Your SlideShare is downloading. ×
CFA II Quantitative Analysis
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Saving this for later?

Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime - even offline.

Text the download link to your phone

Standard text messaging rates apply

CFA II Quantitative Analysis

4,586
views

Published on

CFA Level II Quantitative Analysis.

CFA Level II Quantitative Analysis.

Published in: Education

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
4,586
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
83
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Qunatitative Analysis – I
  • 2.
    • Regression analysis
      • Population Regressions Line
      • Sample Regression Line
      • Hypothesis Testing
      • Explained and Unexplained Variation
      • Residual Analysis
    Agenda
  • 3. Data Trend Model Seasonality Log-Linear Model Linear Model Auto-Regressive Model Regression Analysis Cross-sectional Data Time dependent Data Significant Autocorrelation among Residuals Yes No Significant Autocorrelation among Residuals Significant Autocorrelation among lagged residuals Yes Yes No No Make a Graph Correctly Specified Model
  • 4. Types of Regression Models © Neev Knowledge Management – Pristine Careers Negative Linear Relationship Negative Linear Relationship Relationship NOT Linear No Relationship
  • 5. © Neev Knowledge Management – Pristine Careers Random Error for this x value y x Observed Value of y for x i Predicted Value of y for x i x i Slope = β 1 Intercept = β 0 e i Sample Regression Function
  • 6. Sample Regression Function © Neev Knowledge Management – Pristine Careers Notice the similarity with the Population Regression Function Can we do something of the error term? Estimate of the regression intercept Estimate of the regression slope Independent variable Error term
  • 7.
      • General Multiple Regression Analysis
      • Hypothesis Testing of Coefficients
      • Analysis of Variance (ANOVA) and F-statistic
      • Coefficient of Determination(R 2 ) and Adjusted R 2
      • Heteroskedasticity, Serial Correlation and Multicollinearity
      • Model Misspecifications
      • Models with qualitative dependent variable
    Agenda
  • 8. General Multiple Linear Regression Model
    • In simple linear regression, the dependent variable was assumed to be dependent on only one variable (independent variable)
    • In General Multiple Linear Regression model, the dependent variable derive sits value from two or more than two variable.
    • General Multiple Linear Regression model take the following form:
    • where:
    • Y i = i th observation of dependent variable Y
    • X ki = i th observation of k th independent variable X
    • b 0 = intercept term
    • b k = slope coefficient of k th independent variable
    • ε i = error term of i th observation
    • n = number of observations
    • k = total number of independent variables
    © Neev Knowledge Management – Pristine Careers
  • 9. Assumptions of Multiple Regression Model
    • There exists a linear relationship between the dependent and independent variables.
    • The expected value of the error term, conditional on the independent variables is zero.
    • The error terms are homoskedastic, i.e. the variance of the error terms is constant for all the observations.
    • The expected value of the product of error terms is always zero, which implies that the error terms are uncorrelated with each other.
    • The error term is normally distributed.
    • The independent variables doesn’t have any linear relationships between each other.
    © Neev Knowledge Management – Pristine Careers
  • 10. Analysis of Variance (ANOVA)
    • Analysis of variance is a statistical method for analyzing the variability of the data by breaking the variability into its constituents.
    • A typical ANOVA table looks like:
    • From the above summary(ANOVA table) we can calculate:
      • Standard Error of Estimate(SEE)=
      • Coefficient of determination(R 2 )=
      • =
    © Neev Knowledge Management – Pristine Careers
  • 11.
    • Time Series Analysis
      • Trend Models
      • Autoregressive Models
      • Seasonality
      • Random Walk Process
    Agenda
  • 12. Data Trend Model Seasonality Log-Linear Model Linear Model Auto-Regressive Model Regression Analysis Cross-sectional Data Time dependent Data Significant Autocorrelation among Residuals Yes No Significant Autocorrelation among Residuals Significant Autocorrelation among lagged residuals Yes Yes No No Make a Graph Correctly Specified Model
  • 13. Time Series
    • Time Series is a series of the variable values taken at equal interval of time. The closing price of the IBM stock observed for 10 years constitutes the time series of the IBM stock price.
    • Time series may have a pattern when plotted against the time, which depicts the characteristics of the IBM stock and the capital markets in general.
    • These patterns in the stock price time series are called trends in the time series,
      • An American retail chain (AMR) which sells woolen clothes, will have increased sales pattern in the winters and a moderate sales in the summer.
      • The quarterly sales of AMR when plotted against the time for 4 years will show moderate sales in summers and increased sales in winters
    • The above shown trends in the sales are called seasonal trends
    © Neev Knowledge Management – Pristine Careers Quarterly Sales Time 4 th Quarter
  • 14. Limitation of Trend Models
    • The most important assumption of the linear regression is that the error terms are not correlated with each other.
    • Other important assumption of the linear regression is that the residual term is independently distributed.
    • These two important assumptions when violated becomes the limitation for the trend models as linear regression is used in trend models.
    • To overcome the autocorrelation problem(violation of independent and uncorrelated residuals assumption), log-linear trend model can be used which reduces the serial correlation.
    • After applying the log-linear trend model, the serial correlation may persist, which means even a log-linear trend model is inappropriate for the case. This hints us to use some other form model which are autoregressive models.
    • In Autoregressive(AR) models, the dependent variable is regressed with its lagged term.
    © Neev Knowledge Management – Pristine Careers