Efficient Market Hypothesis ( EMH ) is a really controversial and extremely disputed theory presents. EMH was formulated by Eugene Fama in 1970. It is believed that it is impossible to happen undervalued stocks or predict any tendency in the stock market. There are three identified categorizations of theA EMH ( Strong efficiency, Semi-strong efficiency, Weak efficiency ) which have as an purpose to reflect the grade to which it can be applied to markets.
The chief aim of this single study is to execute some trials for the weak signifier efficiency for three selected stocks ( MARSHALL & A ; ILSLEY CORP, ABERCROMBIE & A ; FITCH CO, ANNALY CAPITAL MANAGEMENT INC ) and two deciles indices ( NYSE/AMEX/NASDAQ index capitalisation-based Deciles 1 and 10 ) .
The construction of this study is organised as follows:
Section I gives a brief description about the companies.
Section II describes the information and the methodological analysis used for the trials of the weak signifier efficiency
Section III discusses the descriptive statistics of the information we used
Section IV presents the consequences
Section I: THE DESCRIPTION OF THE COMPANIES
MARSHALL & A ; ILSLEY CORP ( MI )
Marshall & A ; Ilsley Corporation ( M & A ; I ) is a bank keeping company. M & A ; I provides its subordinates with fiscal and managerial aid, in budgeting, revenue enhancement planning, scrutinizing, conformity, plus and liability direction, investing disposal and portfolio planning, concern development, advertisement and human resources direction. M & A ; I besides provides diversified fiscal services to a assortment of corporate, institutional, authorities and single clients. M & A ; I operates in four concern sections: Commercial Banking, Community Banking, Wealth Management and Treasury. M & A ; I provides banking services, which include loaning to and accepting sedimentations from commercial and community banking clients Source: A Worldscope
ABERCROMBIE & A ; FITCH CO ( ANF )
Abercrombie & A ; Fitch Co. ( A & A ; F ) through its subordinates, is a forte retail merchant that operates shops and direct-to-consumer operations selling insouciant athletic wear dress, including knit and woven shirts, in writing jerseies, fleece, denims and woven bloomerss, shirts, jumpers, overclothes, personal attention merchandises, and accoutrements for work forces, adult females and childs under the Abercrombie & A ; Fitch, abercrombie childs, and Hollister trade names. In add-on, the Company operates shops and direct-to-consumer operations offering bandeaus, underwear, personal attention merchandises, sleepwear and at-home merchandises for adult females under the Gilly Hicks trade name. Beginning: A Worldscope
ANNALY CAPITAL MANAGEMENT INC ( NLY )
Annaly Capital Management, Inc. owns, manages and finances a portfolio of existent estate related investings, including mortgage pass-through certifications, collateralized mortgage duties ( CMOs ) , Agency callable unsecured bonds, and other securities stand foring involvements in the duties backed by pools of mortgage loans. The Company besides invests in Federal Home Loan Bank ( FHLB ) , Freddie Mac and Fannie Mae unsecured bonds. The Company ‘s entirely owned subordinates offer diversified existent estate, plus direction and other fiscal services. It is self-advised and self-managed.
Beginning: A Worldscope
Section II: DATA AND METHODOLOGY
Datas
We use both day-to-day and monthly returns for the three stocks and two deciles indices over the period January 2007 to December 2010. All the day-to-day informations have 1007 observations and the monthly informations have 47 observations. We have besides used logarithmic ( log ) returns and arithmetic returns for the descriptive statistics of each stock
Methodology
B.1.AUTO CORRELATION ANALYSIS
Correlation is a statistical relationship between 2 or more random variables or observed informations values. The correlativity of a series with its ain lagged values is called autocorrelation. The most known step of dependance is the correlativity coefficient and is defined as:
I?k is the autocorrelation at slowdown K
If the autocorrelation is positive or +1 so we have positive additive relationship ( correlativity ) . In instance it is -1 so we have negative additive relationship ( anticorrelation ) . If the value is between a?’1 and 1 indicates the grade of additive dependance between the variables. If it is close to zero so we say that the informations are uncorrelated. If the coefficient is closer to either a?’1 or 1, so the correlativity is stronger between the variables. We have used the autocorrelation coefficients up to 10 slowdowns and they are computed for each stock and decile index.
B.2. DAY OF THE WEEK EFFECT
Seasonal effects in fiscal markets have been perceived and they are frequently called as “ calendar anomalousnesss ” . Some illustrations are the day-of-the-week consequence, open- or close-of-market, January or bank vacation and many others. We may happen that the stock returns are statistically important different during some calendar periods compared to others. If stock returns follow a random walk so at that place must n’t be any difference between returns in different calendar periods. If we have decided to observe seasonality in returns, the most common manner is to utilize a “ Dummy Variable ” arrested development. The coefficients are interpreted as the mean return on each twenty-four hours of the hebdomad
Where is the return at clip T
1 if it is a Monday return
D1t =
0 otherwise
B.3. VARIANCE RATIO TESTS
The discrepancy ratio Test was used by Lo and MacKinlay ( 1988 ) to look into if the information we used, follow random walk. Price motions normally follow random walk. The trial statistic derived by Lo and MacKinlay to prove if a series of monetary value motions follows a random walk is robust to many signifiers of heteroscedasticity and nonnormality. The discrepancy trial is defined as:
If the VR ( Q ) is equal to 1 so we can state that we have the random walk void hypothesis. When VR ( Q ) is bigger than 1 and the void hypothesis is rejected so the return is positively correlated. If the VR ( Q ) is smaller than 1 and the void hypothesis is once more jilted so we can find that the return is negatively correlated.
B.4 VOLATILITY MODELLING
By and large, when we have to prove for heteroscedasticity in econometric theoretical accounts, the best trial is the White trial. However, when we have to cover with clip series informations, we have to utilize the GARCH theoretical account. GARCH ( generalized autoregressive conditional heteroscedasticity ) theoretical account was introduced by Bollerslev in 1986.
In that instance, the GARCH ( P, Q ) theoretical account ( where P is the order of the GARCH footings ~sigma^2 and Q is the order of the ARCH footings ~epsilon^2 ) and it is given by:
sigma_t^2=alpha_0 + alpha_1 epsilon_ { t-1 } ^2 + cdots + alpha_q epsilon_ { t-q } ^2 + eta_1 sigma_ { t-1 } ^2 + cdots + eta_psigma_ { t-p } ^2 = alpha_0 + sum_ { i=1 } ^q alpha_i epsilon_ { t-i } ^2 + sum_ { i=1 } ^p eta_i sigma_ { t-i } ^2
The EGARCH ( exponential general autoregressive conditional heteroskedastic ) theoretical account was introduced by Nelson in 1991 and it is another signifier of the GARCH theoretical account.
An EGARCH ( P, Q ) is defined as:
logsigma_ { T } ^2=omega+sum_ { k=1 } ^ { P } eta_ { K } g ( Z_ { t-k } ) +sum_ { k=1 } ^ { Q } alpha_ { K } logsigma_ { t-k } ^ { 2 }
sigma_ { T } ^ { 2 } Is the conditional discrepancy
If the logsigma_ { T } ^ { 2 } is negative, so there are no limitations on the parametric quantities.
Section III: Discussion OF THE DESCRIPTIVE STATISTICS
We have examined the descriptive statistics from the Table I and Table II so we can place if the distribution of the returns are normal. If they are normal, so they must hold followed the random walk theoretical account. At Table I and Table II are reported the day-to-day and monthly logarithmic returns ( R ) and the day-to-day and monthly arithmetic returns ( R ) .
For the day-to-day frequences, all the mean and median for the returns are positive except from the MI ( -0.00194, -0.00121 ) and the ANF ( -0.00021 ) . The lowest minimal returns are DC1 ( -0.0561 ) and DC10 ( -0.095184 ) which both give the lowest maximal returns 0.062526 and 0.111735 severally. In contrast with them, MI and NLY show the highest maximal returns. As a step of scattering we take the criterion divergence which reveals that DC1 and DC10 are the least volatile from all the information. MI is the most volatile. NLY is the lone one which is positive skewed, which means that the return distribution has a high possibility of gaining positive returns. In contrast MI, ANF, DC1 and DC10 are negatively skewed which means that they have a high possibility of gaining negative returns. All three stocks and the two decile indices have positive kurtosis which means that they have leptokurtic return distributions
Histogram of the return distribution of MI
Time Series of the return Distribution of D1
For the monthly frequences, the stock and the decile indices have in general the same values as in day-to-day frequences. On the steps of cardinal inclination, steps of scattering, and the steps of lopsidedness and kurtosis, they have the same lowest or highest values. We can see on Table II that there is difference if we take the logarithmic returns or the arithmetic returns. The values are wholly different.
Taking into history the lopsidedness, the three stocks and the two decile indices are negatively skewed. On the other manus, kurtosis has big values. Get downing with NLY ( 17.38134 ) and MI ( 11.05521 ) and they are followed by DC10 ( 9.767838 ) , ANF ( 8.844107 ) and DC1 ( 8.116648 ) . Except from MI and NLY, all the other assets are about normal. We configure this by the Jarque – Bera trial from which we can state that they reject to neglect the void hypothesis of normalcy.
Table I
Descriptive Statisticss of Daily Returns
This tabular array shows the descriptive statistics of the day-to-day returns for 5 stocks and 2 deciles indices over the period January 2007 to December 2010. The lower instance R denotes a logarithmic ( log ) return and the upper-case ulterior R denotes an arithmetic ( simple ) return.
MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC. DC1- NYSE/AMEX/NASDAQ Decile1. DC10- NYSE/AMEX/NASDAQ Decile10. Max stands for Maximum. Min. bases for Minimum. Std. Dev. Stands for Standard Deviation. JB STANDS FOR Jarque-Bera. Obs stands for Observations.
Myocardial infarction
ANF
NLY
DC1
DC10
A
R
Roentgen
R
Roentgen
R
Roentgen
R
Roentgen
R
Mean
-0.00194
-0.00042
-0.00021
0.000324
0.000244
0.000708
0.000409
0.000467
0.00000032
Median
-0.00121
-0.00121
0.000369
0.000369
0.001116
0.001117
0.001086
0.001087
0.000899
Max.
0.329341
0.390052
0.175582
0.19194
0.274437
0.315789
0.062526
0.064523
0.111735
Min.
-0.30146
-0.26026
-0.23221
-0.20722
-0.19842
-0.17998
-0.0561
-0.05455
-0.095184
Std. Dev.
0.055064
0.055315
0.032708
0.032558
0.030397
0.030676
0.010712
0.010711
0.017264
Lopsidedness
-0.10445
0.72514
-0.42307
-0.05985
0.278683
1.064435
-0.14067
-0.0256
-0.242333
Kurtosis
11.05521
11.79593
8.844107
8.148605
17.38134
21.0768
8.116648
8.267992
9.767838
JB
2724.358
3334.5
1463.068
1112.838
8690.982
13900.92
1101.794
1164.527
1931.7
JB p-value
0
0
0
0
0
0
0
0
0
Ob river
1007
1007
1007
1007
1007
1007
1007
1007
1007
Table II
Descriptive Statisticss of Monthly Returns
This tabular array shows the descriptive statistics of the monthly returns for 3 stocks and 2 deciles indices over the period January 2007 to December 2010. The lower instance R denotes a logarithmic ( log ) return and the upper-case ulterior R denotes an arithmetic ( simple ) return.
MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC. DC1- NYSE/AMEX/NASDAQ Decile1. DC10- NYSE/AMEX/NASDAQ Decile10. Max stands for Maximum. Min. bases for Minimum. Std. Dev. Stands for Standard Deviation. JB STANDS FOR Jarque-Bera. Obs stands for Observations.
Myocardial infarction
ANF
NLY
DC1
DC10
A
R
Roentgen
R
Roentgen
R
Roentgen
R
Roentgen
R
Mean
-0.04079
-0.02098
-0.00686
0.003159
0.005589
0.008179
0.010004
0.013051
-0.000445
Median
-0.00753
-0.0075
-0.00476
-0.00475
0.011141
0.011203
0.009105
0.009147
0.01316
Max.
0.367885
0.444676
0.225666
0.253158
0.122739
0.130589
0.175197
0.191481
0.09284
Min.
-0.87079
-0.58138
-0.40426
-0.33253
-0.30049
-0.25955
-0.16079
-0.14853
-0.19825
Std. Dev.
0.208479
0.184455
0.145081
0.139956
0.07361
0.07047
0.077933
0.078693
0.060218
Lopsidedness
-1.3345
-0.24794
-0.58973
-0.25698
-1.56381
-1.12723
-0.12042
0.103217
-0.844232
Kurtosis
6.893326
4.041347
2.989927
2.502646
7.723667
5.906776
2.94561
2.95443
3.872671
JB
43.63478
2.605157
2.724526
1.001727
62.8528
26.50002
0.11938
0.08752
7.074418
JB p-value
0
0.27183
0.256081
0.606007
0
0.000002
0.942057
0.957184
0.029094
Ob river
47
47
47
47
47
47
47
47
47
Table III
Autocorrelation and Partial Autocorrelation Trials Log Returns
This tabular array demo the autocorrelation and the partial autocorrelation coefficients up to 10 slowdowns for the log-returns of each stock and each decile index. AC stands for autocorrelation. PAC stands for partial autocorrelation. MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Panel A: Consequences for Daily Log -Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
ACF
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.023
0.023
0.5239
-0.029
-0.029
0.8335
-0.251
-0.251
63.726
0.271
0.271
74.388
-0.111
-0.111
2
-0.032
-0.033
1.56
-0.026
-0.027
1.5077
-0.037
-0.107
65.111
0.217
0.154
121.86
-0.093
-0.107
3
0.064*
0.066
5.7251
-0.047
-0.049
3.7553
-0.036
-0.079
66.423
0.214
0.135
168.01
0.086
0.064
4
-0.027
-0.032
6.4883
0.03
0.026
4.6646
-0.047
-0.089
68.621
0.115
0.008
181.4
-0.033
-0.026
5
-0.017
-0.011
6.7799
-0.018
-0.019
4.9941
0.053*
0.009
71.479
0.071*
-0.011
186.56
-0.032
-0.025
6
-0.037
-0.043
8.1715
-0.094
-0.097
14.05
-0.03
-0.028
72.395
0.041
-0.018
188.27
0.022
0.004
7
-0.021
-0.017
8.639
-0.033
-0.037
15.137
-0.004
-0.023
72.412
0.047*
0.02
190.56
-0.021
-0.02
8
0.023
0.022
9.1587
0.041
0.032
16.861
0.024
0.015
73.019
-0.015
-0.044
190.78
0.018
0.02
9
0.072
0.074
14.384
-0.001
-0.009
16.862
-0.026
-0.018
73.715
0.03
0.035
191.7
0.006
0.003
10
-0.006
-0.008
14.415
0.097*
0.101
26.409
-0.011
-0.027
73.836
0.043
0.035
193.61
0.035
0.044
Panel Bacillus: Consequences for Monthly Log -Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
Actinium
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.137
0.137
0.9345
0.026
0.026
0.0339
-0.102
-0.102
0.5188
0.372
0.372
6.9116
0.294
0.294
2
0.143
0.127
1.9814
-0.11
-0.111
0.6522
-0.191
-0.203
2.3788
0.182
0.051
8.6016
-0.037
-0.136
3
0.037
0.003
2.0546
-0.172
-0.168
2.205
0.131
0.091
3.2747
0.274
0.222
12.518
0.166
0.244
4
0.154
0.136
3.3306
-0.03
-0.037
2.2543
-0.052
-0.07
3.4185
0.216
0.056
15.021
0.281
0.166
5
-0.021
-0.064
3.3552
0.036
0
2.3246
-0.147
-0.124
4.6057
-0.052
-0.213
15.17
-0.061
-0.201
6
-0.154
-0.19
4.6798
-0.046
-0.086
2.443
-0.061
-0.133
4.8149
-0.241
-0.289
18.432
-0.323
-0.275
7
0.033
0.088
4.7431
0.017
0.01
2.459
0.142
0.091
5.9807
-0.079
0.04
18.793
-0.012
0.102
8
0.042
0.057
4.8475
0.137
0.134
3.5745
0.004
0.017
5.9819
0.105
0.282
19.447
0.072
-0.015
9
-0.097
-0.123
5.4216
-0.054
-0.079
3.751
-0.179
-0.149
7.9186
-0.201
-0.179
21.898
-0.187
-0.088
10
-0.184
-0.134
7.5348
-0.099
-0.074
4.3557
0.045
-0.045
8.0455
-0.138
0.007
23.076
-0.135
0.106
Table IV
Autocorrelation and Partial Autocorrelation Trials for Squared Log Returns
This tabular array demo the autocorrelation and the partial autocorrelation coefficients up to 10 slowdowns for the log-returns of each stock and each decile index. AC stands for autocorrelation. PAC stands for partial autocorrelation. MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Panel A: Consequences for Daily Squared Log -Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
Actinium
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.153
0.153
23.599
0.188
0.188
35.555
0.364
0.364
134.1
0.247
0.247
61.744
0.186
0.186
2
0.144
0.124
44.707
0.312
0.287
133.74
0.293
0.184
220.72
0.281
0.235
141.84
0.393
0.371
3
0.158
0.125
69.991
0.148
0.06
156.04
0.304
0.179
314.25
0.17
0.066
171.03
0.16
0.054
4
0.137
0.088
88.886
0.126
0.012
172.1
0.264
0.099
384.75
0.097
-0.013
180.5
0.31
0.17
5
0.127
0.071
105.24
0.156
0.091
196.77
0.267
0.106
456.91
0.147
0.086
202.29
0.353
0.287
6
0.202
0.147
146.7
0.201
0.144
237.65
0.221
0.036
506.48
0.195
0.144
240.85
0.325
0.16
7
0.097
0.016
156.26
0.176
0.076
269.09
0.276
0.126
583.83
0.109
-0.003
252.83
0.333
0.136
8
0.125
0.053
172.19
0.123
-0.012
284.5
0.349
0.187
707.56
0.155
0.05
277.17
0.198
-0.011
9
0.131
0.054
189.71
0.163
0.066
311.69
0.307
0.094
803.71
0.123
0.044
292.58
0.308
0.089
10
0.2
0.131
230.34
0.111
0.031
324.13
0.251
0.015
867.78
0.149
0.073
315.29
0.278
0.101
Panel Bacillus: Consequences for Monthly Squared Log- Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
Actinium
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.49
0.49
12.027
-0.017
-0.017
0.0142
0.008
0.008
0.0034
0.613
0.613
18.789
0.243
0.243
2
0.442
0.266
22.045
-0.026
-0.026
0.0482
0
0
0.0034
0.321
-0.087
24.066
-0.056
-0.122
3
0.183
-0.15
23.807
-0.051
-0.052
0.183
0.165
0.165
1.4352
0.307
0.236
28.992
0.061
0.114
4
0.129
-0.018
24.695
0.03
0.027
0.2306
-0.089
-0.094
1.8608
0.351
0.127
35.588
0.274
0.24
5
-0.023
-0.09
24.725
0.014
0.013
0.2418
-0.037
-0.035
1.9348
0.292
0.002
40.255
0.072
-0.055
6
-0.12
-0.136
25.528
-0.045
-0.046
0.3552
0.192
0.172
3.9983
0.343
0.242
46.87
0.084
0.141
7
-0.07
0.106
25.812
0.167
0.17
1.9597
-0.09
-0.073
4.4654
0.232
-0.21
49.963
-0.055
-0.158
8
-0.137
-0.067
26.92
-0.081
-0.081
2.3451
-0.079
-0.08
4.8331
0.01
-0.199
49.968
-0.123
-0.143
9
-0.148
-0.11
28.245
0.11
0.117
3.0744
0.068
0.016
5.1106
-0.164
-0.25
51.596
0.019
0.083
10
-0.194
-0.061
30.586
-0.105
-0.096
3.7649
-0.079
-0.026
5.4953
-0.057
0.097
51.801
-0.101
-0.255
In the instance when autocorrelation of squared day-to-day logarithmic returns and absolute value of day-to-day logarithmic return is calculated the autocorrelation consequences and partial autocorrelation consequences in all instances are much stronger and statistically of import in 5 % degree for the first 3 slowdowns. For the 4th and 5th slowdowns there is a assorted image between the assets as in ASX and RHT autocorrelation and partial autocorrelation effects are get downing to conk and they showing statistically equal to zero while in indices deciles merely partial autocorrelation is statistically zero in the last two slowdowns. This grounds is being enhanced by the Lhung-Box trial consequences show grounds of consecutive correlativity in all series of our sample. Thus the Weak signifier efficiency market hypothesis is being rejected in this sample.
Table IV
Autocorrelation and Partial Autocorrelation Trials for the Absolute Value of the Log Returns
This tabular array demo the autocorrelation and the partial autocorrelation coefficients up to 10 slowdowns for the log-returns of each stock and each decile index. AC stands for autocorrelation. PAC stands for partial autocorrelation. MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Panel A: Consequences for Daily Absolute Value of Log -Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
Actinium
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.162
0.162
26.512
0.315
0.315
100.31
0.115
0.115
0.6602
0.304
0.304
93.342
0.236
0.236
2
0.19
0.168
62.829
0.339
0.266
216.29
0.033
0.02
0.716
0.31
0.239
190.29
0.36
0.322
3
0.2
0.156
103.5
0.267
0.126
288.54
0.316
0.314
5.9393
0.28
0.159
269.76
0.286
0.18
4
0.184
0.118
137.76
0.277
0.127
366.5
-0.075
-0.162
6.2404
0.226
0.073
321.48
0.329
0.185
5
0.191
0.112
174.76
0.272
0.113
441.36
0.022
0.054
6.2658
0.267
0.128
393.63
0.404
0.267
6
0.185
0.094
209.4
0.329
0.171
551.16
0.271
0.185
10.401
0.274
0.124
469.71
0.354
0.178
7
0.16
0.059
235.48
0.304
0.113
645.13
-0.113
-0.126
11.133
0.237
0.06
526.85
0.387
0.181
8
0.194
0.093
273.9
0.261
0.037
714.55
-0.084
-0.096
11.553
0.237
0.057
584.2
0.29
0.051
9
0.178
0.069
306.03
0.292
0.092
801.48
0.181
0.105
13.547
0.217
0.038
632.03
0.317
0.043
10
0.184
0.072
340.71
0.237
0.018
858.91
-0.109
-0.042
14.284
0.249
0.085
695.11
0.306
0.029
Panel Bacillus: Consequences for Monthly Absolute Value of Log -Returns
ANF
Myocardial infarction
NLY
D1
D10
Slowdown.
Actinium
Political action committee
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
Q Stat.
ACF
PACF
1
0.489
0.489
11.966
-0.017
-0.017
0.0142
0.115
0.115
0.6602
0.552
0.552
15.262
0.194
0.194
2
0.447
0.274
22.212
-0.026
-0.026
0.0482
0.033
0.02
0.716
0.379
0.106
22.604
-0.009
-0.049
3
0.316
0.033
27.442
-0.051
-0.052
0.183
0.316
0.314
5.9393
0.375
0.188
29.959
0.09
0.106
4
0.284
0.059
31.773
0.03
0.027
0.2306
-0.075
-0.162
6.2404
0.446
0.241
40.624
0.326
0.302
5
0.059
-0.217
31.961
0.014
0.013
0.2418
0.022
0.054
6.2658
0.287
-0.11
45.142
0.123
0.013
6
0.011
-0.083
31.968
-0.045
-0.046
0.3552
0.271
0.185
10.401
0.313
0.158
50.633
0.1
0.106
7
0.043
0.119
32.074
0.167
0.17
1.9597
-0.113
-0.126
11.133
0.263
-0.05
54.617
-0.057
-0.147
8
-0.125
-0.187
33.003
-0.081
-0.081
2.3451
-0.084
-0.096
11.553
0.11
-0.214
55.33
-0.15
-0.253
9
-0.166
-0.08
34.672
0.11
0.117
3.0744
0.181
0.105
13.547
-0.094
-0.263
55.86
-0.003
-0.002
10
-0.193
-0.041
36.994
-0.105
-0.096
3.7649
-0.109
-0.042
14.284
0.038
0.105
55.951
-0.041
-0.144
Table Volt
Correlation Matrix Table
The tabular array shows the correlativity between assets for a four twelvemonth period ( 1st January 2007 to 31st December 2010 ) . MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Panel A: Consequences for Daily Log Returns
ANF
Myocardial infarction
NLY
DC10
ANF
1
Myocardial infarction
0.394939
1
NLY
0.400766
0.478346
1
DC10
0.631216
0.621608
0.584086
1
DC1
0.382347
0.399492
0.218922
0.585987
Panel Bacillus: Consequences for Monthly Log Returns
ANF
NLY
Myocardial infarction
DC1
ANF
1
NLY
0.187049
1
Myocardial infarction
0.330498
0.12031
1
DC1
0.457612
0.203086
0.243027
1
DC10
0.700746
0.2563
0.465772
0.741112
The correlativity between the assets indicates a positive, semi-strong correlativity among them. The correlativity coefficients are changing between 0.35 and 0.67 with N/A/M 1 and N/A/M 1 holding the strongest dependance in their returns and ASX and RHT the weakest. In general assets returns bend to travel towards the same way as in the instance of stocks they all belong in the same sector and are being affected from the motions of the market which are being captured by the indices deciles.
Table Six
Day- of- the hebdomad Arrested development
The tabular array shows the twenty-four hours of the hebdomad arrested development consequences of the day-to-day logarithmic returns for a four Year period ( 1st January 2007 to 31st December 2010 ) . MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
ANF
Myocardial infarction
NLY
D1
D10
A
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Prob.
Coefficient
Monday
-0.002027
0.3673
-0.007186
0.0885
-0.001404
0.4865
-0.000137
0.873
-0.000495
0.002248
0.004214
0.002017
0.000858
0.001431
Tuesday
0.000323
0.8751
-0.001972
0.6272
0.003621
0.1294
0.00003780
0.9601
0.00059
0.002052
0.004058
0.002386
0.000755
0.001255
Wednesday
0.001039
0.5956
-0.000902
0.7852
-0.002854
0.1235
0.000537
0.4499
0.000269
0.001958
0.003309
0.001851
0.000711
0.001204
Thursday
0.001309
0.6418
-0.003096
0.4341
-0.001788
0.4921
0.000146
0.8594
-0.000272
0.002814
0.003957
0.002602
0.000825
0.001184
Friday
-0.001848
0.4339
0.003215
0.3895
0.003612
0.0379
0.001448
0.0392
-0.00014
0.002361
0.003734
0.001738
0.000701
0.000943
Roentgen Squared
0.001875
0.003628
0.008565
0.002761
0.000509
Adjusted R Squared
-0.00211
-0.00035
0.004608
-0.00122
-0.003481
Table Six
The Results of the Variance Ratio Test ( excepting outliers )
The tabular array shows the Variance ratio trial consequences of the day-to-day logarithmic returns for a four Year period ( 1st January 2007 to 31st December 2010 ) . MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Panel A: Consequences for day-to-day Log – Tax returns
Number of Observations
Slowdown Orders
A
2
4
8
16
ANF
1006
0.5291
0.2644
0.1267
0.0649
-14.937
0
-12.4718
0
-9.3643
0
-6.7379
-8.4812
0
-7.5364
0
-6.0992
0
-4.5901
Myocardial infarction
1006
0.4996
0.2371
0.1181
0.0627
-15.8724
0
-12.9337
0
-9.4562
0
-6.7536
-7.0907
0
-6.1388
0
-4.9198
0
-3.8135
NLY
1006
0.415
0.2103
0.0987
0.0506
-18.5536
0
-13.3889
0
-9.6638
0
-6.8408
-6.2083
0
-5.1192
0
-4.2436
0.00002
-3.2924
D1
1006
0.5386
0.3053
0.1763
0.0849
-14.6347
0
-11.7781
0
-8.8322
0
-6.5936
-9.0642
0
-7.6095
0
-5.9124
0
-4.5532
D10
1006
0.493
0.2338
0.112
0.0526
-16.0795
0
-12.9908
0
-9.5215
0
-6.8268
A
-7.6834
0
-6.5415
0
-5.0433
0
-3.6543
Table Seven
The Results of the Variance Ratio Test
The tabular array shows the Variance ratio trial consequences of the day-to-day logarithmic returns for a four Year period ( 1st January 2007 to 31st December 2010 ) . MI-MARSHALL & A ; ILSLEY CORP. ANF- ABERCROMBIE & A ; FITCH CO. NLY- ANNALY CAPITAL MANAGEMENT INC DC1 NYSE / AMEX / NASDAQ Decile1. DC10 – NYSE / AMEX / NASDAQ Decile10
Number of Observations
Slowdown Orders
2
4
8
16
ANF
956
1.3652
1.9168
3.1072
5.0306
11.2906
0
15.1519
0
22.026
0
28.3123
4.591
0
6.6971
0
10.0172
0
12.4287
Myocardial infarction
956
1.302
1.8725
2.7829
4.2356
9.3372
0
14.4203
0
18.6358
0
22.7283
3.713
0.0002
5.2844
0
7.1512
0
9.3274
NLY
956
1.3616
1.9955
2.9451
4.8223
11.1797
0
16.4532
0
20.3315
0
26.8491
4.8072
0
7.2772
0
9.3297
0
12.2183
D1
956
1.3579
1.9185
2.6447
4.3758
11.0663
0
15.1796
0
17.1915
0
23.7132
3.1444
0.00166
4.3912
0.00001
5.4345
0
8.7244
D10
956
1.4544
2.1468
3.1658
5.1018
14.0512
0
18.9527
0
22.6387
0
28.8128
5.1171
0
6.8725
0
8.886
0
12.1863
Table Eight
The Table of the Garch theoretical account
A
Myocardial infarction
ANF
NLY
D1
D10
I?1
-0.001592
-0.000616
0.00424
0.000118
0.000599
0.002498
0.5239
0.001482
0.6775
0.001242
0.0006
0.000563
0.8337
0.000808
I?2
0.002670
-0.000085
-0.00481
-0.00053
-0.00066
0.002662
0.3158
0.002339
0.971
0.001664
0.0038
0.000807
0.5087
0.001228
I?3
-0.001734
0.002536
-0.00255
0.000914
0.001127
0.003114
0.5777
0.00199
0.2024
0.001491
0.0876
0.000609
0.1338
0.001184
I?4
0.000127
0.005807
-0.0058
-0.00019
-0.00073
0.003317
0.9695
0.002759
0.0353
0.001988
0.0035
0.000749
0.7999
0.001114
I?5
0.002220
-0.001027
-0.00335
0.001329
-0.00037
0.003169
0.4836
0.002365
0.6643
0.001498
0.0251
0.000739
0.072
0.0011
I?1
0.000880
-0.000098
0.000029
0.000039
0.000066
0.000012
0
0.000051
0.0558
0.000024
0.2184
0.000002
0
0.000003
I?2
-0.001098
0.000140
0.000134
-0.000043
-0.000068
0.000083
0
0.000068
0.0398
0.000070
0.0541
0.000008
0
0.000032
I?3
-0.000872
0.000034
-0.000121
-0.000049
-0.000096
0.000018
0
0.000124
0.783
0.000056
0.0312
0.000007
0
0.000020
I?4
-0.000850
0.000417
0.000047
-0.000031
-0.000056
0.000067
0
0.000131
0.0015
0.000046
0.3098
0.000005
0
0.000009
I?5
-0.000803
-0.000085
-0.000104
-0.000038
-0.000063
0.000102
0
0.000118
0.4704
0.000038
0.0067
0.000005
0
0.000011
I±1
0.294763
0.049335
0.241057
0.247822
0.118943
0.091634
0.0013
0.012352
0.0001
0.086798
0.0055
0.051893
0
0.025517
I?1
0.718643
0.946772
0.760615
0.698386
0.844913
0.064228
0
0.012854
0
0.062008
0
0.047951
0
0.030823
Table Nine
Table of the Egarch Model
A
Myocardial infarction
ANF
NLY
D1
D10
I?1
-0.00061
-0.00106
0.002278
0.000184
0.000713
0.001618
0.7054
0.001487
0.4779
0.001125
0.0428
0.000566
0.7449
0.000797
I?2
0.000829
0.000481
-0.00296
-0.00075
-0.00175
0.003325
0.803
0.002222
0.8287
0.002021
0.1428
0.000717
0.2988
0.001178
I?3
-0.00087
0.00233
-0.00236
0.000629
0.000843
0.002202
0.6939
0.001992
0.2422
0.00155
0.1282
0.000715
0.3787
0.001039
I?4
-0.00179
0.005382
-0.00521
-0.00049
-0.00074
0.002463
0.4685
0.002437
0.0272
0.001864
0.0052
0.000665
0.4635
0.001082
I?5
-0.00104
0.000449
-0.00121
0.001284
-0.00074
0.002311
0.6543
0.002299
0.8451
0.00146
0.4067
0.000748
0.0861
0.001057
w1
-0.45491
-0.10447
-0.64022
-0.42291
-0.30839
0.255134
0.0746
0.099794
0.2952
0.297218
0.0312
0.121026
0.0005
0.094188
w2
0.316505
0.002048
0.414284
0.368262
0.099563
0.102343
0.002
0.013394
0.8785
0.079915
0
0.038549
0
0.024333
w3
-0.06217
-0.07096
-0.08823
-0.01211
-0.15092
0.049522
0.2093
0.010691
0
0.065372
0.1771
0.01609
0.4517
0.01976
w4
0.979579
0.999218
0.959608
0.964866
0.980731
0.010713
0
0.001409
0
0.018725
0
0.008323
0
0.00376
w5
0.38086
-0.00614
0.673158
-0.19826
0.346997
0.224362
0.0896
0.187484
0.9739
0.354439
0.0575
0.155508
0.2023
0.162194
I±
-0.17668
0.049627
-0.63799
-0.36042
-0.28028
0.252313
0.4838
0.165931
0.7649
0.21631
0.0032
0.134325
0.0073
0.166646
I?
0.098961
0.46383
0.515914
-0.14214
0.251806
0.22034
0.6533
0.12404
0.0002
0.315153
0.1016
0.1345
0.2906
0.137409
I?
0.1827
-0.03576
-0.44443
-0.22915
-0.00772
0.402244
0.6497
0.173104
0.8364
0.289316
0.1245
0.146435
0.1176
0.141933
Section IV RESULTS
AUTOCORRELATION TESTS
A.1 TESTS FOR LOG-RETURNS
Table III presents the autocorrelation analysis consequences for logarithmic returns for 3 stocks and 2 decile indices. We have selected 10 slowdowns for the AC and the PAC. From the consequences we can detect that autocorrelation is in the first slowdown for NLY, DC1 and DC10, in the 3rd slowdown of ANF and in the 6th and 10th slowdowns for MI. We can detect similar consequences for partial autocorrelation trial. Overall we can reason that Weak signifier efficiency is being rejected for all the information we have.
A.2 TESTS FOR SQUARED LOG-RETURNS
Table VI presents the consequences of the autocorrelation analysis of squared log returns.
