The problem isn't heteroskedasticity, that's why it's passing the test. The problem is that your model doesn't work well for (at least some of) your observations.
I've never seen anyone analyze stock prices without looking at their differences. Try a Dickey-Fuller test for a unit root---I bet t...
I have replied to mpiktas, before Breusch-Pagan I check the series with: Phillips-Perron and KPSS unit root tests. Unfortunately, the series pass these tests. I also check the cointegration with Johansen and the series pass again(cointegrated). What could I do?
Your data do not reject the null in the KPSS and do reject the null in the Phillips-Perron test?
As I said, BP is telling you that heteroskedasticity isn't a problem here, so you don't need to correct for it. The pattern of your residuals suggests that there may be some kind of time trend lurking around if there isn't a unit root; I added that part to my answer.
Don't worry about heteroskedasiticy (you pass BP), worry about your model.
Suggestions to remove spikes in residuals: Try incorporating time trends or seasonality; try using logs of prices instead.
If you really worry about heteroskedasticity for some reason, even though BP says that you don't need to and your plots suggest that your model needs to be tweaked instead, you can use robust standard errors.
the PP reject the null and KPSS can't reject the null. So the series should not have unit root and should be stationary...and also johansen procedure tell me that the series are cointegrated. My problem is not to correct it, I only what to delete the pair (stockA - stockB) that don't have constant variance. BP test is saying that the data is homoscedastic but is not. So what is the method that i can use to understand if this "variance" is constant for real ?
as you surely understand I need to do the linear regression to know the coefficient, EVERY stock of A how many stocks of B I need to have? If i remove spikes, or doing any other change I cant get fixed coefficients.
When I look at your plots, I don't see heteroskedasticity---I see areas where the model seems inappropriate. Also, you don't want to throw heteroskedastic data away; instead, you correct it using weighted least squares or robust standard errors. I don't understand what you mean by "EVERY stock of A how many stocks of B I need to have?"
so now, after all those tests i would know if the variance is constant.....why? because as you saw i get a lot of plots that shown different variance.....example: at the begginning there is a big more and then flat..... i only want pair with the same variance (less or more)
I mean: prices[,1] is the first stock and prices[,2] is the second stock
When it comes to testing for unit roots, it's best to test each variable before you put them into a regression. Regression only makes sense when the included variables are stationary, as opposed to just the residuals themselves being stationary. Hence, I would test whether the price of stock A is stationary and whether the price of stock B is stationary.
i mean, when i do a linear regression i get the coeffients to understand for 1 stockA how many stocks of b do i have to buy to have the same "value" (less or more)
When you say that the residuals are bigger, note that they are bigger in a positive direction. Heteroskedasticity is about spread. If heteroskedasticity was the real problem, you would see residuals spread highly above and below 0.\
yes i could do it...but i don't know if there is a lot of sense because as i told you i have to "use" a pair...so stock A and stock B.....so maybe stock A is not stationary but if it is compared to another it should be.
You have a bunch of points way above 0, but few below in some points and the opposite situation in others. This makes me believe that there is some kind of missing variable or pattern; a time trend, for instance.
My opinion is that the negative spike at around 180 in your index or 14 in your fitted values makes me wonder whether the linear model is working well for those points. I would worry about this before I worried about heteroskedasticity, a point echoed by the results of the BP test that you're getting. If you aren't worried about this, but are worried about heteroskedasticity, all you have to do is apply robust standard errors and you're finished.
No, you don't have to remove those pairs. Robust standard errors corrects for their heteroskedasticity.
Also, note that heteroskedasticity doesn't give you bad coefficients, only bad standard errors.
Indeed, if you use robust standard errors, your coefficients are exactly the same as they are under OLS.
You could do weighted least squares, which is more complicated and I wouldn't recommend it for your particular situation. This is another way to correct for heteroskedasticity. In neither case do you remove any data.
one moment....I told heterodastic because i find on wikipedia that heterodastic has different variance....so i need to find homoscedastic variance....but if it is not a good test.. is not a problem for me...
so one moment....recap, please:
1. UNIT ROOT TESTS
2. COINTEGRATION TESTS
3. ?
as i told you the link i gave you has a good spread for me...i need to have this kind of spread
I'm sorry, what are you asking? What procedure to follow? I 1. Test every variable in my model for a unit root. Take a difference if there is one. My guess is that you test each price, as opposed to the residuals from your regression, you'll get unit roots. 2. Run your regression (you don't need to worry about cointegration if you fix unit roots in step 1). 3. You should test your residuals for serial correlation/autocorrelation in the context of time series data. 4. Apply robust standard errors to correct for heteroskedasticity and, potentially, autocorrelation.
What do you mean by "i need to have this kind of spread"?
yes the procedure to follow....i need this spread because i'm studing pair trading, so i need to have pairs (Stocks) that have constant variance but after N days they reconvert to the mean.... i can know that with UNIT Root but as i told you i don't want to use pair that have different moves...only constant.... .I read your procedure
so 1 ok, 2 ok.....about the third point are you referring to Durbin-Watson test ?
So are you saying that you need pairs with constant variance because: (1) You need this assumption to get good estimates from OLS or (2) Because those are the stock pairs (A and B) that you are interested in finding?
wow, sure i'm reallyu interesting in econometrics...
i try to exlpain....
i have many stocks.... i have to compare two stocks each time... example:
AAA - BBB
AAA - CCC
(are the symbols)
then....i do all the test i wrote you because...i need to find a good pair that their "errors" (divergence) are not too much (<---probably i wrote it very very wrong in english :)
Suppose that the price of AAA is 10 and BBB is 1. The coefficient may be 2. This would say that on the day when AAA=10 and BBB=1, you need 10 BBB to have the same value as AAA. But, for the change in the value in AAA to equal that of BBB on ANY average day, you need 2 BBB for 1 AAA.
always paul teetor said: "I forced the zero intercept because of the economic logic of the spread: If one leg of the spread is priced at zero, the other leg should be zero, too. Or, in common sense terms, if one stock is worth nothing, the related stock should be worth nothing, too. If I did not force a zero intercept, the regression might find a non-zero intercept (just by chance), and the intercept would be meaningless and difficult to interpret; but more seriously it would distort the model."
I can't tell what his data look like, but if gld and gdx don't have exactly mean 0, then you actually get biased coefficients. It's usually a bad idea to force the intercept to be 0.
The intercept is positive, so price movements between these stocks are positively related---one goes up, we expect the other to go up. If you were hedging, you'd want the opposite. So you could buy AAA and short BBB to get a lower variance/risk.
If so, you want to minimize the variance of the returns. You shouldn't regress one price on the other, you want to regress the return (today's price minus yesterday's divided by yesterday's) for one on the return for the other.
If you hedge as he's showing you, you get 0 return in expectation. This is what an airline would want to do to avoid getting beat up by price spikes in fuel.
when the spread touch a standard dev it meand that one of the stocks is outoerforming respect to the other...so you will earn when the stocks return to the mean
I'm an airline. I need to buy fuel in the future but I sell tickets today. I want to avoid losing money when fuel goes up. So I buy fuel future. My futures go up, making money, but my costs go up, losing money. On net, I'm even. He's calculating how to come out even.
Suppose that you get a regression of the price of AAA on the price of BBB with a coefficient of $2. Then, if the price of BBB goes up by $1, you expect the price of AAA to go up by $2. If it the price of AAA goes up by only $1, that's less than you would have expected. Maybe you'd want to buy AAA in that case.
Charlie, do you have skype? there we could have more fast chat...i can see you some chart to explain better....then if you want you can remove my account..... I hope not :)
Okay, well I don't know anything about trading really; finance isn't my field. But I'll say this: If the coefficient in your regression is 2, then, if you hold two BBB stocks and sell 1 AAA stock, then you expect the price change in any period to be 0.
wait, one moment...what do you mean? before you told me BG is better then durbin watson, but how to use it with my prices matrix (two list of prices stocks)
Discussion between Dail and Charlie
Discussion between Dail and Charlie