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he123456 · 2022年01月03日

n-Ku-1自由度问题

  1. FRM I
  2. Quantitative

NO.PZ2020010801000037

问题如下：

You are interested in understanding the determinants of the yield spread of corporate bonds above a maturity matched sovereign bond. You include three explanatory variables: the leverage defined as the ratio of long-term debt to the book value of assets, a dummy variable for high yield, and a measure of the volatility of the profitability of the issuer. You are interested in testing whether there are nonlinear effects of some of these variables, and so use a RESET test including both the squared and cubic term. The R2R^2 of the original model is 68.6%, and the R2R^2 from the model that includes both additional terms is 68.9%. You have 456 observations. What do you conclude about the specification of the model?

选项：

解释：

The RESET test examines whether the two additional explanatory variables that squared and cubed fitted values have zero coefficients. It is implemented using an F-test:

(0.689−0.6862)/(1−0.689456−6) F2,450(\frac{0.689-0.686}{2})/(\frac{1-0.689}{456-6})~F_{2,450}

The F-test examines the difference between the R2R^2 in the two models. The critical value for an F2,450F_{2,450} is 3.01 (F.INV. RT(0.05,2,450) in Excel). The value of the test statistic is 2.17, which is less than the critical value, and so the null that the coefficient on the squared and cubic terms is 0 is not rejected.

为什么自由度是456-6，Ku不是full explanatory variables3吗，所以分母除的自由度不是因该为456-3-1吗

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李坏_品职助教 · 2022年01月04日

嗨，爱思考的PZer你好：


这道题原来有三个explanatory variables（the leverage defined as the ratio of long-term debt to the book value of assets, a dummy variable for high yield, and a measure of the volatility of the profitability of the issuer），


又新增了两个变量（the squared and cubic term.意思是某个变量的二次项和三次项，具体是哪一个没说清楚。。。）


所以自由度应该是456-5-1

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he123456 · 2022年01月09日

好吧，我没理解use a RESET test including both the squared and cubic term的意思

李坏_品职助教 · 2022年01月10日

嗨，努力学习的PZer你好：


嗯，这个意思就是新的检验模型里面包含了平方项和立方项，等于是多了俩解释变量。

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