BUSI4528 QRMFI Minds UNNC

金融与投资定量研究方法（宁波诺丁汉大学）

QRMFI(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