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In the Johansen methodology there are five models unrestricted constant and unrestricted trend unrestricted constant and restricted trend unrestricted constant and no trend restricted constant and no trend no constant and no trend. As these models are nested they can be tested sequentially using likelihood ratio tests. For the usual sample sizes these ...

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Machine learning is a very wide field. Most often it is used for classification or regression tasks when you have labelled data to train the model. For example you show thousands of labeled pictures with an apple and computer "learns" what set of features gives high probability that picture contains an apple (for example, round, red etc). Now in your case ...

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The factor models are based on the following linear regression model: $(R_t - R_f)$ = $\alpha$ + $\beta_{mkt}$*$(R_{mkt} - R_f)$ + $\sum\limits_{i=1}^n {x_{k,t}}$ + $\epsilon_t$ $\alpha$ is the regression model intercept and indicates the portfolio performance in excess to the market excess return and the other factor; It has to be strictly positive and ...

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The R function you have to use is the lm() function. On QuickR you can find a simple and clear tutorial on how to estimate a linear (multiple) regression model generally using the lm(). As further reference, I suggest you to read the Introducing R tutorial about linear model by G. Rodriguez. I did not read the paper you cited, but, anyway, you should ...

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The relation between volume and the price dynamics (via volatility and jumps), has been explored by various academic papers. Just cite this one and its contained references: Wang, T., & Huang, Z. (2012). The relationship between volatility and trading Volume in the Chinese Stock Market: A volatility decomposition perspective. Annals of Economics and ...

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