Update 16_AR.ipynb

typo

Author: clemsadand

16_AR.ipynb

@@ -14,7 +14,7 @@
         "\n",
         "ARIMA is an abbreviation for  <font color='orange'>autoregressive integrated moving average</font> and these models are what the tin says: they include autoregressive, differencing, and moving average components.\n",
         "\n",
-        "A common way to work with time series data, is to decompose it into the trend and seasonality components, and then model thre residual random effect with ARIMA. We can view the trend and seasonality parts as the fixed effect of the model, and the residual effect as the random effect:\n",
+        "A common way to work with time series data, is to decompose it into the trend and seasonality components, and then model the residual random effect with ARIMA. We can view the trend and seasonality parts as the fixed effect of the model, and the residual effect as the random effect:\n",
         "\n",
         "$$\n",
         "\\begin{align*}\n",
@@ -25,7 +25,7 @@
         "\n",
         "Here $r$ is the seasonality period.\n",
         "\n",
-        "In this lecture we are interested in looking at time series structure through the temporal random effects lens. I.e. we assume that that trend and seasonality have already been deducted $x_t := y_t - \\mu_t$. We will consider a specific subclass of ARIMA family. Namely, the autoregressive models.\n",
+        "In this lecture we are interested in looking at time series structure through the temporal random effects lens. I.e. we assume that trend and seasonality have already been deducted $x_t := y_t - \\mu_t$. We will consider a specific subclass of ARIMA family. Namely, the autoregressive models.\n",
         "\n",
         "<font color='orange'>Autoregressive</font> models are statistical models that use a linear combination of past observations of a time series $x_{t-1}, x_{t-2},... $ to predict future values, where each observation is regressed on previous observations.\n",
         "\n",
@@ -617,7 +617,7 @@
       "source": [
         "## Random walk model\n",
         "\n",
-        "Another class of widely used models for time series datat is the random walk. It is a stochastic process where future values are dependent on the current value and a random shock. Here's a description of the random walk model:\n",
+        "Another class of widely used models for time series data is the random walk. It is a stochastic process where future values are dependent on the current value and a random shock. Here's a description of the random walk model:\n",
         "\n",
         "$$\n",
         "x_t = x_{t-1} + \\epsilon_t.\n",