Questions tagged [hypothesis-testing]
In statistics, hypothesis testing assesses whether data are inconsistent with a given hypothesis.
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Portion of Derivation of F-test
In Greene's Econometric Analysis there is a derivation regarding the F stat. The setup is a null hypothesis of the form: $H_0: R\beta =q$ where $\beta$ is a $k\times 1$ vector of parameters, $R$ is a ...
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Testing asset pricing models with Roll's critique in mind
Roll's critique (Roll, 1977) can be summarized as follows (quoting Wikipedia):
Mean-variance tautology: Any mean-variance efficient portfolio $R_{p}$ satisfies the CAPM equation exactly:
$$
E(R_{i})-...
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Do t-stats created with robust standard errors follow a t-distribution in finite samples?
I am creating econometrics notes and proved that, with normally distributed errors, homoskedasticity, and no serial correlation, t-stats based on baseline OLS standard errors do in fact follow a t-...
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Construction of F-Test
While constructing the F-test with matrix notation,
For the Unrestricted model, we have:
$$ y=X_{1}\cdot b_{1}+X_{2}\cdot b_{2}+e $$
For the Restricted model;
$$ y=\widehat{X}_{1}.b_{1}+e_{R} $$
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Why is N*R^2 called an "LM test"?
After OLS, one can test the null hypothesis that all coefficients are 0 by calculating $N\cdot R^2$, which is distributed $\chi^2_{k}$ where $k$ is the number of $\beta$ (excluding the constant).
I ...
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Interpreting an ADF test in R
Although being a mathematician, I am fairly new to time series and R. On an assignment I was being asked to check a time series for stationarity in R, only using the $\texttt{adf.test}$ function that ...
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Econometrics - Need help interpreting results
My absolute t-value is greater than t-critical value. This means that I can reject my null hypothesis which was that $\beta_1\leq 0$. Therefore, $\beta_1\gt 0$ and my alternative hypothesis is correct....
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How does one do a hypothesis test for elasticity?
Given the regression output
$$\widehat{\ln cons} = \underset{(0.6018)}{0.4054} + \underset{(0.0744)}{1.2739}\, \ln m - \underset{(0.1902)}{0.6666}\, \ln p_1 -\underset{(0.2645)}{1.6146}\, \ln p_2$$
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