Quant concepts

fullset wrote:
Dude how the f*ck are you a level 1 candidate lol?
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I appreciate the compliment! But seriously, I’ve had a good deal of exposure to statistics, so I try to help where I can. The topics I’ve spent time with just happen to be what the CFAI likes to test!
 
Tickersu - strong concepts I must say.
Just to clarify my confusion once again, by testing the significance of the slope co-efficient, we intend to say that to does the independent variable significantly explain the variation in dependent variable or not. and in order to test the significance, we employ two methods i.e confidence interval and t-stat. For the CI, if the interval does not include zero in it, then we can say with x% (Whatsoever the CI is) that slope co-efficient is significantly different from zero which in turn means that it significantly explains the variation in dependent variable. In the case of t-test, is the calculted t stat exceeds the critical t-value, then we can say that independent variable significantly explains the variation in dependent variable. Am I correct?
 
I want to discuss autocorrelation a bit further.
Suppose yesterday’s stock price is $10. Today, based on yesterday’s stock price, the price predicted by regression is $12. Now, can you please share with me two sets of data which shows the prices of stock x at day 1 to day 7. One data set has no autocorrelation and the other data set should reflect the behavior of autocorrelation. that will help me compare the difference between the two
 
The difference between the R(square) and F-stat is that R(square) explains the variation in dependent variable due to one independent variable whereas F-stat tells us about the significance of a group of independent variables as a whole. Correct?
 
In heteroskedasticity(HR), the variance of residual is not constant across all observations. I am sharing an example, pls let me know if my concept is right. First, I want to tell you what exactly variance is. If the variance in stock price 4, it means that the price of the stock can move (+)(-) 4. If the variance is 6 it means the price can be (+)(-)6. hence the variance has increased from 4 to 6. Now coming to HR, by this we mean that if the variance of the observation changes then HR is present in regression. Here one question arises, why does the variance needs to be constant? If the variance is changing, what effect will it have on regression which makes it unfit for forecasting? Also, tell me what is actually meant by the variance of the residual? very simple and daily life example would help me a lot here
 
In multicollinearity(MC), we say that independent variables are correlated with another. Can somebody please share an example of this case? How does the correlation of independent variables effect the standard errors and co-efficient of standard errors? why are the standard errors are artificially inflated in MC problem? Going through a example is the best way for me to understand any concept. Try and share a daily-life example.
 
What is a ‘estimator’ in a regression equation?
what is meant by an unbiased estimator and a consistent estimator? Pls give examples of each.
 
haiderraza wrote:
Tickersu - strong concepts I must say.
Just to clarify my confusion once again, by testing the significance of the slope co-efficient, we intend to say that to does the independent variable significantly (by significantly I mean in a statistical sense) explain the variation in dependent variable or not. and in order to test the significance, we employ two methods i.e confidence interval and t-stat. For the CI, if the interval does not include zero in it, then we can say with x% (Whatsoever the CI is) that slope co-efficient is significantly different from zero which in turn means that it is a statistically significant predictor of the dependent variable [slope is non-zero]. Note, this doesn’t necessarily mean it’s “good” at predicting the DV, just that there is a statistical relationship, and it is better than nothing.
In the case of t-test, is the calculted t stat exceeds the critical t-value in magnitude, then we can say that independent variable is a statistically significant predictor of the dependent variable (the slope is non-zero). Am I correct? Yes
I only made some edits to clarify that statistically significant does not mean it is practically/economically useful. For example, let’s say we have a simple model (x predicts y). The slope could be statistically different from zero (statistically significant), but the R-squared might be very low or the model standard deviation (SER) could be very large (poor explanatory power and accuracy of x for y). This is possible.
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To answer the question “Is X1 (IV) a statistically useful predictor of Y (DV)?” We can use either the t-test or the confidence interval, or both. The confidence interval gives you more information because it gives you a range for the true value, whereas the test statistic merely lets you make a conclusion for your hypothesis test.
So a confidence interval can let you avoid doing any t-tests. For example, you want to see if the slope is different from zero, so you do a t-test. Significant– now you want to see if the slope is greater than 1, and you conduct another t-test. Your chance of making a Type I Error (compound) has gone up since you are conducting more tests. However, a confidence interval would tell us the answer to both questions in one step.
I think you have the idea!
 
haiderraza wrote:
I want to discuss autocorrelation a bit further.
Suppose yesterday’s stock price is $10. Today, based on yesterday’s stock price, the price predicted by regression is $12. Now, can you please share with me two sets of data which shows the prices of stock x at day 1 to day 7. One data set has no autocorrelation and the other data set should reflect the behavior of autocorrelation. that will help me compare the difference between the two
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Not sure entirely what you mean here. The important thing about autocorrelation is that it can only occur in time-series data. However, the tests (Durbin-Watson), can “detect” autocorrelation in non time-series data (a false alarm). This is why it is important to ONLY test for autocorrelation in time-series data that are likely to exhibit the autocorrelation.
A good way to see autocorrelation is to look at a plot of the model errors (residuals) against time. Since time series data are ordered through time, a plot of the residuals will show a trend if strong autocorrelation is present. For example, the plot may show a long positive trend (positive residuals), followed by a long negative trend (negative residuals), and this can reverse. This would be an example of positive autocorrelation. If the data do not exhibit autocorrelation, the residuals plotted against time would likely not show a pattern like this (again autocorrelation can “appear” in cross sectional data, but this is a false alarm– only do this with time-series data to avoid incorrect conclusions).
 
haiderraza wrote:
The difference between the R(square) and F-stat is that R(square) explains the variation in dependent variable due to one independent variable whereas F-stat tells us about the significance of a group of independent variables as a whole. Correct?
Click to expand...
R-square tells us the percentage of sample variation in the DV explained by the model, however many independent variables are in the model– can be one or many.
The F-statistic for the entire model could be used for a model with one IV or many, it just tells us in a statistical sense how much “better” our model (IVs) are at explaining the DV, than a model using only the average DV value for prediction.
Both can be referring to one or many. However, the F-statistic in regression typically is used for joint hypotheses, as you are saying, many IVs, as a group.
 
haiderraza wrote:
In heteroskedasticity(HR), the variance of residual is not constant across all observations. I am sharing an example, pls let me know if my concept is right. First, I want to tell you what exactly variance is. If the variance in stock price 4, it means that the price of the stock can move (+)(-) 4. If the variance is 6 it means the price can be (+)(-)6. hence the variance has increased from 4 to 6. Now coming to HR, by this we mean that if the variance of the observation changes then HR is present in regression. Here one question arises, why does the variance needs to be constant?If the variance is changing, what effect will it have on regression which makes it unfit for forecasting? Also, tell me what is actually meant by the variance of the residual? very simple and daily life example would help me a lot here
In multicollinearity(MC), we say that independent variables are correlated with another. Can somebody please share an example of this case? How does the correlation of independent variables effect the standard errors and co-efficient of standard errors? why are the standard errors are artificially inflated in MC problem? Going through a example is the best way for me to understand any concept. Try and share a daily-life example.
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I’ve made some posts on these in the past (long posts).Try using the search function, or filter through my posts first. If you still have some questions let me know. This would be a little easier since I am at work.
 
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