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CFA Level II > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

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1
Q

Covariance Stationary

A

Mean and variance don’t change over time

Determined by:

  1. Plotting data
  2. Run an AR model and test correlations
  3. Perform Dickey Fuller Test

Note: Most economic and financial time-series are not stationary

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2
Q

T-Test Significance and Z-Test

90%, 95%, 99%

A

90%: 1.645

95%: 1.96

99%: 2.326

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3
Q

When can we reject the null hypothesis

A

If the t-stat is too big

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4
Q

What is covariance

A

How 2 variances move together

  1. Very sensitive when only 2 variables
  2. Can be negative infinite or positive infinite
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5
Q

Increasing Adjusted R² means _______

A

The added variables are worth keeping

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6
Q

T-Stat Formula

A

Coefficient / Standard Error

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7
Q

Model Misspecification

A

Types:

  1. Time-series: Serial correlation with a lagged variable, or forecasting the past
  2. Functional: Omitting a variable or data pooled improperly
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8
Q

Correlation Squared Purpose

A

Explains the variability

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9
Q

Correlation

A

cov / (std of X * std of Y)

OR

(X - Xbar)(Y-Ybar) / √(X-Xbar)²(Y-Ybar)²

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10
Q

MSE

A

SSE / n - k - 1

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11
Q

ANOVA Table

A

Source DOF SOS Mean SOS
Regression(explained) K RSS MSR = RSS/K

Error (unexplained) n-k-1 SSE MSE = SSE/n-k-1

Total n-1 SST

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12
Q

R² from ANOVA

A

Name: Coefficient of Determination

Formulas: RSS / SST
SST - SSE / SST
Correlation²

Purpose: This is the % of variability of Y explained by X’s

Analysis: The higher the better fit

Problem: Always increase as variables are added

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13
Q

Random Walk

A

Unit root: coefficient = 1
This means the null (g = 0), cannot be rejected

Does not have a mean reverting level

Not stationary

Correct by first differencing

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14
Q

MSR

A

RSS / k

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15
Q

RMSE

A

Purpose: to compare the accuracy of AR models for our-of-sample

Formula: √Average squared error

Analysis: lower the better

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16
Q

Multiple Regression Analysis Steps

A
  1. Is there model mispecification
  2. Is the t-test significant? If no, use another model
  3. Is the F-Stat significant? If no, use another model
  4. Check for Hetero, serial correlation, and multicollinearity
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17
Q

When using Dummy Variables

A

They are either on of off

Always use n-1 or it will suffer from multcollinearity
Example: If using quarters per year, use 3

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18
Q

Log-Linear Trend Model

A

Purpose: Used when there is exponential growth or there is serial correlation

Formula: y = e^b0 + b1(t)

Use the time/observations for t

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19
Q

Sample Correlation Coefficient Other Formulas

A

Covariance / (Std X * Std Y)

OR

√R²

OR

Covariance / √X * √Y

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20
Q

F-Stat

A

Use: To see if any X’s explain a significant portfolio of Y

Formula: MSR / MSE (only use when DOF is 1 or n-1)

Other forumla: (RSS/k) / (SSE / n-k-1)

21
Q

SST

A

RSS + SSE

22
Q

Sample Covariance Formula

A

(X-Xbar)(Y-Ybar) / n - 1

23
Q

Sample Covariance Steps

A
  1. Create a table

Period 1 2 3 4
X-Xbar -.1 .2 .8 -0.9
Y-Ybar -.7 .5 1.1 -0.9 Sum
(X-Xbar)(Y-Ybar) .07 .10 .88 .86 1.86

Then take sum / n - 1

1.86 / 3 = 0.62

24
Q

Multicollinearity

A

Purpose: High correlation among X’s (Higher than 0.7)

Detect: T-test indicate no coefficients are different from 0
Correct: Drop a variable

Effects: F-Test is significant
R² is too high
All t-stats are below 2

25
Q

Sample Correlation Coefficient (R)

A

covariance / (sample √X) (sample √Y)

(sample √X) = sum of (X-Xbar)² / n - 1
(sample √Y) = sum of (Y-Ybar)² / n - 1

26
Q

AR Models

A

Use previous values to get the next one. They build upon each other.

Correct if autocorrelation of residuals not significant.

27
Q

Mean Reversion

A

b0 / (1 - b1)

28
Q

Adding additional variables are best evaluated by using….

A

Adjusted R²

29
Q

Seasonality

A

Purpose: Model will be misspecified unless the AR model incorporates the effects of seasonality

Detect: statistically significant lagged error term

Correct: Add an additional term (e.g. last year’s quarter)

30
Q

Cointegration

A

Purpose: Two time-series are economically linked

Correct: Regress one variable against the other with the Dickey Fuller

Analysis: If null is rejected, they are covariance stationary

31
Q

What does the T-Test Mean

A

Gives more confidence

Will be high if: correlation is high
Sample is high

32
Q

Assumptions of Regression: Simple and Multiple

A

Simple

  1. Linear relationship between X and Y
  2. Expected value of error term = 0
  3. Variance of error term is constant (Heteroskasticity)
  4. Errors not serially correlated (Autocorrelation)
  5. Error term normally distributed

Multiple
All the above plus:
No exact linear relationship among X’s (Multicolinearity)

33
Q

SEE

A

Name: Standard Error of Estimate (STANDARD DEVIATION)

Purpose: Gauges the fit of the regression line. Smaller the better

Formula 1: √MSE
Formula 2: √ SSE / n - k - 1

34
Q

Covariance Formula

A

√R² * √X * √Y

35
Q

Confidence Interval

A

coefficient +/- (critical t value * standard error)

Side note: Standard error is SEE

36
Q

When is the slope coefficient significant?

A

When zero is not included in the range

37
Q

Smallest Alpha to reject the null hypothesis? Under what value?

A

Answer: p-value

Under: 0.5

If under .001 then ARCH exists

38
Q

In/Out of Sample Forecasts

A

In-sample: estimating data within the range provided

Out-of-sample: Estimating outside the range
Important b/c it proves whether the model describes the time-series

39
Q

T-Test Formula for Hypothesis

A

Estimate - Hypothesis / Standard Error (SEE)

40
Q

Limitations of Regression Analysis

A
  1. Parameter Instability
  2. Outliers may affect the estimated regression line
  3. Spurious Correlation (appearance of a linear line)
41
Q

Degrees of Freedom

A

Simple Regression: n - 2

Multiple Regression
n - k - 1

42
Q

Heteroskedasticity

A

Purpose: Data spread out on one tail

Types: Unconditional and conditional (only conditional has issues)

Effects: Non constant error variance
F-Test is unreliable
Biased T-Statistics

Detect: Breusch-Pagan –> Takes errors and compares to X, If R² > 0 then it exists

Correct: White-corrected Standard errors (AKA Robust)

43
Q

T-Test Steps

A
  1. Use the formula to calculate the T-Test
  2. Look up value of t-table
  3. Reject if t > Tcritical or > -Tcritical
44
Q

Autocorrelation

A

AKA: serial correlation

Purpose: correlation among error terms

Detect: Durbin Watson (does not work with AR models)

DW = 2 * (1 - correlation)
If DW is close to 2: No serial correlation
If DW is less than 2: Positively correlated
If DW is greater than 2: negatively correlated

Correct: Hansen

45
Q

Adjusted R² Formula

A

Purpose: Eliminates the impact of additional variables

Formula: 1 - [(n-1 / n-k-1) * (1-R²)]

Note: Will always be lower than R²

46
Q

Slope Coefficient and Intercept Term

A

Slope Coefficient: covariance / variance (or std²)

Explain: How much coefficient will move for every 1% change

Intercept Term: y - b1(x)

Explain: when X is zero

47
Q

ARCH

A

Purpose: based on a regression of the squared residuals on their lagged values

48
Q

Effects of Model Misspecification

A
  1. Coefficients are biased and inconsistent

2. Lack of confidence in hypothesis

CFA Level II (13 decks)

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