2Introduction Describe the nature of financial data. Assess the concepts underlying regressions analysisDescribe some examples of financial models.Examine the Ordinary least Squares (OLS) technique and hypothesis testing
3Financial dataThe 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 qualityRecorded asset prices are usually those at which the transaction took place. Little possibility for measurement error.
4Financial 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.
5Time Series dataExamples 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
6Cross-Sectional dataCross-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
7Model Estimation Economic or Financial Theory (Previous Studies) Formulation of an Estimable Theoretical ModelCollection of DataModel EstimationIs the Model Statistically Adequate?No YesReformulate Model Interpret ModelUse for Analysis
12The 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
13Least Squares Approach The aim of this approach is to minimize the residual for all residualsWe square the residual before minimizingWe can then derive our intercept and slope parameter using basic calculus
14RegressionRegression is the degree of dependency of the dependent variable on the explanatory variablesCorrelation measures the strength of a linear association between two variablesCausation suggests the dependent variable depends on previous values of the explanatory variableRegression does not imply causaltion
15R-Squared StatisticThis statistic explains the proportion of total variation in the dependent variable which is explained by the regressionThe 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.)
16Interpretation of Results Consider the type of model being estimatedWhat are the units of measurement of the variables (unless all the variables are in logarithmic form)The range of observationsThe signs of the variables, does it accord with the theoretical modelAre the magnitudes of the parameters plausibleWe need to remember it is only a model, the parameters are estimates, so it describes average values, individual cases may vary
19Hypothesis TestingTest the significance of the constant term in the same way as the slope parameterAlthough the conventional test for significance is at the 5% level, we also test at the 1% and 10% levelsUse 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 freedomThe t-test can be applied to either one or two tailed testsThe t-test is an absolute value, so we can ignore the sign
20The T-testIf 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 significantIf 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.
21ConclusionFinancial data tends to be more plentiful and of better quality than other data.Regression analysis involves fitting a line to a scatter diagramThe error term describes the random component of the regressionOrdinary Least Squares (OLS) involves minimizing the sum of the square of the residuals