1. Ordinary least Squares

2. Introduction Describe the nature of financial data.
Assess the concepts underlying regressions analysis
Describe some examples of financial models.
Examine the Ordinary least Squares (OLS) technique and hypothesis testing

3. Financial data
The data can be high frequency, i.e. daily or even every minute.
i.e. Stock market prices are measured every time there is a trade or somebody posts a new quote.
The data is usually good quality
Recorded asset prices are usually those at which the transaction took place. Little possibility for measurement error.

4. Financial Data Financial Data is affected by risk.
Most financial data is affected by not just return but also risk, which requires specialist modelling.
Financial data is ‘noisy’
It is often difficult to pick up patterns in the data due to the variable nature of financial data.

5. Time Series data
Examples of Problems that Could be Tackled Using a Time Series Regression
- How the value of a country’s stock index has varied with that country’s macroeconomic fundamentals.
- How the value of a company’s stock price has varied when it announced the value of its dividend payment.
- The effect on a country’s currency of an increase in its interest rate

6. Cross-Sectional data
Cross-sectional data are data on one or more variables collected at a single point in time, e.g.
- A poll of usage of internet stock broking services
- Cross-section of stock returns on the New York Stock Exchange
- A sample of bond credit ratings for UK banks

7. Model Estimation Economic or Financial Theory (Previous Studies)
Formulation of an Estimable Theoretical Model
Collection of Data
Model Estimation
Is the Model Statistically Adequate?
No Yes
Reformulate Model Interpret Model
Use for Analysis

8. Financial Data MI i 18 3 21 4 20 23 25 6 27 26 28 5 30 32

9. Regression

10. Econometric Model

11. Estimates

12. The Residual Term (Also called the error term and disturbance term)
It describes the random component of the regression. It is caused by:
- Omission of explanatory variables
- The aggregation of the variables
- Mis-specification of the model
- Incorrect functional form of the model
- Measurement error

13. Least Squares Approach
The aim of this approach is to minimize the residual for all residuals
We square the residual before minimizing
We can then derive our intercept and slope parameter using basic calculus

14. Regression
Regression is the degree of dependency of the dependent variable on the explanatory variables
Correlation measures the strength of a linear association between two variables
Causation suggests the dependent variable depends on previous values of the explanatory variable
Regression does not imply causaltion

15. R-Squared Statistic
This statistic explains the proportion of total variation in the dependent variable which is explained by the regression
The statistic explains the explanatory power of the regression and measures how good a fit the data is.
The value of this statistic lies between 0 and 1(when all the scatter plots lie on the regression line.)

16. Interpretation of Results
Consider the type of model being estimated
What are the units of measurement of the variables (unless all the variables are in logarithmic form)
The range of observations
The signs of the variables, does it accord with the theoretical model
Are the magnitudes of the parameters plausible
We need to remember it is only a model, the parameters are estimates, so it describes average values, individual cases may vary

17. Significance Testing

18. Hypotheses Test

19. Hypothesis Testing
Test the significance of the constant term in the same way as the slope parameter
Although the conventional test for significance is at the 5% level, we also test at the 1% and 10% levels
Use of the t-distribution tells us what to expect ‘by chance’
For finite samples, when applying the t-test, we need to allow for degrees of freedom
The t-test can be applied to either one or two tailed tests
The t-test is an absolute value, so we can ignore the sign

20. The T-test
If the t-test statistic exceeds the critical value, reject the null hypothesis, if we are testing if the coefficient equals zero, this means it is significant
If the test statistic is below the critical value accept the null hypothesis.
To find the critical value, you need to know the degrees of freedom, which equal n-k-1.

21. Conclusion
Financial data tends to be more plentiful and of better quality than other data.
Regression analysis involves fitting a line to a scatter diagram
The error term describes the random component of the regression
Ordinary Least Squares (OLS) involves minimizing the sum of the square of the residuals