Update autoregressive-model.md

Author: yuqirose

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

@@ -2,8 +2,10 @@
 title: Autoregressive Model (AR)
 slug: /autoregressive
 ---
-Assume we are given a time series $$x_1,\cdots, x_t$$, autoregressive (AR (p)) models the output as a linear combination of the input sequence
+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
 
-$x_t = \sum_{i=1}^p a_p x_{t-i} + e_t$ 
+$x_t = \sum_{i=1}^P a_i x_{t-i} + e_t$ 
 
-where $\{e_t\}$ can represent etierh a controlled external input or noise.
+where $\{a_i]}$ are the coefficients. The series $\{e_t\}$ can represent either a controlled external input or noise.
+
+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.