Essay About Statistical Models And Related Hypothesis Tests

Methods of Financial Data Analysis
Introduction Regression model is a statistical tool to analyse the relationship among variables.  In the last several decades, statistical models have been introduced and heavily used in the economic studies and financial market analyses. To explore this topic, this report is going to use a regression model to analyse the relationship between returns of an individual company () and the market returns (). Based on the Gauss-Markov assumptions, estimated parameters (beta) and related hypothesis tests will be used to explain the relationship between the movement of prices of individual stocks and the general markets.[pic 1][pic 2]Regression modelA univariate regression model is built up in this report, as follow:[pic 3]The independent variable is the S&P 500 index return series, which represents general market movements. The dependent variable is the return series of one selected company, Google. In this model, β specify the linear relationship between the price change of Google and the general US market. α represents the excess performance, if there is any, of Google that cannot be explained by market returns. 1,258 daily return data are collected in the sample period between 29th November 2010 and 29th November 2015 for each of these two series.Ordinary least squares (OLS) approach is used upon these historical data to estimate the value of α and β. OLS could deliver the best linear unbiased estimates (BLUE) grounded on a set of assumptions (see discussions in the following sections). Before OLS estimation, we use a scatter graph to visualize the relationship between these two return series (see EViews graph in appendix 1). From this graph, a positive relationship between these two series can be easily detected.  This finding could justify the formal statistical estimation through OLS in the next step.Parameter estimation and hypothesis testing: α and βThe two parameters (α, β) are estimated and tested against null hypotheses following the OLS approach. The following table presents the parameter estimates and their test statistics. VariablesCoefficientT-statisticIntercept (α)0.0003420.962564Slope coefficient (β)0.96362726.27278Two-tailed hypothesis tests are carried out for both parameters to check if these estimates are significantly different from zero, within 95% confidence intervals.  Firstly, the intercept (α) estimate is very close to zero, which indicates a small outperformance of 0.03%. The hull hypothesis is specified that the intercept is equal to 0, and alternative hypothesis that it is not equal to 0. The null and alternative hypothesis can be written as follows: