# How to use multi-periods and mult-factors to predict stock price by linear regression?

Give data in $$t_n$$ denoted by $$[x_1^n, x_2^n, ... x_d^n]$$ and label $$y_n$$ to be predicted. We can just train a $$d$$-dimensional linear regression $$y_n=\sum b_ix_i^n$$ to make a prediction. However, I think the data in $$t_{n-1}$$ can also be helpful to predict $$y_n$$. So my way is to concatenate data in $$t_{n-1}$$ and $$t_n$$ by $$[x_1^n, x_2^n, ... x_d^n, x_1^{n-1}, x_2^{n-1}, ... x_d^{n-1}]$$ (i.e., multi-periods data) and use a $$2d$$-dimensional linear regression to predict $$y_n$$.

The problems of my method are: 1st $$[x_1^n, x_2^n, ... x_d^n]$$ and $$[x_1^{n-1}, x_2^{n-1}, ... x_d^{n-1}]$$ seems to be much correlated, so feature can be very redundant. 2nd, some normalization may be conducted on $$[x_1^n, x_2^n, ... x_d^n]$$ and $$[x_1^{n-1}, x_2^{n-1}, ... x_d^{n-1}]$$ to form a good concatenation, but how to do? 3rd, if we think that data in $$t_{n-100}$$ is also help to predict $$y_n$$, then $$100d$$ dimension is very high.

So could anyone solve my above problems? or have other ways to use multi-periods data.