Quantitive methods in Finance Flashcards
What is DGP?
In regression analysis, the data generating process (DGP) refers to the actual process that generates the data observed in the real world. It encompasses all the factors and variables that influence the outcome being studied. On the other hand, a model in regression analysis is a simplified representation of the DGP, often expressed as an equation or set of equations that attempt to capture the relationships between the variables of interest.
Can you explain the Ordinary Least squares?
OLS is a method used in econometrics and statistics to estimate the unknown parameters in a linear regression model. The goal of OLS is to find the best-fitting line through a set of data points by minimizing the sum of the squared differences between the observed values and the values predicted by the linear model.
What is the Properties of OLS?
The OLS estimator provides estimates for the parameters of the linear regression model, including the intercept and slopes for the independent variables. These estimates are chosen to minimize the sum of the squared differences between the observed values and the values predicted by the linear model. When the OLS assumptions are met, the OLS estimator is unbiased, consistent, and efficient, making it a widely used and valuable tool for estimating linear regression models.
What is the assumptions of OLS?
The OLS assumptions include linearity, independence, homoscedasticity, and normality. Linearity assumes that the relationship between the dependent variable and the independent variables is linear. Independence assumes that the errors are not correlated with each other or with the independent variables. Homoscedasticity assumes that the variance of the errors is constant across all values of the independent variables. Normality assumes that the errors are normally distributed.
Tell me about The variance of OLS Estimates
The variance of the OLS Estimates is a measure of how much the estimates of the coefficients in a linear regression model are expected to vary from sample to sample. It provides insights into the precision and reliability of the OLS estimators. Let’s break down the key concepts
- The square root of the variance of an OLS estimate is called the standard error
- Confidence intervals and hypothesis tests use standard errors to make inferences about the population parameters.
Can you name and describe the Regression outputs?
- Estimate: The estimate is the coefficient value estimated by the regression model. It represents the expected change in the dependent variable for a one-unit increase in the corresponding independent variable, holding all other variables constant.
- Standard Error: The standard error is a measure of the precision of the estimated coefficient. It represents the standard deviation of the sampling distribution of the coefficient estimate.
- T-value: The T-value is the ratio of the estimated coefficient to its standard error. It measures the number of standard errors that the estimated coefficient is away from zero.
- P-value (PR(>t)): The p-value (PR(>t)) is the probability of obtaining a T-value as extreme or more extreme than the observed T-value, assuming the null hypothesis that the coefficient is equal to zero.
Can you Name the Performance metrics of the Linear Regression (OLS)
- Degrees of Freedom (df): Degrees of freedom refer to the number of independent observations in the data set that are available to estimate the parameters of the model.
- Residual Standard Error (RSE): The residual standard error is a measure of the average deviation of the observed values from the predicted values of the dependent variable.
- F-Statistics: The F-statistic is a measure of the overall significance of the regression model. It is calculated as the ratio of the explained variance to the unexplained variance and is used to test the null hypothesis that all of the regression coefficients are equal to zero.
- R-Squared (R2): R-squared is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variables in the model.
- Adjusted R-Squared: The adjusted R-squared is a modified version of the R-squared that considers the number of independent variables in the model.
- Standard Error of the Coefficients: The standard error of the coefficients is a measure of the precision of the estimated regression coefficients.
Can you Explain Hyphothesis testing, T-test and F-test?
- Formulation of Hypotheses: In hypothesis testing, the first step is to formulate the null hypothesis (H0) and the alternative hypothesis (H1). In the context of regression analysis, the null hypothesis typically involves statements about the population parameters, such as the absence of a relationship between a specific independent variable and the dependent variable, or the overall model’s lack of explanatory power. The alternative hypothesis represents the opposite of the null hypothesis and is what the researcher aims to provide evidence for.
T-Test: The T-test is used to assess the significance of individual coefficients in a regression model. The null hypothesis for a T-test typically states that a particular coefficient is equal to zero, indicating that the corresponding independent variable has no effect on the dependent variable.
F-Test: The F-test is used to assess the overall significance of a regression model. The null hypothesis for an F-test typically states that all of the coefficients in the model are equal to zero, indicating that none of the independent variables have an effect on the dependent variable.
What is Heteroscedasticity?
Can you explain the White test?
Can you explain the White Correction (HC)?
What is Autocorrelation?
Can you explain the Breusch-Godfrey test?
Can you explain the HAC Correction?
What is Skewness and Kurtosis?
