 12.77 12.85 12.92 12.95 13.9 14.46 14.85
P Value 0.02 0.06 0.06 0.04 0.07 0.11 0.14 0.2 0.23 0.24 0.3 0.38 0.45 0.46 0.49 0.54
ATX   Autocorrelation 0.17 0.03 0.03 0.02 -0.02 -0.03 -0.01 0.02 -0.06 -0.11 0.08 -0.05 0 0 -0.02 -0.01
Value 7.53 7.8 7.98 8.04 8.18 8.4 8.45 8.56 9.46 12.58 14.1 14.65 14.65 14.65 14.72 14.75
P Value 0.01 0.02 0.05 0.09 0.15 0.21 0.3 0.38 0.4 0.25 0.23 0.26 0.33 0.4 0.47 0.54
BEL-20   Autocorrelation 0.1 -0.04 0.01 0.07 -0.08 -0.09 -0.01 -0.01 -0.05 -0.01 0.04 -0.03 0.06 0.01 -0.05 -0.05
Value 2.43 2.82 2.85 4.27 5.92 8 8 8.01 8.57 8.58 8.92 9.1 10.05 10.1 10.8 11.54
P Value 0.12 0.24 0.42 0.37 0.31 0.24 0.33 0.43 0.48 0.57 0.63 0.7 0.69 0.76 0.77 0.78
CAC 40 Autocorrelation 0.08 -0.08 0 0 0 -0.07 0.03 0.02 -0.07 0.01 0.08 0.02 0.05 0.06 -0.08 -0.01
Value 1.47 2.97 2.97 2.97 2.97 4.29 4.6 4.67 6 6.01 7.52 7.6 8.17 9.05 10.97 10.98
P Value 0.23 0.23 0.4 0.56 0.71 0.64 0.71 0.79 0.74 0.81 0.76 0.82 0.83 0.83 0.76 0.81
DAX   Autocorrelation 0.15 0.01 0 0 -0.02 -0.06 0.03 0 -0.06 0.1 0.13 0.05 0.03 0.01 -0.12 -0.06
Value 5.88 5.89 5.89 5.9 5.98 7.05 7.27 7.28 8.25 10.84 15.15 15.82 16 16.05 20.01 21.11
P Value 0.02 0.05 0.12 0.21 0.31 0.32 0.4 0.51 0.51 0.37 0.18 0.2 0.25 0.31 0.17 0.17
FTSE 100   Autocorrelation 0.18 -0.11 -0.06 0 0.01 -0.06 0.02 0 -0.12 -0.02 0.1 -0.03 0.03 0 -0.02 0.03
Value 8.49 11.74 12.57 12.57 12.58 13.45 13.53 13.53 16.97 17.11 19.77 19.96 20.21 20.21 20.33 20.59
P Value 0 0 0.01 0.01 0.03 0.04 0.06 0.1 0.05 0.07 0.05 0.07 0.09 0.12 0.16 0.2
Stockholm General   Autocorrelation 0.2 -0.07 -0.02 -0.02 -0.04 -0.02 0.06 0.04 -0.06 -0.03 0.03 -0.03 -0.05 -0.08 -0.08 -0.03
Value 10.72 11.9 11.99 12.06 12.41 12.5 13.51 13.91 14.86 15.08 15.34 15.58 16.23 17.82 19.59 19.81
P Value 0 0 0.01 0.02 0.03 0.05 0.06 0.08 0.1 0.13 0.17 0.21 0.24 0.22 0.19 0.23
OSE All Share   Autocorrelation 0.23 0.02 0.04 0.11 -0.08 -0.02 0.04 0.04 0.02 -0.08 0.01 -0.03 0 -0.06 -0.01 0.01
Value 13.04 13.16 13.54 16.79 18.58 18.68 19.07 19.43 19.51 20.95 20.98 21.26 21.27 22.07 22.1 22.15
P Value 0 0 0 0 0 0.01 0.01 0.01 0.02 0.02 0.03 0.05 0.07 0.08 0.11 0.14
Swiss Market   Autocorrelation 0.16 -0.13 -0.07 -0.06 0.05 -0.08 -0.03 0.02 -0.06 0.01 0.13 0.01 -0.01 -0.1 -0.09 0.03
Value 6.45 10.86 12.07 12.91 13.55 15.06 15.22 15.34 16.21 16.23 20.38 20.39 20.42 23.15 25.47 25.72
P Value 0.01 0 0.01 0.01 0.02 0.02 0.03 0.05 0.06 0.09 0.04 0.06 0.09 0.06 0.04 0.06

Table 7: Serial Auto correlation Statistic in forth year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.13 -0.12 -0.09 0.07 0.03 -0.07 0.07 0.14 0.04 -0.05 -0.03 0.02 -0.05 -0.04 -0.06 0.09
Value 4.54 8.5 10.79 11.99 12.27 13.68 15.09 20.37 20.73 21.37 21.56 21.69 22.39 22.93 24.07 26.12
P Value 0.03 0.01 0.01 0.02 0.03 0.03 0.04 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.06 0.05
Athex Composite Share Price Index   Autocorrelation 0.28 -0.08 0.06 0.09 -0.04 -0.09 -0.05 -0.02 -0.07 0 -0.02 -0.06 0.06 0.01 -0.04 0.01
Value 19.31 20.95 21.87 24.15 24.61 26.91 27.67 27.81 29.17 29.17 29.31 30.17 31.22 31.24 31.72 31.74
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01
ATX   Autocorrelation 0.27 -0.08 -0.01 0 -0.03 0 0.02 0.01 0 -0.08 -0.08 0.03 0.08 0.01 -0.01 0.13
Value 18.77 20.54 20.55 20.55 20.72 20.72 20.86 20.88 20.88 22.4 24.26 24.48 26.12 26.14 26.18 30.73
P Value 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.02 0.02 0.03 0.04 0.02
BEL-20   Autocorrelation 0.18 -0.1 -0.08 0.13 0.08 -0.06 0.04 0.16 0.01 -0.13 -0.05 0.06 -0.01 -0.09 -0.18 0.03
Value 8.19 10.79 12.31 16.66 18.54 19.4 19.78 26.59 26.6 31.21 31.85 32.75 32.8 35.25 44.13 44.45
P Value 0 0.01 0.01 0 0 0 0.01 0 0 0 0 0 0 0 0 0
CAC 40 Autocorrelation 0.1 -0.18 -0.11 0.14 -0.01 -0.07 0.02 0.04 -0.05 -0.06 -0.02 0.05 -0.07 -0.05 -0.08 0.08
Value 2.37 10.94 14.06 19.07 19.11 20.57 20.7 21.19 21.91 22.97 23.09 23.81 25.06 25.81 27.49 29.14
P Value 0.12 0 0 0 0 0 0 0.01 0.01 0.01 0.02 0.02 0.02 0.03 0.03 0.02
DAX   Autocorrelation 0.13 -0.12 -0.05 0.1 -0.02 -0.07 0.03 -0.08 0 0.05 -0.03 -0.07 -0.03 -0.1 -0.1 0.05
Value 4.24 8.23 8.77 11.36 11.42 12.82 13.06 14.96 14.96 15.76 16.08 17.23 17.42 19.95 22.58 23.2
P Value 0.04 0.02 0.03 0.02 0.04 0.05 0.07 0.06 0.09 0.11 0.14 0.14 0.18 0.13 0.09 0.11
FTSE 100   Autocorrelation 0.21 -0.19 -0.04 0.1 -0.05 -0.11 0.07 0.05 0.03 -0.04 -0.01 -0.05 0 -0.09 -0.11 0.04
Value 11.15 20.43 20.77 23.62 24.39 27.46 28.89 29.45 29.72 30.18 30.2 30.93 30.93 33.21 36.74 37.12
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Stockholm General   Autocorrelation 0.28 -0.15 -0.02 0.04 -0.06 -0.12 0.02 0.02 -0.07 -0.12 -0.01 0.09 0.04 -0.05 -0.07 0.1
Value 19.54 24.9 24.96 25.36 26.36 30.02 30.17 30.31 31.49 35.06 35.09 37.36 37.7 38.42 39.54 42.06
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
OSE All Share   Autocorrelation 0.28 -0.08 -0.04 0 -0.04 -0.05 0.05 -0.03 0.07 -0.02 -0.09 -0.04 0.07 0.08 0.02 0.11
Value 20.53 22.3 22.67 22.68 23.04 23.61 24.36 24.57 25.92 26 28.12 28.53 29.83 31.36 31.49 34.82
P Value 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0
Swiss Market   Autocorrelation 0.13 -0.19 -0.07 0.13 -0.09 -0.16 -0.05 0.04 0.03 0.04 -0.01 0 -0.04 -0.02 -0.09 0.02
Value 4.23 13.65 14.94 19.19 21.18 27.78 28.53 29.04 29.26 29.65 29.66 29.66 30.12 30.24 32.59 32.69
P Value 0.04 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01

Table 8: Serial Auto correlation Statistic in fifth year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.27 -0.05 -0.09 0 0.03 -0.09 -0.07 -0.02 -0.03 -0.05 -0.04 0.02 0.1 0.03 -0.03 -0.05
Value 19.59 20.14 22.08 22.08 22.28 24.23 25.36 25.45 25.77 26.43 26.92 27 29.47 29.79 30.07 30.83
P Value 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.01 0.01
Athex Composite Share Price Index   Autocorrelation 0.3 -0.07 -0.07 -0.02 -0.04 -0.02 0.14 0.07 -0.05 -0.07 0.01 0.16 0.09 0.03 0.03 0.04
Value 23.18 24.31 25.46 25.56 26.05 26.13 31.16 32.25 32.89 34.08 34.12 40.96 43.14 43.34 43.52 43.9
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ATX   Autocorrelation 0.33 -0.04 -0.11 -0.06 -0.05 -0.06 -0.03 -0.07 -0.07 -0.04 -0.14 -0.05 0.12 0.03 0.01 0.05
Value 28.04 28.39 31.28 32.24 32.86 33.65 33.84 35.26 36.36 36.82 41.72 42.39 46.49 46.8 46.84 47.47
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
BEL-20   Autocorrelation 0.15 -0.1 -0.06 -0.15 -0.09 0 0.09 0.12 0.06 -0.03 -0.09 0.06 0.15 0.06 -0.01 0.03
Value 2.45 3.64 4.01 6.48 7.44 7.44 8.44 10.2 10.66 10.77 11.67 12.15 15.02 15.45 15.47 15.6
P Value 0.12 0.16 0.26 0.17 0.19 0.28 0.3 0.25 0.3 0.38 0.39 0.43 0.31 0.35 0.42 0.48
CAC 40 Autocorrelation 0.27 -0.06 -0.09 0 0.08 -0.05 -0.05 0.02 -0.02 -0.05 -0.08 0.01 0.07 0.05 0 -0.04
Value 19.6 20.46 22.4 22.4 23.94 24.48 25.09 25.21 25.3 26.09 27.97 27.98 29.23 29.95 29.95 30.3
P Value 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01 0.02
DAX   Autocorrelation 0.29 -0.04 -0.07 -0.01 0.1 -0.01 -0.08 -0.03 0.01 0.02 -0.06 -0.04 0.06 0.05 -0.03 -0.04
Value 22.55 23.05 24.36 24.38 27.14 27.19 29.04 29.27 29.28 29.39 30.44 30.93 32.02 32.78 33.09 33.56
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01
FTSE 100   Autocorrelation 0.29 -0.05 -0.08 -0.08 0.05 0.02 0.07 0.09 0.04 -0.08 -0.17 -0.03 0.03 0.06 0.05 -0.02
Value 21.51 22.04 23.63 25.25 26.03 26.12 27.41 29.35 29.72 31.23 38.57 38.85 39.04 39.87 40.51 40.57
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Stockholm General   Autocorrelation 0.14 -0.07 -0.07 -0.07 -0.04 -0.09 0.1 0.01 0.06 -0.01 -0.1 0.05 0.06 -0.02 0.03 0.07
Value 4.72 5.82 7.04 8.44 8.95 10.91 13.51 13.54 14.34 14.35 17.16 17.94 18.75 18.81 19.05 20.44
P Value 0.03 0.05 0.07 0.08 0.11 0.09 0.06 0.1 0.11 0.16 0.1 0.12 0.13 0.17 0.21 0.2
OSE All Share   Autocorrelation 0.33 -0.03 -0.09 -0.07 -0.01 0 -0.03 -0.01 -0.04 -0.01 -0.02 -0.03 0.16 0.09 -0.05 0
Value 28.57 28.87 30.85 32.26 32.27 32.27 32.51 32.56 33.01 33.04 33.12 33.36 40.01 42.02 42.74 42.75
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Swiss Market   Autocorrelation 0.08 -0.11 -0.14 -0.06 0.15 -0.02 -0.12 -0.01 -0.01 0.05 -0.02 -0.02 0.11 -0.01 -0.07 -0.02
Value 1.65 4.63 9.54 10.36 16.23 16.31 20.01 20.04 20.08 20.63 20.79 20.86 23.94 23.95 25.48 25.61
P Value 0.2 0.1 0.02 0.04 0.01 0.01 0.01 0.01 0.02 0.02 0.04 0.05 0.03 0.05 0.04 0.06

Table 9: Serial Auto correlation Statistic in sixth year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General Autocorrelation 0.119 0.055 -0.06 -0.042 -0.059 -0.027 -0.059 -0.09 -0.113 0.044 0.022 0.171 0.031 -0.084 -0.116 -0.04
Value 3.735 4.539 5.488 5.968 6.886 7.078 8.005 10.217 13.668 14.189 14.317 22.334 22.598 24.569 28.278 28.728
P Value 0.053 0.103 0.139 0.202 0.229 0.314 0.332 0.25 0.135 0.165 0.216 0.034 0.047 0.039 0.02 0.026
Athex Composite Share Price Index   Autocorrelation 0.295 -0.095 -0.144 -0.074 0.02 0.075 0.042 0.07 -0.003 -0.081 -0.074 -0.001 0.146 0.162 -0.009 -0.117
Value 22.394 24.715 30.113 31.536 31.643 33.109 33.574 34.856 34.859 36.613 38.099 38.099 43.878 50.989 51.012 54.737
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ATX   Autocorrelation 0.351 -0.011 -0.068 -0.093 -0.088 -0.112 -0.011 0.012 0.052 0.106 0.066 0.005 -0.069 -0.057 -0.094 -0.083
Value 31.453 31.487 32.676 34.894 36.922 40.21 40.242 40.283 40.989 43.983 45.135 45.142 46.405 47.28 49.654 51.516
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
BEL-20   Autocorrelation 0.052 -0.002 -0.04 -0.058 -0.085 0.009 -0.14 -0.093 -0.092 0.068 -0.048 0.153 0.005 -0.09 -0.052 0.022
Value 0.661 0.662 1.044 1.861 3.633 3.655 8.533 10.659 12.776 13.932 14.522 20.473 20.48 22.527 23.211 23.341
P Value 0.416 0.718 0.791 0.761 0.603 0.723 0.288 0.222 0.173 0.176 0.205 0.059 0.084 0.068 0.08 0.105
CAC 40 Autocorrelation 0.151 0.02 -0.046 -0.041 -0.047 0.005 -0.031 -0.094 -0.111 0.002 0.019 0.133 0.049 -0.09 -0.063 -0.029
Value 6.004 6.11 6.675 7.119 7.719 7.727 7.979 10.386 13.736 13.738 13.838 18.671 19.329 21.571 22.671 22.913
P Value 0.014 0.047 0.083 0.13 0.172 0.259 0.334 0.239 0.132 0.185 0.242 0.097 0.113 0.088 0.091 0.116
DAX   Autocorrelation 0.153 -0.002 -0.031 -0.018 -0.073 -0.105 -0.037 -0.077 -0.102 0.009 0.032 0.119 0.06 -0.088 -0.022 -0.03
Value 6.122 6.123 6.374 6.461 7.872 10.821 11.185 12.807 15.639 15.662 15.943 19.846 20.833 22.988 23.123 23.38
P Value 0.013 0.047 0.095 0.167 0.163 0.094 0.131 0.119 0.075 0.11 0.143 0.07 0.076 0.06 0.082 0.104
FTSE 100   Autocorrelation 0.252 -0.005 0.069 0.046 -0.102 -0.086 -0.104 -0.11 -0.031 0.088 0.055 0.055 0.025 -0.039 -0.044 -0.045
Value 16.378 16.384 17.619 18.18 20.91 22.859 25.692 28.908 29.168 31.254 32.069 32.89 33.065 33.469 33.995 34.539
P Value 0 0 0.001 0.001 0.001 0.001 0.001 0 0.001 0.001 0.001 0.001 0.002 0.002 0.003 0.005
Stockholm General   Autocorrelation 0.195 -0.018 -0.092 -0.067 -0.049 -0.057 -0.048 -0.023 0.015 -0.014 0.1 0.037 0.024 -0.066 -0.1 0.007
Value 9.887 9.975 12.206 13.367 14.005 14.862 15.482 15.628 15.686 15.74 18.444 18.824 18.985 20.183 22.93 22.942
P Value 0.002 0.007 0.007 0.01 0.016 0.021 0.03 0.048 0.074 0.107 0.072 0.093 0.124 0.124 0.086 0.115
OSE All Share   Autocorrelation 0.369 0.035 -0.095 -0.108 -0.139 -0.12 0.01 0.001 0.001 0.046 -0.012 -0.04 -0.008 0.036 -0.041 -0.139
Value 34.91 35.221 37.547 40.579 45.607 49.325 49.349 49.349 49.349 49.901 49.942 50.365 50.384 50.726 51.176 56.424
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Swiss Market   Autocorrelation 0.203 -0.012 -0.044 0.007 -0.016 -0.06 -0.081 -0.143 -0.094 0.088 0.067 -0.014 -0.042 -0.067 -0.041 -0.057
Value 10.86 10.896 11.411 11.423 11.491 12.446 14.194 19.711 22.118 24.225 25.456 25.51 25.999 27.227 27.695 28.599
P Value 0.001 0.004 0.01 0.022 0.042 0.053 0.048 0.011 0.009 0.007 0.008 0.013 0.017 0.018 0.024 0.027

Table 10: Serial Auto correlation Statistic in seventh year.

Name of country Indices Lag 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AEX General   Autocorrelation 0.22 0 -0.09 -0.11 0 0.02 0 -0.02 -0.12 -0.01 0.06 -0.02 0.08 0.02 -0.02 0.07
Value 12.69 12.69 14.68 17.71 17.71 17.83 17.83 17.9 21.55 21.57 22.55 22.62 24.34 24.45 24.55 25.87
P Value 0 0 0 0 0 0.01 0.01 0.02 0.01 0.02 0.02 0.03 0.03 0.04 0.06 0.06
Athex Composite Share Price Index   Autocorrelation 0.21 -0.15 -0.03 0.08 0.01 -0.03 -0.02 0.08 0.05 -0.02 -0.03 0.05 -0.03 -0.13 0.03 0.12
Value 11.04 16.51 16.82 18.28 18.32 18.62 18.77 20.65 21.22 21.33 21.57 22.13 22.38 27.07 27.27 31.31
P Value 0 0 0 0 0 0.01 0.01 0.01 0.01 0.02 0.03 0.04 0.05 0.02 0.03 0.01
ATX   Autocorrelation 0.26 0.02 -0.15 -0.05 -0.02 0 0.07 -0.03 -0.1 0 -0.04 0.04 0.05 0.04 0.06 0.05
Value 17.83 17.93 23.59 24.22 24.34 24.34 25.68 25.94 28.33 28.33 28.66 29.02 29.77 30.1 31.06 31.76
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01 0.01
BEL-20   Autocorrelation 0.18 -0.05 -0.14 -0.11 -0.05 -0.03 -0.01 -0.02 -0.08 -0.01 0.06 -0.04 0.1 0.03 0.01 0.07
Value 8.22 8.85 14.21 17.21 17.99 18.17 18.19 18.28 19.94 19.95 20.99 21.5 24.14 24.33 24.35 25.72
P Value 0 0.01 0 0 0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.03 0.04 0.06 0.06
CAC 40 Autocorrelation 0.27 -0.08 -0.14 -0.1 0.03 0.01 0 -0.03 -0.1 0 0.06 -0.03 0.01 -0.01 0.01 0.12
Value 19.03 20.54 25.66 28.54 28.77 28.79 28.79 29.06 31.7 31.7 32.59 32.76 32.78 32.8 32.82 36.58
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0
DAX   Autocorrelation 0.24 -0.06 -0.11 -0.09 -0.03 -0.03 0.09 0.03 -0.08 0.08 0.06 0.03 0.07 0.01 0 0.08
Value 15.63 16.42 19.52 21.89 22.14 22.31 24.38 24.6 26.33 27.85 28.97 29.19 30.49 30.53 30.53 32.32
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.01 0.01
FTSE 100   Autocorrelation 0.31 -0.02 -0.17 -0.16 0.01 -0.02 -0.05 -0.05 -0.07 0.03 0.02 -0.05 0.04 0.03 0.07 0.05
Value 25.28 25.35 32.51 39.1 39.13 39.26 39.92 40.48 41.7 41.88 42.02 42.77 43.12 43.3 44.68 45.28
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Stockholm General   Autocorrelation 0.28 -0.04 -0.12 -0.12 -0.01 -0.05 -0.02 -0.02 -0.12 0.06 0.14 0.06 0.05 -0.01 0.03 0.06
Value 20.55 21.01 24.69 28.42 28.44 29 29.11 29.2 32.88 33.96 38.88 39.7 40.36 40.38 40.6 41.52
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
OSE All Share   Autocorrelation 0.35 0.05 -0.08 -0.14 -0.07 -0.09 -0.06 0 -0.09 -0.01 0.07 -0.02 0.04 -0.02 0.04 0.07
Value 31.34 32.08 33.8 39.14 40.6 42.8 43.65 43.65 45.76 45.77 46.96 47.05 47.48 47.55 48.08 49.29
P Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Swiss Market   Autocorrelation 0.23 0.01 -0.09 -0.13 0.02 -0.03 -0.02 -0.01 -0.11 0.07 0.05 -0.06 0.03 0.05 0 0.01
Value 13.92 13.93 15.99 20.59 20.66 20.91 20.99 20.99 24.25 25.4 26.02 26.95 27.16 27.81 27.81 27.86
P Value 0 0 0 0 0 0 0 0.01 0 0.01 0.01 0.01 0.01 0.02 0.02 0.03

Table 11: Serial Auto correlation Statistic in eighth year.

It can be seen from in Tables 4-11 that majority of country indices correlation coefficient found to be significant at five percent and one percent level for up to 16 days lags. Thereafter, there are few observation correlation coefficient are showing insignificance autocorrelation. Thus, the result of autocorrelation test of price changes in most of the cases does not supports the applicability of random walk model in order to describe share price behaviors in majority of European country indices during recent time period. Curiously all indices do not support the independence of stock prices. Thus, the overall significance of autocorrelation coefficient points to the efficiency of European markets is not in its weak form. However, it can be observed that with the increase in time lag significant auto correlated converted in insignificant. It can be said that memory related to prices decreases with increases in time period in case of few indices. One of the features of the result based on autocorrelation analysis is that this analysis overcomes the limitations of run test.

Conclusions

Thus, in most of cases the result of Run test of price changes does not supports the randomness in the stock prices because large number of country Z value are found to be significant. Run test reveals that majority of European country indices correlation coefficient is significant for the different years. It is also note that similar trends obtained even when the runs are calculated through median and mean. It is inferred that stock prices does not exhibit random behavior and thus not support the weak form of market efficiency. In run test, there is one limitation that is only sign is considered but not the absolute change. In order to overcome this limitation autocorrelation test is used in which raw value and sign are considered. Serial correlation coefficient statistics does not clearly indicates the all indices are in weak form efficiency. It indicates that majority of statistics are significantly auto correlated. The result indicates that weak form efficiency does not exist related to indices. On comparing the present study with the previous studies, it has been found that there is variation in the results of various studies. Some studies totally states that there is existence of weak form efficiency and some studies totally opposes it. The present study does not fully support either of the researchers. The results indicate that European stock market is the mixture of significant auto correlated country and insignificant auto correlated country. But majority indicts random behavior does not exist.

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