Fix AR equations and reword page (#123)

Author: klane

website/docs/classic-time-series-models/autoregressive-model.md

@@ -2,10 +2,16 @@
 title: Autoregressive Model (AR)
 slug: /autoregressive
 ---
-Assume we are given a time series $$x_1,\cdots, x_t$$, P-th order autoregressive (AR (P)) models the output as a linear function of the input series
+Assume we are given a time series $x_1,\ldots,x_t$, a $P$-th order autoregressive model (denoted AR(P)) is defined as a linear function of the input series $x$:
 
-$x_t = \sum_{i=1}^P a_i x_{t-i} + e_t$
+$$
+x_t = \sum_{i=1}^P a_i x_{t-i} + e_t
+$$
 
-where $\{a_i]}$ are the coefficients. The series $\{e_t\}$ can represent either a controlled external input or noise.
+where $\{a_i\}$ are the model coefficients. The series $\{e_t\}$ can represent either a controlled external input or noise. Note that:
 
-Note that the equation $\sum_{i=1}^p$ a_i x_{t-i} = a_1x_{t-1} + a_2x_{t-2}+\cdots + \cdots + a_Px_{t-P}$ describes a convolution filter. We can implement AR(P) using either a feedforward neural networks with rolling window or a  convolutional network on the entire series.
+$$
+\sum_{i=1}^P a_i x_{t-i} = a_1x_{t-1} + a_2x_{t-2} + \cdots + a_Px_{t-P}
+$$
+
+describes a convolution filter. We can implement AR(P) using either a feedforward neural network with a rolling window or a convolutional network on the entire series.