BST956 Quantitative Methods in Finance: Regression and Econometrics

This report delves into quantitative methods used in finance, addressing key concepts such as multicollinearity in regression models and methods for mitigating its effects. It explains the purpose and application of dummy variables in regression analysis, interpreting results related to height, weight, and gender. The report also discusses autocorrelation, its causes, and the implications for Ordinary Least Squares (OLS) estimators, including a review of the Durbin-Watson test and its limitations. Furthermore, it contrasts fixed effect and random effect models, highlighting their differences in handling individual-specific effects and the nature of their inferences. Desklib offers a platform for students to access similar solved assignments and study resources to enhance their understanding of complex topics.

BST956 Quantitative
Methods in Finance

TABLE OF CONTENTS
QUESTION 1...................................................................................................................................3
Explaining the model suffering from multicollinearity problem and fixing it............................3
QUESTION 3...................................................................................................................................4
A. Dummy variable and its purpose............................................................................................4
B. Kind of test being conducted..................................................................................................5
C. Interpreting the results............................................................................................................5
QUESTION 4...................................................................................................................................5
A. Meaning and causes of autocorrelation and problem of presence in OLS estimator.............5
B. Durbin Watson test and its drawbacks...................................................................................6
QUESTION 5...................................................................................................................................6
REFERENCES................................................................................................................................8

QUESTION 1
Explaining the model suffering from multicollinearity problem and fixing it
The multicollinearity problem is the one which occurs in case independent variable is
highly correlated with one or more independent variables. This occurs in case of multiple
regression and this includes the occurrence of high inter- correlation among two or more
independent variables. This multicollinearity involve the wider confidence intervals and this
produces less reliable probabilities with respect to the independent variable within the model
(Daoud 2017). This is problem because of the reason that there are many different independent
factors and it takes a lot of time in analysing that which factor has caused what kind of change
within the dependent factor. Hence, the present case of the demand function as well there is a
problem of multicollinearity. The reason pertaining to the fact is that in case there are different
independent factor like new car consumer price, consumer price index, personal disposable
income, interest rate and employed civilian labour force. All these factors are independent and
the demand of passenger car is dependent on all these factors.
In the present case of demand of car as there are large number of independent factor so
all these actor creates different impact over the working of the dependent factor. There are many
different factors which even causes negative impact over the working and demand of the
passenger car. This simply implies that the working of the dependent factor that is demand of
car, it will be affected by the independent variables in different manner. The reason underlying
this fact is that all these factors affect the dependent variable to different extent and as a result of
this the working of the demand is affected in both negative and positive manner. For instance, in
the present demand function it can be seen that consumer price index is negatively correlated
with the dependent factor that is demand of the car. As per the views of Shrestha (2020) the
consumer price index is being defined as the average changes in prices which the consumer pays
for the goods and services for a particularly period of time. This is being negatively related with
the dependent factor of demand because in case the prices paid by the consumer is increasing
then as a result of this the demand will reduce. The reason pertaining to the fact is that in case the
prices will be high then the consumer will not be willing to pay more and they will tend to think
that when prices will fall then they will purchase it.

Moreover, another independent variable that is personal disposable income increases then
this will create a positive impact over the demand of the car. The reason pertaining to the fact is
that when the income of the consumer is increasing then they will wish to buy premium and
luxury items and product. Hence, as a result of this, the demand of passenger car will increase
and due to this, it is positively corrected with the demand of car that is dependent factor. Thus,
with this evaluation it can be stated that the model of regression faces the problem of
multicollinearity.
Thus, there is requirement of fixing the problem of multicollinearity so that the regression
model is free from any of the problem. Hence, in case of fixing the problem it is necessary to
remove some of the highly correlated independent variables from the regression model. This is
particularly because of the reason that multicollinearity affects the specific independent variable
which are highly correlated with the dependent variable (Roozbeh, Babaie-Kafaki and Sadigh,
2018). In addition to this, another way through which the problem of multicollinearity can be
fixed is to undertake the use of the partial least square regression PLS or the principal component
analysis. This is particularly because of the reason that these regression methods will result in
cutting the number of predictors within the smaller set of uncorrelated components.
QUESTION 3
A. Dummy variable and its purpose
The dummy variable is a type of numerical variable which is being used in the regression
analysis. This variable is being used for representing the subgroups of the sample involved
within the study. this dummy variable is a kind of numeric variable which represent the
categorical data which can be anything like age, gender, height, weight and any other variable.
The purpose of using the dummy variable within the regression equation is that this assist the
person in using the single regression equation for representing the multiple groups. In addition to
this the dummy variable are dichotomous and the range of value is small and also they can only
take the two quantitative values (Canela, Alegre and Ibarra, 2019). Moreover, the use of dummy
variable is being undertaken for the reason that this provides a single way of using the
categorical predictor variable. Also, the suitability of dummy variable is to analyse the regression
equation in case when one or more independent variable present are categorical.

B. Kind of test being conducted
In the present case the test which is being conducted is the regression analysis. The
regression analysis is the one which assist in analysing and evaluating the impact of one variable
over the other. This simply means that the regression analysis assists in identifying the relation
being present within the two variables that is one dependent and another independent (Mummolo
and Peterson, 2018). This method is also used as it also outlines that trend being present within
the data and how it can be used in making decision for the betterment of the concept and variable
being tested.
C. Interpreting the results
With the analysis of the regression table it is clear that the result of height and male is
correlated with the weight. This simply implies that the height coefficient implies that there is
4.006 correlation being present in height and weight. This simply means that the changes within
the height will bring some change within the weight of the person as well. Moreover, the
coefficient of male that is 13.76 implies that any change within the males will cause a 13.76
times of change within the females. Thus, this simply means that both the male and females are
being correlated with one another and this will result in change in one factor due to change in
another factor.
QUESTION 4
A. Meaning and causes of autocorrelation and problem of presence in OLS estimator
The autocorrelation is a characteristic of data which outlines the degree of similarity
within the time series and the lagged version of same data over a successive period of time. This
measures the relation presents between the current value of the variable and the past value of the
same variable. The major cause of autocorrelation is that the it occurs in case the observation are
dependent on the aspect other than time. In addition to this, another reason for the occurrence of
autocorrelation is that is occurs in cross- sectional data (Moore and et.al., 2018). This simply
means that in case when the observations are being related to other in the same manner. For
example, in a survey people may expect respondent to be from the nearby geographic region
only. Another example can be that the survey being conducted within the college may assumed
that all the student might be belonging to the same class.

In addition to this, the OLS estimator involves the inefficient and will not be longer blue
in case of autocorrelation. Moreover, the autocorrelation causes the problem in case of
conventional analysis which assumed that independence of observation. In case of regression, the
autocorrelation relating to the regression residuals can also occur in case the model is incorrectly
specified. Moreover, the another problem which the being identified due to autocorrelation is
that the errors are serially dependent and this is due to the autocorrelation (Teng and et.al., 2018).
Hence, this will be impacting the working of the regression model in negative manner.
Moreover, the autocorrelation also causes the problem that there is also a problem of the missing
variable and this will also be missed in case of the autocorrelation.
B. Durbin Watson test and its drawbacks
The Durbin Watson test is the test conducted for the autocorrelation within the residual
from the statistical model or the regression analysis. This statistic test is always range from the
value of 0 to 4. Moreover, the value of 2 implies that there is no any autocorrelation being
present within the sample. In addition to this, the test is implemented for the detecting the
presence of the autocorrelation at the lag 1 within the prediction errors coming from the
regression analysis.
Along with this there are some limitations as well for this test which can restrict the
working to a great extent. the major limitation of the Durbin Watson is that the statistics is not an
appropriate measure for autocorrelation (Mahaboob and et,.al., 2019). Moreover, this is also an
inappropriate tool for testing the higher order serial correlation or for the other forms of
autocorrelation only. Moreover, another limitation of using this method is that this test is
inconclusive if computed values remain between d1 and du.
This test is not considered as an appropriate measure for autocorrelation. This test
contains its own limitation which does not allow the scholar to derive the best possible results
outcome. This test is completely considered an inappropriate for testing the higher order serial
correlation. Any form of correlation this test completely found as void.
QUESTION 5
The fixed effect model considers or assumes that the individual specific effect is
correlated to the independent variables. On the other hand random effect model allows making
inferences on the population data based on the assumption of normal distribution. The fixed

effect variable demonstrate the fact that explanatory variable contain the fixed nature or effect
with the response variable across all the observations. The fixed effect model is more specific
and confined whereas the random effect model is not considered as majorly precise by nature.
From the static point of view fixed effect model derive better and clearer results out of the entire
interpretation whereas, random effect model derive results out of random interpretation in
respect to data and the information (Park and Beretvas, 2019). The fixed effect provides the clear
outcome in against to interpreting information and data. Statistics point of view is more
comprehensive and clear if the data collected with certain and right or authentic sources. In case
of random effect model data is also collected with some random source that may or may not
derive the complete information about the topic of study. The fixed effect model provides the
fixed direction to the study is conducted and on the others side random effect model do not
provide the clear and certain direction.
Fixed effect model contain its own nature that is fixed. This would go by the fixed pattern
that will only bring the standard results or near possible to such standard results. The other side
random effect model provides the unexpected results. As this model do not go with the fixed
nature or pattern that do not further support with the fixed sense of results. This nature of random
model to be able to generate unexpected results makes it more conventional than the other
category of techniques or model. This technique is capable enough to derive better outcome and
results (Stoffel, Nakagawa and Schielzeth, 2017). The key difference between the fixed effect
model and the random effect model is such that in case of fixed effect technique certain
boundaries are already set and entire interpretation and study will go around such a set pattern. In
case of random effect there is not any fixed nature of boundary or pattern that is set. So the
capability to generate the new ideologies is more in context to the random effect technique in
comparison to the fixed effect technique or model. In the practical situation the random effect
model is more favourable as it do not require any extra attention to implement rather it is more
casual in nature. The other side fixed effect is more like congested in nature to implement. The
role of the random effect model is more comprehensive in comparison to the fixed effect model.
Te term fixed effect itself demonstrate about the fact that it must have been following the fixed
nature or pattern that would derive the set or fixed length of results. The random effect is mostly
used by the scholar as it can be used in any given situation or mode. The use of the technique
become important for the scholar and in case of the random effect model there is not such fixed

technique or process that is identified which make the technique more simple and easy to use and
adopt.

REFERENCES
Books and Journals
Canela, M.Á., Alegre, I. and Ibarra, A., 2019. Dummy variables. In Quantitative Methods for
Management (pp. 57-63). Springer, Cham.
Daoud, J.I., 2017, December. Multicollinearity and regression analysis. In Journal of Physics:
Conference Series (Vol. 949, No. 1, p. 012009). IOP Publishing.
Mahaboob, B., and et,.al., 2019, December. On misspecification tests for stochastic linear
regression model. In AIP Conference Proceedings (Vol. 2177, No. 1, p. 020039). AIP
Publishing LLC.
Moore, T.E., and et.al., 2018. Spatial autocorrelation inflates niche breadth–range size
relationships. Global Ecology and Biogeography. 27(12). pp.1426-1436.
Mummolo, J. and Peterson, E., 2018. Improving the interpretation of fixed effects regression
results. Political Science Research and Methods. 6(4). pp.829-835.
Park, S. and Beretvas, S. N., 2019. The multivariate multiple-membership random-effect model:
An introduction and evaluation. Behavior research methods. pp.1-17.
Roozbeh, M., Babaie-Kafaki, S. and Sadigh, A.N., 2018. A heuristic approach to combat
multicollinearity in least trimmed squares regression analysis. Applied Mathematical
Modelling. 57. pp.105-120.
Shrestha, N., 2020. Detecting multicollinearity in regression analysis. American Journal of
Applied Mathematics and Statistics. 8(2). pp.39-42.
Stoffel, M. A., Nakagawa, S. and Schielzeth, H., 2017. rptR: Repeatability estimation and
variance decomposition by generalized linear mixed‐effects models. Methods in Ecology
and Evolution. 8(11). pp.1639-1644.
Teng, S.N., and et.al., 2018. Effects of intrinsic sources of spatial autocorrelation on spatial
regression modelling. Methods in Ecology and Evolution. 9(2). pp.363-372.