Microsoft Word - MBAF502_ProjectI II PROJECT II Course Name and Number: MBAF 502: Quantitative Reasoning & Analysis Project II: Regression Analyses and Forecasting Weight = 25% Due June 13, 2022, at...

Microsoft Word - MBAF502_ProjectI II
Explain Stationarity
Stationarity is the phenomenon when our time series data does not depend on time series. In the most natural sense, stationarity implies that the measurable properties of a cycle creating a period series don't change after some time. It doesn't imply that the series doesn't change after some time, simply that the manner in which it changes doesn't itself change over the long haul. The mathematical identical is in this way a direct capacity, maybe, and not a steady one; the worth of a straight capacity changes as ? develops, yet the manner in which it changes stays consistent — it has a steady slant; one worth that catches that pace of progress.
For what reason is this significant? In the first place, on the grounds that fixed cycles are more straightforward to dissect. Without a conventional definition for processes producing time series information (yet; they are called stochastic cycles and we will get to them in a second), it is now evident that fixed cycles are a sub-class of a more extensive group of potential models of the real world. This sub-class is a lot simpler to demonstrate and explore. The above casual definition additionally indicates that such cycles ought to be feasible to anticipate, as the manner in which they change is unsurprising.
The last explanation, consequently, for stationarity's significance is its omnipresence in time series examination, making the capacity to comprehend, identify and demonstrate it important for the utilization of numerous conspicuous apparatuses and methods in time series investigation. Without a doubt, for some cases including time series, you can find that you need to decide whether the information was created by a fixed cycle, and perhaps to change it so it has the properties of an example produced by such an interaction.
Data Noise:
Unit root test:
P value is greater than 0.05 which implies there is a stationarity in the data.
    Augmented Dickey-Fuller test for Close_intel
testing down from 6 lags, criterion AIC
sample size 504
unit-root null hypothesis: a = 1
test with constant
including 0 lags of (1-L)Close_intel
model: (1-L)y = b0 + (a-1)*y(-1) + e
estimated value of (a - 1): -0.0216778
test statistic: tau_c(1) = -2.27994
asymptotic p-value 0.1786
1st-order autoco
elation coeff. for e: -0.042
with constant and trend
including 0 lags of (1-L)Close_intel
model: (1-L)y = b0 + b1*t + (a-1)*y(-1) + e
estimated value of (a - 1): -0.0258278
test statistic: tau_ct(1) = -2.52172
asymptotic p-value 0.3175
1st-order autoco
elation coeff. for e: -0.041
Unit root test:
P value is greater than 0.05 which implies there is a stationarity in the data.
Augmented Dickey-Fuller test for Close_AMD
testing down from 64 lags, criterion AIC
sample size 504
unit-root null hypothesis: a = 1
test with constant
including 0 lags of (1-L)Close_AMD
model: (1-L)y = b0 + (a-1)*y(-1) + e
estimated value of (a - 1): -0.0118239
test statistic: tau_c(1) = -1.96841
asymptotic p-value 0.3011
1st-order autoco
elation coeff. for e: -0.056
with constant and trend
including 0 lags of (1-L)Close_AMD
model: (1-L)y = b0 + b1*t + (a-1)*y(-1) + e
estimated value of (a - 1): -0.0189328
test statistic: tau_ct(1) = -2.09058
asymptotic p-value 0.5505
1st-order autoco
elation coeff. for e: -0.
Histograms:
Forecasting: Using the linear trend equations for the factors under consideration to a
ive at and display estimates for future time periods
Model 6: ARMA, using observations 2020-05-18:2022-04-22 (T = 505)
Dependent variable: Close_intel
Standard e
ors based on Hessian
    
    Coefficient
    Std. E
o
    z
    p-value
    
    const
    53.1814
    2.38429
    22.30
    <0.0001
    ***
    phi_1
    0.980822
    0.00885941
    110.7
    <0.0001
    ***
    theta_1
    −0.0416817
    0.0445246
    −0.9361
    0.3492
    
    Mean dependent va
     53.39149
    
    S.D. dependent va
     5.531841
    Mean of innovations
    −0.024877
    
    S.D. of innovations
     1.175047
    R-squared
     0.954811
    
    Adjusted R-squared
     0.954721
    Log-likelihood
    −799.6189
    
    Akaike criterion
     1607.238
    Schwarz criterion
     1624.136
    
    Hannan-Quinn
     1613.866
    
    
    Real
    Imaginary
    Modulus
    Frequency
    AR
    
    
    
    
    
    
    Root 1
    1.0196
    0.0000
    1.0196
    0.0000
    MA
    
    
    
    
    
    
    Root 1
    23.9914
    0.0000
    23.9914
    0.0000
PART 2: Inferential Statistic- Regression Analyses
Here you will perform regression analyses and hypotheses testing.
Step 1. Identify the core research problems for analyses and propose the hypotheses that applies to the case under consideration. Notes For your analyses and report
We want to identify and estimate the relationship between intel close price and AMD close price over the period of two year. We have considered Intel Close price as dependent variable or response variable and AMD Close price as independent variable or explanatory variable. We have also considered year as explanatory variable. First, we have run co
elation analysis to identify the relationship between intel close price and AMD close price. We have evaluated hypothesis evaluate our assumptions.
Null Hypothesis: There is no association between intel close price and AMD close price.
Alternative Hypothesis: There is a association between intel close price and AMD close price.
As we can see from co
elation analysis output, p-value=0.0873 and at 10 percent significance level null hypothesis will be rejected and alternative hypothesis will be accepted. The co
elation coefficient between intel close price and AMD close price is negative and moderate, which implies increase in one will cause decrease in other. AMD close price has negative influence over the intel close price. Increase in intel price will cause decrease in AMD close price.
.
Co
elation coefficients, using the observations 2020-05-18 - 2022-04-22
5% critical value (two-tailed) = 0.0873 for n = 505
    Close_intel
    Close_AMD
    
    1.0000
    -0.4175
    Close_intel
    
    1.0000
    Close_AMD
    
    
    
We have plot scatter plot between Intel close price and AMD close price. The r square value is 0.1743 which implies 17.43 percent variability in Intel close price can explain with this model. We have negative beta coefficient of -0.0965, which implies increase in one dollar AMD price will cause 0.0965-dollar decrease in intel price. The intercept value is 62.534.
1.1 Regress the dependent variable on the set of independent variables
    SUMMARY OUTPUT
    
    
    
    
    
    
    
    
    
    
    
    
    
    Regression Statistics
    
    
    
    
    
    Multiple R
    0.423209919
    
    
    
    
    
    R Square
    0.179106635
    
    
    
    
    
    Adjusted R Square
    0.175836144
    
    
    
    
    
    Standard E
o
    5.021997045
    
    
    
    
    
    Observations
    505
    
    
    
    
    
    
    
    
    
    
    
    
    ANOVA
    
    
    
    
    
    
     
    df
    SS
    MS
    F
    Significance F
    
    Regression
    2
    2762.368117
    1381.184
    54.76444004
    3.06177E-22
    
    Residual
    502
    12660.66807
    25.22045
    
    
    
    Total
    504
    15423.03619
     
     
     
    
    
    
    
    
    
    
    
     
    Coefficients
    Standard E
o
    t Stat
    P-value
    Lower 95%
    Upper 95%
    Intercept
    -1269.977442
    778.2572579
    -1.63182
    0.103344069
    -2799.020134
    259.0652507
    Yea
    0.65987294
    0.385400407
    1.712175
    0.087481999
    -0.097323565
    1.417069445
    Close_AMD
    -0.107098227
    0.011216119
    -9.5486
    5.76771E-20
    -0.129134545
    -0.08506191
As we can see from regression output, F(2,502)=54.76 | P value
0.05. Hence our model is statistically significant to predict the intel close price. We have also added year as independent variable. At five percent significance level year is statistically insignificant P value > 0.05.
Hypothesis testing for predictors:
Null Hypothesis: Beta coefficient is not different from zero
Alternative hypothesis: Beta coefficient is different from zero.
The adjusted r square value is 0.1758 which implies 17.58 percent variability in Intel close price can explain with this model. We have negative beta coefficient of -0.1070, which implies increase in one dollar AMD price will cause 0.1070-dollar decrease in intel price. The intercept value is 1269.977.
Boxplot of intel close price shows, there is no outliers in intel close price. Outliers adversely affects the regression model performance.
.
Conclusion:
As we can see from co
elation analysis output, p-value=0.0873 and at 10 percent significance level null hypothesis will be rejected and alternative hypothesis will be accepted. If we lower the significance level then the variables are not significantly co
elated. Model significance and validity depends upon the defined significance level.
We have negative beta coefficient of -0.1070, which implies increase in one dollar AMD price will cause 0.1070-dollar decrease in intel price. The intercept value is 1269.977. There are no outliers in intel close price. Outliers adversely affects the regression model performance. We can collect more data to build more accurate model. Also there are many forecast model available for forecast.
Close_intel    y = -0.0965x + 62.534
R² =...