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Statistical Inference & Regression PDF

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Added on  2020-05-16

Statistical Inference & Regression PDF

   Added on 2020-05-16

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Statistical Inference & Regression Analysis
Report
On
Stock Analysis
(IBM Vs Boeing
using S & P 500)
1
Statistical Inference & Regression PDF_1
Abstract
This analysis is done to understand the various parameters before investing in
any stocks. The requirements for this analysis are done using Excel Data
Analysis. The data is used from yahoo for reading the historical data of stock
closing prices of Boeing & IBM, the standard index used as market portfolio and
the interest rate on 10-year US treasury bill used as an interest-free rate. This
study has used the concepts and models of statistical inference and financial
model.
Data Exploration: Close Prices of S & P, Boeing and IBM
Some features of the plot:
S & P: The series is showing an upward trend in the data. There is no
seasonality as the data are annual data. There are no outliers visible.
Boeing: The series is showing slight upward trend in the data with some
variation. There is no seasonality as the data are annual data. There are no
outliers visible
IBM: The series is showing a downward trend in the data. There is no seasonality
as the data are annual data. There are no outliers visible.
Return Analysis:
Returns
Summary S & P Boeing IBM
Mean 0.00045 0.00103
-
0.0000
6
Standard
Error 0.00021 0.00036
0.0003
1
Median 0.00035 0.00118
0.0000
0
Mode 0.00000
0.0000
0
Standard
Deviation 0.00781 0.01325
0.0114
9
Sample 0.00006 0.00018 0.0001
2
Statistical Inference & Regression PDF_2
Variance 3
Kurtosis 2.21387 5.37221
6.3001
8
Skewness -0.26270 -0.03995
-
0.9176
5
Range 0.07845 0.18808
0.1331
5
Minimum -0.03941 -0.08929
-
0.0827
9
Maximum 0.03903 0.09879
0.0503
6
Sum 0.62952 1.42389
-
0.0771
7
Count 1385 1385 1385
The data of 1385 observations are considered to analyse the adjusting returns.
The average returns of Boeing taken from this sample is 10% while the average
returns of IBM are -0.01%. The variation in the returns from the mean is about
13% in Boeing while its 11% in IBM. These statistics give an indication that
investing in Boeing will give better returns compared to investment done in IBM.
Higher returns are accompanied by higher risk. Investment is Boeing will be
riskier compared to IBM because the average return in Boeing is high when
compared with IBM. Risk shows the volatility of stocks compared to market and
here, Boeing is more volatile when compared to IBM.
Jarque-Bera test to check Normality distribution of returns of Boeing
and IBM:
This test is done to confirm normality in large dataset. The formula for the
Jarque-Bera test statistic is:
JB = n [(√b1)2 / 6 + (b2 – 3)2 / 24]
Where, n is the sample size
√b1 is the sample skewness coefficient
b2 is the kurtosis coefficient
Null Hypothesis: The data is normally distributed, skewness is zero and
excess kurtosis is zero.
Alternate Hypothesis: The data does not show normal distribution.
A normal distributed data will have a skew value of 0 and a kurtosis of 3. This
test can be compared with chi-square distribution with 2 degrees of freedom.
The null hypothesis of normality is rejected if the calculated test statistic will
exceed critical value from the chi-square distribution.
Level α
Critical Value
3
Statistical Inference & Regression PDF_3

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