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Descriptive Statistics 337 of component y on the occurrence of value v of component x. The influence, as will be shown later, is ...

338 The Basics of financial economeTrics That is, for any pair (v, w), the joint frequency is the mathematical product of their ...

Descriptive Statistics 339 In equation (A.11), for each observation, the deviation of the first com- ponent from its mean is mul ...

340 The Basics of financial economeTrics x= 0 and y= 0 , respectively. The resulting sample covariance according to equation (A. ...

Descriptive Statistics 341 This problem is apparent from the following illustration. Suppose we have two variables, x and y, wit ...

342 The Basics of financial economeTrics The intuition behind equation (A.13) is to measure the average squared deviations of th ...

343 Appendix B Continuous probability distributions Commonly Used in Financial econometrics i n this appendix, we discuss the mo ...

344 The Basics of financial economeTrics Normal Distribution The first distribution we discuss is the normal distribution. It is ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 345 A problem is that the distribution function can ...

346 The Basics of financial economeTrics Property 2. The distribution is stable under summation. That is, if X has a normal dist ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 347 values, n < 30 justifies the use of the stan ...

348 The Basics of financial economeTrics In words, the sum is again distributed chi-square but this time with n degrees of freed ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 349 Student’s t-Distribution An important continuou ...

350 The Basics of financial economeTrics Student’s t-distribution has a similar shape to the normal distribution, but with thick ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 351 dispersion from S relative to the standard norm ...

352 The Basics of financial economeTrics F-Distribution Our next distribution is the F-distribution. It is defined as follows. L ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 353 The mean is given by = − EX > n n () n 2 (^2 ...

354 The Basics of financial economeTrics density with a low α = 1.5.^4 The density graphs are obtained by fitting the distributi ...

Continuous Probability Distributions Commonly Used in Financial Econometrics 355 Possible values of the parameters are listed be ...

356 The Basics of financial economeTrics the “kurtosis”of the density), for the case of β = 0, μ = 0, and σ = 1. As the values o ...