國際金融學習記事 (Learning Notes) 丁淑妤 10292026

2015/10/19

Tools (methods) for econometric modeling in Int. Finance

1.       Classical assumption on residuals of OLS (Gauss – Markov theorem)
à to ensure the randomness of OLS residuals
à in multiple regression: X and Z should be independent

2.       Testing classical assumptions on residuals
à   E(u_t) = 0 (ignored if there is an intercept in OLS)

è Cov(u_t,u_t-j) = 0  for j¹1 (no autocorrelation in u_t)

è Var(u_t) = s_u for all t (Homoskedasticity)

è Jarque-Bera (JB) test (Test if the residual is normally distributed)

3.       Doornick-Hansen test (for multivariate normality)

4.       Statistical significance testing P-values
- Choose the certain a (level of significance), for example 5%
- If p-value > a, fail to reject Ho
- If p-value  < a, reject Ho

5.       Testing for no-autocorrelation (Q Tests)
à H0: there is no autocorrelation among residuals (u_t) up to lag p
       -   If reject H0, there exists autocorrelation among u_t and u_t-j 

-   If fail to reject H0,  no autocorrelation among u_t and u_t-j

6.       Testing for homeskedasticity (Q² tests)
à H0: there is no ARCH-type heteroscedasticity among residuals (u_t) up to lag p
       -  If reject H0,  there exists (ARCH-type) heteroskedasticity among u_t
       -  If fail to reject H0,  homeskedasticity, no (ARCH-type) heteroskedasticity among u_t

7.       JB Normality test on residuals
ex: Jarque-bera test = 0.310095, with P-Value 0.856374 we can say that P-Value of JB test suggest failure to reject HO. It means that “residuals are normally distributed”

Notes:
* Check OLS residuals before estimating the result of OLS in order to get BLUE estimates
BLUE means: Best, Liniear, Unbiased, Estimators.
* make sure that there are no autocorrelation, homoscesadticity, in small sample (N<30)
* Implication of the autocorrelation in residuals à Estimated coefficients are not BLUE
* Possible rescues for problems in OLS diagnosis
   - Re-estimate OLS with “robut standard errors”
   - model/Time sereies/AR(1)
   - Re-specify the model

News Related to International Finance:

1.       Discordant Financial Messages From China Spur Global Unease
(http://www.nytimes.com/2015/10/20/business/international/discordant-financial-messages-from-china-spur-global-unease.html?_r=0)

2.       Federal Reserve Beige Book Reveals Strong US Dollar Is Restraining Manufacturing Activity

(http://www.ibtimes.com/federal-reserve-beige-book-reveals-strong-us-dollar-restraining-manufacturing-2141667)