evandietrich / quant-finance-projects

Quantitative Finance & Statistics Projects. Topics including multiple linear regression, variance and instability estimates, display methodology.

market-analysis

• Variance & Measures of Dispersion
  Dispersion measures how spread out our dataset is. Variance and standard deviation tell us how volatile a quantity is, but do not differentiate between deviations upward and deviations downward. Although, we have addt'l tools for this.

• Simple Displays
  Representing data graphically to learn how data behaves and seeing potential structure or flaws. Plots are good to use when formulating a hypothesis, but should not be used to test a hypothesis.

• Statistical Moments
  How more moments than just mean and variance can be used to describe data. How to use a Jarque Bera test to check for normality. Whether or not returns are likely to follow a normal distribution.

• Linear Correlation Analysis
  The correlation coefficient measures the extent to which the relationship between two variables is linear. Its value is always between -1 and 1.

• Instability of Parameter Estimates
  Quantify the uncertainty in our estimates by looking at how the parameter changes as we look at different subsets of the data. By looking at how much this moving estimate fluctuates as we change our time window, we can compute the instability of the estimated parameter.

• Intro Linear Regression
  A technique that measures the relationship between two variables. If we have an independent variable X, and a dependent outcome variable Y, linear regression allows us to determine which linear model Y=α+βX best explains the data.

• Regression Model Instability
  Regression analysis allows us to estimate coefficients in a function which approximately relates multiple data sets. We hypothesize a specific form for this function and then find coefficients which fit the data well, working under the assumption that deviations from the model can be considered noise.

• Multiple Linear Regression
  Probably the single most used technique in modern quantitative finance. Multiple linear regression is just like single linear regression, except you can use many variables to predict one outcome and measure the relative contributions of each.

• Violations of Regression Models
  Assumptions of regression analysis must be satisfied to ensure good parameter estimates and accurate fit statistics. We would like parameters to be unbiased, consistent, and efficient. Here are some ways these assumptions can be violated and the effect on the parameters and fit statistics.