# P1.T2. Quantitative Analysis

Practice questions for Quantitative Analysis: Econometrics, MCS, Volatility, Probability Distributions and VaR (Intro)

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1. ### P1.T2.707. Gaussian Copula (Hull)

Learning objectives: Define copula and describe the key properties of copulas and copula correlation. Explain tail dependence. Describe the Gaussian copula, Student’s t-copula, multivariate copula, and one-factor copula. Questions: 707.1. Below are the joint probabilities for a cumulative bivariate normal distribution with a correlation parameter, ρ, of 0.30. If V(1) and V(2) are each...
Learning objectives: Define copula and describe the key properties of copulas and copula correlation. Explain tail dependence. Describe the Gaussian copula, Student’s t-copula, multivariate copula, and one-factor copula. Questions: 707.1. Below are the joint probabilities for a cumulative bivariate normal distribution with a correlation parameter, ρ, of 0.30. If V(1) and V(2) are each...
Learning objectives: Define copula and describe the key properties of copulas and copula correlation. Explain tail dependence. Describe the Gaussian copula, Student’s t-copula, multivariate copula, and one-factor copula. Questions: 707.1. Below are the joint probabilities for a cumulative...
Learning objectives: Define copula and describe the key properties of copulas and copula correlation. Explain tail dependence. Describe the Gaussian copula, Student’s t-copula, multivariate...
Replies:
0
Views:
43
2. ### P1.T2.706. Bivariate normal distribution (Hull)

@David Harper CFA FRM, makes perfect sense now. thanks for taking the time again.
@David Harper CFA FRM, makes perfect sense now. thanks for taking the time again.
@David Harper CFA FRM, makes perfect sense now. thanks for taking the time again.
@David Harper CFA FRM, makes perfect sense now. thanks for taking the time again.
Replies:
8
Views:
98
3. ### P1.T2.705. Correlation (Hull)

Thank you emilioalzamora and David for such a detailed explanation.
Thank you emilioalzamora and David for such a detailed explanation.
Thank you emilioalzamora and David for such a detailed explanation.
Thank you emilioalzamora and David for such a detailed explanation.
Replies:
13
Views:
148
4. ### P1.T2.704. Forecasting volatility with GARCH (Hull)

HI @jjman2000 Not from volatility. EWMA is easier to understand first, I think. As Hull shows, the EWMA formula for the estimate of current variance, σ^2(n) = λ*σ^2(n-1) + (1-λ)*µ^2(n-1), is a recursive solution to the (infinite) series σ^2(n) = (1-λ)*µ^2(n-1) + (1-λ)*λ*µ^2(n-2) + (1-λ)*λ^2*µ^2(n-3) + .... so keeping in mind that simple historical variance is just an average of squared returns...
HI @jjman2000 Not from volatility. EWMA is easier to understand first, I think. As Hull shows, the EWMA formula for the estimate of current variance, σ^2(n) = λ*σ^2(n-1) + (1-λ)*µ^2(n-1), is a recursive solution to the (infinite) series σ^2(n) = (1-λ)*µ^2(n-1) + (1-λ)*λ*µ^2(n-2) + (1-λ)*λ^2*µ^2(n-3) + .... so keeping in mind that simple historical variance is just an average of squared returns...
HI @jjman2000 Not from volatility. EWMA is easier to understand first, I think. As Hull shows, the EWMA formula for the estimate of current variance, σ^2(n) = λ*σ^2(n-1) + (1-λ)*µ^2(n-1), is a recursive solution to the (infinite) series σ^2(n) = (1-λ)*µ^2(n-1) + (1-λ)*λ*µ^2(n-2) +...
HI @jjman2000 Not from volatility. EWMA is easier to understand first, I think. As Hull shows, the EWMA formula for the estimate of current variance, σ^2(n) = λ*σ^2(n-1) + (1-λ)*µ^2(n-1), is a...
Replies:
2
Views:
61
5. ### P1.T2.703. EWMA versus GARCH volatility (Hull)

Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties. Calculate volatility using the GARCH(1,1) model. Questions: 703.1. The most recent estimate of the daily volatility of an asset is 4.0% and the price...
Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties. Calculate volatility using the GARCH(1,1) model. Questions: 703.1. The most recent estimate of the daily volatility of an asset is 4.0% and the price...
Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties. Calculate volatility using the GARCH(1,1) model....
Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model...
Replies:
0
Views:
36
6. ### P1.T2.699. Linear and nonlinear trends (Diebold)

Hi @clexuan That's very observant! I followed Diebold's example, to my knowledge, here by giving the assumption (emphasis mine): "y(t) = β(0) + β(1)*TIME(t) + e(i), where e(i) ~ N(0, σ^2), obtaining the estimates β(0) = 0.510, β(1) = 2.30, and σ^2 = 16." In this way, e(i) is the disturbance (or to be more technical, I think it's the residual as estimator of the population's disturbance, where...
Hi @clexuan That's very observant! I followed Diebold's example, to my knowledge, here by giving the assumption (emphasis mine): "y(t) = β(0) + β(1)*TIME(t) + e(i), where e(i) ~ N(0, σ^2), obtaining the estimates β(0) = 0.510, β(1) = 2.30, and σ^2 = 16." In this way, e(i) is the disturbance (or to be more technical, I think it's the residual as estimator of the population's disturbance, where...
Hi @clexuan That's very observant! I followed Diebold's example, to my knowledge, here by giving the assumption (emphasis mine): "y(t) = β(0) + β(1)*TIME(t) + e(i), where e(i) ~ N(0, σ^2), obtaining the estimates β(0) = 0.510, β(1) = 2.30, and σ^2 = 16." In this way, e(i) is the disturbance (or...
Hi @clexuan That's very observant! I followed Diebold's example, to my knowledge, here by giving the assumption (emphasis mine): "y(t) = β(0) + β(1)*TIME(t) + e(i), where e(i) ~ N(0, σ^2),...
Replies:
7
Views:
96
7. ### P1.T2.702. Simple (equally weighted) historical volatility (Hull)

Learning objectives: Define and distinguish between volatility, variance rate, and implied volatility. Describe the power law. Explain how various weighting schemes can be used in estimating volatility. Questions 702.1. Consider the following series of closing stock prices over the tend most recent trading day (this is similar to Hull's Table 10.3) along with daily log returns, squared...
Learning objectives: Define and distinguish between volatility, variance rate, and implied volatility. Describe the power law. Explain how various weighting schemes can be used in estimating volatility. Questions 702.1. Consider the following series of closing stock prices over the tend most recent trading day (this is similar to Hull's Table 10.3) along with daily log returns, squared...
Learning objectives: Define and distinguish between volatility, variance rate, and implied volatility. Describe the power law. Explain how various weighting schemes can be used in estimating volatility. Questions 702.1. Consider the following series of closing stock prices over the tend most...
Learning objectives: Define and distinguish between volatility, variance rate, and implied volatility. Describe the power law. Explain how various weighting schemes can be used in estimating...
Replies:
0
Views:
24
8. ### P1.T2.701. Regression analysis to model seasonality (Diebold)

Many thanks for you lovely comment, Brian. It is nothing special I guess, I have just read a few textbooks that's it. The modelling (implementation work) is another kettle of fish. These "goodness of fit" tests are technically quite complex. Again, thanks for your like!
Many thanks for you lovely comment, Brian. It is nothing special I guess, I have just read a few textbooks that's it. The modelling (implementation work) is another kettle of fish. These "goodness of fit" tests are technically quite complex. Again, thanks for your like!
Many thanks for you lovely comment, Brian. It is nothing special I guess, I have just read a few textbooks that's it. The modelling (implementation work) is another kettle of fish. These "goodness of fit" tests are technically quite complex. Again, thanks for your like!
Many thanks for you lovely comment, Brian. It is nothing special I guess, I have just read a few textbooks that's it. The modelling (implementation work) is another kettle of fish. These "goodness...
Replies:
11
Views:
91
9. ### P1.T2.700. Seasonality in time series analysis (Diebold)

Learning objective: Describe the sources of seasonality and how to deal with it in time series analysis. Questions 700.1. Which of the following time series is MOST LIKELY to contain a seasonal pattern? a. Price of solar panels b. Employment participation rate c. Climate data data recorded from a weather station once per year d. Return on average assets (ROA) for the large commercial bank...
Learning objective: Describe the sources of seasonality and how to deal with it in time series analysis. Questions 700.1. Which of the following time series is MOST LIKELY to contain a seasonal pattern? a. Price of solar panels b. Employment participation rate c. Climate data data recorded from a weather station once per year d. Return on average assets (ROA) for the large commercial bank...
Learning objective: Describe the sources of seasonality and how to deal with it in time series analysis. Questions 700.1. Which of the following time series is MOST LIKELY to contain a seasonal pattern? a. Price of solar panels b. Employment participation rate c. Climate data data recorded...
Learning objective: Describe the sources of seasonality and how to deal with it in time series analysis. Questions 700.1. Which of the following time series is MOST LIKELY to contain a seasonal...
Replies:
0
Views:
42
10. ### P1.T2.602. Bootstrapping (Brooks)

a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! Imagine a simulation of earthquakes or flood levels or survival in space.....
a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! Imagine a simulation of earthquakes or flood levels or survival in space.....
a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! ...
a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be...
Replies:
4
Views:
116
11. ### P1.T2.601. Variance reduction techniques (Brooks)

Learning objectives: Explain how to use antithetic variate technique to reduce Monte Carlo sampling error. Explain how to use control variates to reduce Monte Carlo sampling error and when it is effective. Describe the benefits of reusing sets of random number draws across Monte Carlo experiments and how to reuse them. Questions: 601.1. Betty is an analyst using Monte Carlo simulation to...
Learning objectives: Explain how to use antithetic variate technique to reduce Monte Carlo sampling error. Explain how to use control variates to reduce Monte Carlo sampling error and when it is effective. Describe the benefits of reusing sets of random number draws across Monte Carlo experiments and how to reuse them. Questions: 601.1. Betty is an analyst using Monte Carlo simulation to...
Learning objectives: Explain how to use antithetic variate technique to reduce Monte Carlo sampling error. Explain how to use control variates to reduce Monte Carlo sampling error and when it is effective. Describe the benefits of reusing sets of random number draws across Monte Carlo...
Learning objectives: Explain how to use antithetic variate technique to reduce Monte Carlo sampling error. Explain how to use control variates to reduce Monte Carlo sampling error and when it is...
Replies:
0
Views:
84
12. ### P1.T2.600. Monte Carlo simulation, sampling error (Brooks)

Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each...
Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should...
Replies:
4
Views:
131
13. ### P1.T2.512. Autoregressive moving average (ARMA) processes (Diebold)

Learning outcomes: Define and describe the properties of the autoregressive moving average (ARMA) process. Describe the application of AR and ARMA processes. Questions: 512.1. Each of the following is a motivating for an autoregressive moving average (ARMA) process EXCEPT which is not? a. AR processes observed subject to measurement error also turn out to be ARMA processes b. When we need...
Learning outcomes: Define and describe the properties of the autoregressive moving average (ARMA) process. Describe the application of AR and ARMA processes. Questions: 512.1. Each of the following is a motivating for an autoregressive moving average (ARMA) process EXCEPT which is not? a. AR processes observed subject to measurement error also turn out to be ARMA processes b. When we need...
Learning outcomes: Define and describe the properties of the autoregressive moving average (ARMA) process. Describe the application of AR and ARMA processes. Questions: 512.1. Each of the following is a motivating for an autoregressive moving average (ARMA) process EXCEPT which is not? a. AR...
Learning outcomes: Define and describe the properties of the autoregressive moving average (ARMA) process. Describe the application of AR and ARMA processes. Questions: 512.1. Each of the...
Replies:
0
Views:
81
14. ### P1.T2.511. First-order autoregressive, AR(1), process (Diebold)

[USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
[USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
[USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
[USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
Replies:
8
Views:
161
15. ### P1.T2.510. First-order and general finite-order moving average process, MA(1) and MA(q) (Diebold)

If the roots are real and not complex, I believe.
If the roots are real and not complex, I believe.
If the roots are real and not complex, I believe.
If the roots are real and not complex, I believe.
Replies:
2
Views:
209
16. ### P1.T2.509. Box-Pierce and Ljung-Box Q-statistics (Diebold)

Hi Joyce, Wonder how I made a mistake - yes, you are right, I was looking at Chi-square 95%, 24 instead of Chi-square 5%, 24 = 36.415! Thanks a tonne Jayanthi
Hi Joyce, Wonder how I made a mistake - yes, you are right, I was looking at Chi-square 95%, 24 instead of Chi-square 5%, 24 = 36.415! Thanks a tonne Jayanthi
Hi Joyce, Wonder how I made a mistake - yes, you are right, I was looking at Chi-square 95%, 24 instead of Chi-square 5%, 24 = 36.415! Thanks a tonne Jayanthi
Hi Joyce, Wonder how I made a mistake - yes, you are right, I was looking at Chi-square 95%, 24 instead of Chi-square 5%, 24 = 36.415! Thanks a tonne Jayanthi
Replies:
3
Views:
154
17. ### P1.T2.508. Wold's theorem (Diebold)

[USER=42750]@ Okay great. No worries, honestly I learn something new almost every time that I take a fresh look at something! Good luck with your studies ...
[USER=42750]@ Okay great. No worries, honestly I learn something new almost every time that I take a fresh look at something! Good luck with your studies ...
[USER=42750]@ Okay great. No worries, honestly I learn something new almost every time that I take a fresh look at something! Good luck with your studies ...
[USER=42750]@ Okay great. No worries, honestly I learn something new almost every time that I take a fresh look at something! Good luck with your studies ...
Replies:
4
Views:
222
18. ### P1.T2.507. White noise (Diebold)

Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true EXCEPT which is false? a. If a process is zero-mean white noise, then is must be Gaussian white...
Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true EXCEPT which is false? a. If a process is zero-mean white noise, then is must be Gaussian white...
Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works. Questions: 507.1. In regard to white noise, each of the following statements is true...
Learning outcomes: Define white noise, describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag...
Replies:
0
Views:
131
19. ### P1.T2.506. Covariance stationary time series (Diebold)

Hi [USER=46018]@ See below I copied Diebold's explanation for partial autocorrelation (which is excellent, in my opinion). If you keep in mind the close relationship between beta and correlation, then you can view this is analogous to the difference between (in a regression) a univariate slope coefficient and a partial multivariate slope coefficient. We can extract correlation by multiplying...
Hi [USER=46018]@ See below I copied Diebold's explanation for partial autocorrelation (which is excellent, in my opinion). If you keep in mind the close relationship between beta and correlation, then you can view this is analogous to the difference between (in a regression) a univariate slope coefficient and a partial multivariate slope coefficient. We can extract correlation by multiplying...
Hi [USER=46018]@ See below I copied Diebold's explanation for partial autocorrelation (which is excellent, in my opinion). If you keep in mind the close relationship between beta and correlation, then you can view this is analogous to the difference between (in a regression) a univariate slope...
Hi [USER=46018]@ See below I copied Diebold's explanation for partial autocorrelation (which is excellent, in my opinion). If you keep in mind the close relationship between beta and correlation,...
Replies:
6
Views:
178
20. ### P1.T2.505. Model selection criteria (Diebold)

Hi @DTu Yes, but depending on the author, (k) can is sometimes defined as the number of independent variables or the number of parameters. For example, consider y = b + m1*x1 + m2*x2 + m3*x3 + e, is a regression model with three independent variables (x1, x2, x3), four total variables (including), and four parameters (slope b, m1, m2, m3). The degrees of freedom, df = n-4 because four...
Hi @DTu Yes, but depending on the author, (k) can is sometimes defined as the number of independent variables or the number of parameters. For example, consider y = b + m1*x1 + m2*x2 + m3*x3 + e, is a regression model with three independent variables (x1, x2, x3), four total variables (including), and four parameters (slope b, m1, m2, m3). The degrees of freedom, df = n-4 because four...
Hi @DTu Yes, but depending on the author, (k) can is sometimes defined as the number of independent variables or the number of parameters. For example, consider y = b + m1*x1 + m2*x2 + m3*x3 + e, is a regression model with three independent variables (x1, x2, x3), four total variables...
Hi @DTu Yes, but depending on the author, (k) can is sometimes defined as the number of independent variables or the number of parameters. For example, consider y = b + m1*x1 + m2*x2 + m3*x3 + e,...
Replies:
2
Views:
260
21. ### P1.T2.504. Copulas (Hull)

Hello The practice questions that David writes are focused around the learning objectives in the GARP curriculum, but many times, his questions are more difficult. He writes them at a higher level to ensure that our members understand the concepts in depth. So while this question may be more difficult than the questions that you will see on the exam, the concepts are still testable, as they...
Hello The practice questions that David writes are focused around the learning objectives in the GARP curriculum, but many times, his questions are more difficult. He writes them at a higher level to ensure that our members understand the concepts in depth. So while this question may be more difficult than the questions that you will see on the exam, the concepts are still testable, as they...
Hello The practice questions that David writes are focused around the learning objectives in the GARP curriculum, but many times, his questions are more difficult. He writes them at a higher level to ensure that our members understand the concepts in depth. So while this question may be more...
Hello The practice questions that David writes are focused around the learning objectives in the GARP curriculum, but many times, his questions are more difficult. He writes them at a higher...
Replies:
25
Views:
870
22. ### P1.T2.503. One-factor model (Hull)

@hellohi, This is how I have solved: e1=z1= -0.88 e2= pz1 + z2*sqrt(1-p^2) e2= [0.70*(-0.88)] + [0.63*sqrt(1-(0.7)^2) e2= -0.16609 U= Mean + (SD*e1) U= 5 + [3*(-0.88)] U= 2.36 V= Mean + (SD*e2) V= 10 + [6*(-0.16609)] V= 9.00346 Thanks, Rajiv
@hellohi, This is how I have solved: e1=z1= -0.88 e2= pz1 + z2*sqrt(1-p^2) e2= [0.70*(-0.88)] + [0.63*sqrt(1-(0.7)^2) e2= -0.16609 U= Mean + (SD*e1) U= 5 + [3*(-0.88)] U= 2.36 V= Mean + (SD*e2) V= 10 + [6*(-0.16609)] V= 9.00346 Thanks, Rajiv
@hellohi, This is how I have solved: e1=z1= -0.88 e2= pz1 + z2*sqrt(1-p^2) e2= [0.70*(-0.88)] + [0.63*sqrt(1-(0.7)^2) e2= -0.16609 U= Mean + (SD*e1) U= 5 + [3*(-0.88)] U= 2.36 V= Mean + (SD*e2) V= 10 + [6*(-0.16609)] V= 9.00346 Thanks, Rajiv
@hellohi, This is how I have solved: e1=z1= -0.88 e2= pz1 + z2*sqrt(1-p^2) e2= [0.70*(-0.88)] + [0.63*sqrt(1-(0.7)^2) e2= -0.16609 U= Mean + (SD*e1) U= 5 + [3*(-0.88)] U= 2.36 V= Mean +...
Replies:
20
Views:
834
23. ### P1.T2.502. Covariance updates with EWMA and GARCH(1,1) models (Hull)

Hi @Spinozzi That's a fair observation. I did parrot Hull's language here, such that he does refer to these given assumptions as "current daily volatilties" (see emphasized text below; which is solved above in the XLS snapshot on the column next to BT 502.2). I also cross-checked his usage in OFOD 10th edition and he similarly refers to these assumptions as "current daily volatilities." (e.g.,...
Hi @Spinozzi That's a fair observation. I did parrot Hull's language here, such that he does refer to these given assumptions as "current daily volatilties" (see emphasized text below; which is solved above in the XLS snapshot on the column next to BT 502.2). I also cross-checked his usage in OFOD 10th edition and he similarly refers to these assumptions as "current daily volatilities." (e.g.,...
Hi @Spinozzi That's a fair observation. I did parrot Hull's language here, such that he does refer to these given assumptions as "current daily volatilties" (see emphasized text below; which is solved above in the XLS snapshot on the column next to BT 502.2). I also cross-checked his usage in...
Hi @Spinozzi That's a fair observation. I did parrot Hull's language here, such that he does refer to these given assumptions as "current daily volatilties" (see emphasized text below; which is...
Replies:
23
Views:
582
24. ### P1.T2.501. More Bayes Theorem (Miller)

great - thanks again
great - thanks again
great - thanks again
great - thanks again
Replies:
16
Views:
370
25. ### P1.T2.500. Bayes theorem (Miller)

Testing Amazon link
Testing Amazon link
Testing Amazon link
Testing Amazon link
Replies:
25
Views:
402
26. ### Quiz-T2P1.T2.409 Volatility, GARCH(1,1) and EWMA

Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha - gamma)] = sqrt[0.0000960/(1 - 0.060 - 0.880)] = sqrt[0.0000960/0.060] = 4.0% (+1 star for @Robert...
Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha - gamma)] = sqrt[0.0000960/(1 - 0.060 - 0.880)] = sqrt[0.0000960/0.060] = 4.0% (+1 star for @Robert...
Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega = long-run variance*gamma, the long-run volatility = SQRT[omega/gamma] = sqrt[omega/(1 - alpha -...
Per @Robert Paterson 's correction, the first bullet under 409.2.A corrected to read: In regard to (a), this is FALSE: because the weights sum to one (i.e., alpha + beta + gamma = 1.0) and omega...
Replies:
2
Views:
155
27. ### Quiz-T2P1.T2.408. Multivariate linear regression

In case of heteroskedasticity there will be always a downward bias on the standard error, making the T statistics (and obviously F statistics) higher. So, in that way, B is correct too. I am not saying D is incorrect. D is obviously correct as in case of multicollinearity, there will be an large standard errors of the coefficients (independent variables), rendering low t statistics for them,...
In case of heteroskedasticity there will be always a downward bias on the standard error, making the T statistics (and obviously F statistics) higher. So, in that way, B is correct too. I am not saying D is incorrect. D is obviously correct as in case of multicollinearity, there will be an large standard errors of the coefficients (independent variables), rendering low t statistics for them,...
In case of heteroskedasticity there will be always a downward bias on the standard error, making the T statistics (and obviously F statistics) higher. So, in that way, B is correct too. I am not saying D is incorrect. D is obviously correct as in case of multicollinearity, there will be an large...
In case of heteroskedasticity there will be always a downward bias on the standard error, making the T statistics (and obviously F statistics) higher. So, in that way, B is correct too. I am not...
Replies:
7
Views:
202
28. ### Quiz-T2P1.T2.407. Univariate linear regression

Hello @uness_o7 Thank you for pointing this out. I will get this fixed as soon as possible. Nicole
Hello @uness_o7 Thank you for pointing this out. I will get this fixed as soon as possible. Nicole
Hello @uness_o7 Thank you for pointing this out. I will get this fixed as soon as possible. Nicole
Hello @uness_o7 Thank you for pointing this out. I will get this fixed as soon as possible. Nicole
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12
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222
29. ### Quiz-T2P1.T2.406. Distributions II

Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to...
Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e.,...
Replies:
21
Views:
304
30. ### Quiz-T2P1.T2.405. Distributions I

Hi @uness_o7 There are two issues, I think. First, if we were conducting a test of the sample mean (e.g., what is the probability of obtaining a sample mean profit of $25 million next week), then we need the standard error. If we know the population variance (which is not given) we can assume Z = (mean X - µ)/SQRT[σ(p)^2/n]. But realistically (as is also the case in this question) we don't... Hi @uness_o7 There are two issues, I think. First, if we were conducting a test of the sample mean (e.g., what is the probability of obtaining a sample mean profit of$25 million next week), then we need the standard error. If we know the population variance (which is not given) we can assume Z = (mean X - µ)/SQRT[σ(p)^2/n]. But realistically (as is also the case in this question) we don't...
Hi @uness_o7 There are two issues, I think. First, if we were conducting a test of the sample mean (e.g., what is the probability of obtaining a sample mean profit of $25 million next week), then we need the standard error. If we know the population variance (which is not given) we can assume Z... Hi @uness_o7 There are two issues, I think. First, if we were conducting a test of the sample mean (e.g., what is the probability of obtaining a sample mean profit of$25 million next week), then...
Replies:
16
Views:
435