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I have 2 stocks and How should I decide on the independent variable while testing for co integration? We can not say which one is dependent on other. We can consider any one of them as independent but which stock as independent variable would make more sense? 1. S1 ~ S22. S2 ~ S1how to decide between 1 and 2? Another question:Let us say we want to analyze pairs with basket of stocks. While regressing one basket of stocks vs the other basket of stocks, which basket should be on right and which should be on left?

Use an orthogonal regression, then it doesn't matter.

one can have a look at 3.2 Total Least Squares of Paul Teetor's paper Better Hedge Ratios for Spread Trading .here, pb273 comments that orthogonal regression is "far more unstable" than regression of A on B or B on A.

How to choose the dependent variable and set of independent variables if I regress S1 ~ S2+S3+S4Where S1,S2,S3,S4 are 4 different stock price.How to decide S1 should be dependent, or S2, S3, S4?

Ordinary regression assumes that the independent variables (the right-hand side of your eqn.) have no noise, measurement imperfections, etc. and that only the value of the dependent variable has such disturbances. So if one stock price is "imperfect" and the rest are "perfect" then that's your answer.But if the independent variables do have measurement error, then you get biased results.Methods such as orthogonal regression and total least squares can cope with the situation in which all stock prices contain some noise or error.

Can we say like this? Let us say variance (S1) > variance(S2) and variance (S1) > variance(S3) andvariance (S1) > variance(S4)Then, can we say the variable which has highest variance should be dependent variable? This is true for the case like S1 ~ S2. But not sure about basket on one side and single stock on another.

QuoteOriginally posted by: humtumiitI have 2 stocks and How should I decide on the independent variable while testing for co integration? We can not say which one is dependent on other. We can consider any one of them as independent but which stock as independent variable would make more sense? 1. S1 ~ S22. S2 ~ S1how to decide between 1 and 2? Market Cap is very well test. If s1 - 10Billion and s1 - 2Billion, s1 independent, s2-dependent

QuoteOriginally posted by: PavelGQuoteOriginally posted by: humtumiitI have 2 stocks and How should I decide on the independent variable while testing for co integration? We can not say which one is dependent on other. We can consider any one of them as independent but which stock as independent variable would make more sense? 1. S1 ~ S22. S2 ~ S1how to decide between 1 and 2? Market Cap is very well test. If s1 - 10Billion and 21 - 2Billion, s1 independent, s2-dependent

QuoteOriginally posted by: PavelGQuoteOriginally posted by: PavelGQuoteOriginally posted by: humtumiitI have 2 stocks and How should I decide on the independent variable while testing for co integration? We can not say which one is dependent on other. We can consider any one of them as independent but which stock as independent variable would make more sense? 1. S1 ~ S22. S2 ~ S1how to decide between 1 and 2? Market Cap is very well test. If s1 - 10Billion and s2 - 2Billion, s1 independent, s2-dependent

QuoteOriginally posted by: PavelGQuoteOriginally posted by: PavelGQuoteOriginally posted by: humtumiitI have 2 stocks and How should I decide on the independent variable while testing for co integration? We can not say which one is dependent on other. We can consider any one of them as independent but which stock as independent variable would make more sense? 1. S1 ~ S22. S2 ~ S1how to decide between 1 and 2? Market Cap is very well test. If s1 - 10Billion and s2 - 2Billion, s1 independent, s2-dependent

In co integration relationship for pairs trading, we regress S1 ~ S2 without intercept. But we know, regression without intercept increases R square dramatically. How to handle this? R square change dramatically, how can we say that this fitting is not spurious?