导图社区 BUSI4528 QRMFI Minds UNNC
金融与投资定量研究方法(宁波诺丁汉大学)
编辑于2022-03-08 21:17:00QRMFI(BUSI4528)
Binary choice model(LPM)
Definition
Binary variable, predict the outcome
LPM shortcomings
1. The error term is not normally distributed
2. The error term is heteroscedastic
3. Constant slope
4. Predicted probabilities can be out of range
Logit(Logistic) & Probit(Normal)
Made for binary dependent variables and always result in 0<y<1
Likelihood function estimator
Goodness of fit(R2)
Count R2
is not valid with qualitative response models
Pseudo R2
Stationary time series model
Definition
A series of data points indexed in time order
Series regressions(Autocorrelation)
Definition
it exhibits correlation over time, in the error term
Consequence
1. OLS estimators are still unbiased, but inefficient
2. Standard errors are invalid
Detection
1. Graphical Analysis
2. Durbin-Watson (DW) test
Estimate the above model and obtain the residuals ε(t)
Compute DW's d-statistic
Limitation
It applies only to AR (1) serial correlation
3. LM test
Solution
1. Neway-Wet standard errors
Apply OLS anyway, and "fix" the formula for the estimated standard errors
2. (Feasible)GLS
Transform the data so that the Gauss-Markov conditions are met
3. Nonlinear least squares
Non-stationary time series model
Spurious regression
Definition
Unit Root
Dickey-Fuller (DF) test
H0: Series contains a unit root H1: Series is stationary
Augmented Dickey-Fuller(ADF)
Eliminate the influence of autocorrelation
Cointegration
Definiton
Two or more time series variables are non-stationary
Long-run & shotrt-run
Detection
Engle-Granger test
1. Determine whether the time series variables are non-stationary
2. Estimate the regression in levels
3. To test for cointegration, test for stationarity of the estimated error term
4. Estimating the error-correction model
Panel data
Definition
Balanced or Unbalanced
Pooled model or others
F-test or LM test
H0: PEM H1:Ohters
Fixed model or Random model
Hausman test
H0: FEM H1:REM
Simple linear regressions(LRM)
Gauss-Markov theorem
Collinearity
Definition
Multi-collinearity
Correlation among variables
Consequence
1. Cannot get estimate of beta(k)
2. Insignificant of the coefficients
3. The addition or deletion of a few observations
Detection
1. Auxiliart regression(coefficient, R(2))
2. VIF(>10,high collinearity)
Solution
1. Find out and drop the troublesome variables
2. Reduce the variance of parameter estimator
Heteroskedasticity
Definition
Consequence
1. The linear and unbiased estimator is no longer best
2. Usual t-test and F-test are unreliable
Detection
1. Residual charts
2. Breusch-Pagan(BP) test
3. LM test
4. White test
Solution
1. WLS
Weight+OLS
2. Robust standard error
Apply correction to standard errors
Dummy variables or Indicator variables
Definition
0 or 1
Indicator variable Trap
Dummy variables required one less than categories of qualitative variable
Applications
1. Controlling for some qualitative features, time, season etc
2. Interactions between qualitative factors
3. Testing the equivalence of two regressions
Introduction to econometrics
Central limit theorem
≈Standard normal distribution, samples>30
Hypothesis testing
Null(H0) and Alternate(H1) hypotheses