done

data-modeling/seasonality-modeling-WJ.ipynb

@@ -547,14 +547,11 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
+   "cell_type": "markdown",
+   "metadata": {},
    "source": [
-    "![Time Series](../img/zipcode-heat-map.jpg)"
+    "\n",
+    "<img src=\"../img/average price time series.png\" width=\"400\">"
    ]
   },
   {
@@ -565,29 +562,33 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<img src=\"../img/1 difference.png\" width=\"400\">\n",
+    "\n",
+    "This looks a lot better so then we can look at the ACF and PACF graphs to estimate the parameters of the ARIMA model. The ACF supports our analysis from the averages in that there is high autocorrelation in the multiples of lag=7.\n",
+    "\n",
+    "<img src=\"../img/ACF.png\" width=\"400\">\n",
+    "<img src=\"../img/PACF.png\" width=\"400\">\n",
+    "\n",
+    "Lastly, we use the forecast package in R to have it choose the best model based on lowest AIC. We ultimately come up with a model of ARIMA(4,0,3) as highlighted by this output from R\n",
+    "<img src=\"../img/arima model.png\" width=\"400\">\n"
+   ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "However, this area perhaps is the most promising because it shows that many Airbnb listers are not taking advantage of dynamic pricing by the day of the week, something that is important to establish optimal pricing. Already, there are some promising results-- people should price Friday and Saturday the highest and Tuesday and Wednesday the lowest. With further refinements to our model, such as looking at various seasonal time series models, hopefully people can look at the trends and be able to price their AirBnB listings more appropriately with more concrete percentage change suggestions.\n"
+    "This was just a beginning exploration, however with more comprehensive data, this type of modeling could prove to be very powerful for understanding the seasonal nature of the pricing data. With only one year at our disposal though, it is hard to project forward prices and understand annual pricing trends. However, this is very promising!"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Seasonality is perhaps the most promising area of the entire project because it shows that many Airbnb listers are not taking advantage of dynamic pricing by the day of the week, something that is important to establish optimal pricing. Already, there are some promising results-- people should price Friday and Saturday the highest and Tuesday and Wednesday the lowest. With further refinements to our model, such as looking at various seasonal time series models, hopefully people can look at the trends and be able to price their AirBnB listings more appropriately with more concrete percentage change suggestions.\n"
+   ]
   }
  ],
  "metadata": {