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If I have two variables that have different sampling frequencies, one of the first steps is to align the frequencies; could someone explain the intuition of this alignment without being too technical. I am reading some theory on doing MIDAS regression and can't grasp this concept.

What does it mean to align data frequencies? for my case; I have a lower frequency variable Yt which is sampled monthly, and one higher frequency variable that is sampled daily.

dayum

For my purposes I need only one explanatory variable, so my mapping should only require the first row of the matrix.

A simple example would help me a lot!

Thank you

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Well in this particular document (of which I am one of the authors and from which the excerpt was taken) aligning time-series means simply forming the matrix $\mathbf{X}$. Here is the simple example. Let $y_t$ be a quarterly time series and $x_\tau$ be a monthly time series. Suppose we are interested in a model, where we try to explain what happens to $y$ in one quarter using the the monthly data in that quarter. So for quarter $t=1$ we have the monthly data $\tau=1,2,3$. Then the MIDAS regression model is the following:

$$y_t=x_{3t}\beta_0+x_{3t-1}\beta_1+x_{3t-2}\beta_2+\varepsilon_t$$

In this case we aligned high frequency variable $x_\tau$ into a vector $X_t=[x_{3t},x_{3t-1},x_{3t-2}]$. This operation can be called embedding, or another term.

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  • $\begingroup$ Hey mpiktas, so will I be right if I say the main purpose of aligning data frequency is to get a common time notation between the Y variable and X variable? We can throw away the 'τ' notation and switch it to 't' notation; because in terms of doing regression calculations all we care about is how much the HF lagged variables are affecting the LF variables, and not how the sampling frequencies differ between the two variables. $\endgroup$ Commented Dec 2, 2013 at 8:28
  • $\begingroup$ Yes, we can say that. $\endgroup$
    – mpiktas
    Commented Dec 2, 2013 at 8:43
  • $\begingroup$ thanks for your answer and example, the rest of the excerpt is easy to understand now! $\endgroup$ Commented Dec 2, 2013 at 8:52

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