# Turning general regression into time-series prediction

Suppose you have a general regression model, which behaves like a black-box to you. All you have is a $\ \ \text{train}(X,Y) \ \$ function, where you input your predictor matrix $X \in \mathbb R^{N\times M}$ and target vector $Y \in \mathbb R^N$, as well as a $\ \ \text{predict}(x) \ \$ function which takes a row-vector $x \in \mathbb R^{1\times M}$ and produces the prediction $y \in \mathbb R$.

Consider further the task of time-series prediction, i.e. there is a multivariate time series $\{\mathbf x_0, \mathbf x_1,\ldots\, \mathbf x_t\}$, where $\mathbf x_k \in \mathbb R^{1\times M}$, and you want to predict the outcome $y_{t+n} \in \mathbb R\ \$(here $n>0$, and often $n=1$).

Two common methods to achieve this are

• autoregressive approach: choose an order $q$ and take several samples $\big\{(\mathbf x_{t-q+1},\ldots, \mathbf x_t),y_{t+n} \big\}$ and feed it into your regression model.

• autoregressive–moving-average approach: further add earlier prediction results, i.e. use data $\big\{(\mathbf x_{t-q+1},\ldots, \mathbf x_t),(y_{t-r},\ldots, y_{t+s}),y_{t+n} \big\}$, where $s<n$ (--not necessarily, but I would assume it to be reasonable).

Beside these obvious approaches, do you have other suggestions/references for using a general regression method for time-series prediction? Further comments on the above methods are also welcome.