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# Financial Modelling (Research Paper Sample)

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This is a term paper on financial modeling techniques. The first section elaborates on the “Least Squares method” as an optimal method for obtaining a best-fit line in multiple regression analysis with some of its benefits and limitations. Additionally, it delves into “confidence intervals,”; what they signify in modeling/simulation, and the underlying statistical rationale necessary for their justification. Plus, the paper briefly mentions the “significance level” in statistical hypothesis testing and alludes to the possible distortion caused by omitted variables in statistical modeling. Part two addresses the question of choosing between different regression models based on their information criteria, with the Bayesian Information Criteria (BIC) and Akaike Information Criteria (AIC) explained in more detail, along with requirements and caveats when comparing models based on these criteria. source..

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FINANCIAL MODELLING TECHNIQUES
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FINANCIAL MODELLING TECHNIQUES
This is a term paper. The answers provided are for two of the six questions that were provided.
1 Explain ALL of the following concepts.
* The least-squares principle;
One method of finding the line of best fit is by using the eye-fit method. This method has the disadvantage that two people can pick different lines. Also, the eye fit method can only be used for two variables. Therefore, there is a need for another mathematical method whereby everybody who uses the method correctly arrives at the same answer, which can be used for more than two variables.
The least-squares principle states that the line of best fit should be chosen in such a way that makes the sum of the squares of the deviations (errors) of the data points from the line in the vertical direction as minimum as possible (Stewart, R.M., 1913, 359). There are two reasons for using the squares of the deviations rather than the deviations themselves. The first reason is that squares are positive, thereby avoiding negative and positive errors canceling out. Secondly, squares give the larger errors a bigger weight in the total sum.
This method has advantages because it is straightforward to understand and can be applied easily. The limitations of the least squares principle are that the method may give unreliable results when data is not evenly distributed, and the method is sensitive to outliers.
* Confidence intervals;
A confidence interval is a range of values within which it is expected, with a quantifiable level of confidence, that a particular unknown value falls (Petty, M.D., 2012, 10). Confidence intervals are commonly used in modeling and simulation
as a quantitative validation method.
A single value estimate, such as the population mean, is known as a point estimate in a population. However, the point estimate may be different from the population parameter it estimates. An interval estimate is a range or interval of values in which the population parameter value is expected to be. It can not be said with absolute certainty that the population parameter value falls within the interval estimate because the population parameter value is unknown. Therefore, there should be a statistically justifiable level of confidence that the unknown population parameter value falls within the interval estimate. A confidence interval can, therefore, be defined as an interval estimate of an unknown population parameter value calculated from a sample of the same population for which there is a known and statistically justifiable confidence level that the unknown population parameter value falls within the interval estimate (Petty, M.D., 2012, 10). The confidence level must be statistically justifiable and is usually expressed as a percentage.
* Significance level in the statistical tests of hypothesis;
The p-value denotes the level of statistical significance. There are two types of hypotheses: null hypothesis (h0) and alternative hypothesis (ha). Significance testing starts with the null hypothesis because it is the control hypothesis. The null hypothesis may represent a theory being put forward, e.g., that the theory is true, or it may be in the form of a basis for an argument. The alternative hypothesis is an assertion of what a statistical hypothesis test is designed to prove. An example of a null hypothesis could be that a new drug has a different effect compared to the current drug, and the alternative hypothesis for that would be that a new drug does not have a different effect compared to the current drug. After the test, the conclusion is to reject the null hypothesis and accept the alternative hypothesis or not reject the null hypothesis (Dhinu, M.R., 2021, p.113).
The choice of whether to reject the null hypothesis and accept the alternative hypothesis or to not reject the null hypothesis is informed by the significance required. If the p-value is 0.03 and the required significance value is 0.05, the alternative hypothesis is accepted, whereas the null hypothesis is rejected. Should the p-value be greater than 0.05, the null hypothesis is not rejected, and the alternative hypothesis is accepted.
* Omitted variables bias.
Omitted variable bias is the error that occurs when a statistical model fails to include one or more relevant variables. It can also be defined as the difference between an estimator's expected value and the actual value of the underlying parameter. It results from failing to account for a pertinent explanatory variable or factors. This error cannot be solved by increasing the sample size or repeating the study several times (Busenbark, J.R. et al., 2022, 17).
2 Answer ALL parts of this question.
a) What are the main information criteria for the selection of a suitable regression
model?
The Bayesian information criterion (BIC) and the Akaike Information Criterion (AIC) are the main information criteria for selecting a suitable regression model.
The Bayesian information criterion (BIC) is one of the most well-known and frequently applied tools in statistical model selection. This information criteria for selecting a suitable regression model is popular because of its efficient performance in numerous modeling frameworks, including Bayesian applications where prior distributions may be tricky, and its computational simplicity. Schwarz created the Bayesian information criterion (BIC) as an asymptotic approximation to change a candidate model's Bayesian posterior probability (Neath, A.A. and Cavanaugh, J.E., 2012, 199).
The other main information criterion for selecting a suitable regression model is the Akaike Information Criterion (AIC). The Akaike Information Criterion (AIC) is a statistical tool used to analyze potential models and choose the one that provides the best fit for the data. This information criterion determines how many independent variables were used to create the mode and the model's maximum likelihood estimation (how well the model reproduces the data). According to the Akaike Information Criterion (AIC), the best fit is the model that explains the most variance with the fewest independent variables. However, the Akaike Information Criterion (AIC) cannot guarantee the quality of a model in contrast to other models because it is not founded on a hypothesis test. It will only show the model that fits the available data or observations somewhat better than the other models if all the models being evaluated fit poorly with respect to a specific set of data or observations (Profillidis, V.A. and Botzoris, G.N., 2019, 225).
b) What are the conditions which must be satisfied when using information criteria to compare alternative specifications?
The conditions which must be satisfied when using information criteria to compare alternative specifications are as follows:
* Parsimony
The parsimony principle dictates that one should select a model that is as simple as possible. This usually means the model with the fewest possible parameters will be selected. One must try to choose the most significant variables while being aware that many variables will affect the dependent variable. More parsimonious models are produced by placing limitations on the model's coefficients (Wooldridge, J.M., 2020).
* Identifiability
For a model to be identifiable, only one set of parameters should be consistent with a data set. In other words, parameter values must result in various probability distributions of the observable variables. It is pointless to try to estimate the parameters of an unidentifiable model (Wooldridge, J.M., 2020).
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