Time-series modeling

Question

I'm wondering what methods can be used to predict a future value using past values. I looked into linear regression modeling, but this doesn't allow for a time value.

As an example, say I have an independent variable $y$, that represents annual income for a business. Add a couple of dependent variables that are correlated to $y$: let $x_1$ represent the number of employees at time $t$ and $x_2$ represent the number of customers at time $t$.

I'd like to compute optimal values $a0$, $a1$, and $a2$ for an equation of this form:

$y(t) = a_0 y(t-1) + a_1 x_1(t) + a_2 x_2(t)$

Would a standard linear regression technique apply here, where I simply let $x_0(t) = y(t-1)$, or am I missing something important?

$y(t) = a_0 x_0(t) + a_1 x_1(t) + a_2 x_2(t)$

Answer 1

In essence, you can use regression techniques or black box techniques for predicting values (eg arima models or simplified exponential smoothing methods). If you use regression techniques, the goal is to find good dependent variables (features) that explains the history the most (r squared value) and at the same time don't fit on randomness (p value is an indication). In Python, you can easily program this and test what is best. I actually experience simple arima models are better than regression techniques.