{"id":8402,"date":"2021-07-26T10:05:01","date_gmt":"2021-07-26T10:05:01","guid":{"rendered":"https:\/\/wealthrevelation.com\/data-science\/2021\/07\/26\/predicting-zori-using-covid-19-and-census-data\/"},"modified":"2021-07-26T10:05:01","modified_gmt":"2021-07-26T10:05:01","slug":"predicting-zori-using-covid-19-and-census-data","status":"publish","type":"post","link":"https:\/\/wealthrevelation.com\/data-science\/2021\/07\/26\/predicting-zori-using-covid-19-and-census-data\/","title":{"rendered":"Predicting ZORI using COVID-19 and Census Data"},"content":{"rendered":"<div>\n<p><span><strong>In the process of editing<\/strong><\/span><\/p>\n<h2>Introduction<\/h2>\n<p><span>The COVID-19 pandemic drastically shifted consumer preferences in housing. This created a scenario that made housing prices difficult to model, with price variability changing constantly as the pandemic continues.<\/span><\/p>\n<p><b>Objective<\/b><\/p>\n<p><span>To observe these changes and how they will affect the future of the market, we created models that can accurately forecast and predict the Zillow Observed Rent Index (ZORI) by using historical ZORI, US Census, and Covid-19 data. Predictions can be used to see which areas are recovering from Covid-19 more quickly. This kind of information can be useful to:<\/span><\/p>\n<ul>\n<li><span>Government Organizations: find areas in need of resources<\/span><\/li>\n<li><span>Investors: find which neighborhoods to start businesses in and which to stay away from<\/span><\/li>\n<li><span>Business Owners: gain insight into your own neighborhood to decide when to increase or decrease inventory<\/span><\/li>\n<\/ul>\n<h2>Datasets<\/h2>\n<p><a href=\"https:\/\/www.zillow.com\/research\/data\/\"><b>Zillow Observed Rent Index<\/b><\/a><\/p>\n<ul>\n<li><span>Monthly rent prices of the center 20% (40th-60th percentile) of the entire observed market, Smoothed &amp; Seasonally adjusted. (Jan. 2014 &#8211; June 2021)<\/span><\/li>\n<li><span>1743 rows by 93 cols.<\/span><\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/data.census.gov\/cedsci\/\"><b>US Census Data<\/b><\/a><\/p>\n<ul>\n<li><span>Yearly data collected and\/or predicted by the US Census Bureau pulled from BigQuery (2014-2018)<\/span><\/li>\n<li><span>Housing, Income and Demographic datasets pulled from the Census Website (2019)<\/span><\/li>\n<li><span>33,120 rows by 232 cols, 6 years of data<\/span><\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/github.com\/CSSEGISandData\/COVID-19\"><b>COVID-19 Data from Johns Hopkins<\/b><\/a><\/p>\n<p><span>Data collected by the Johns Hopkins Center for Systems Science and Engineering (JHCSSE)<\/span><\/p>\n<ul>\n<li><span>Daily counts of US COVID-19 cases and deaths by US county (Jan 22 2020 &#8211; July 17 2021)<\/span><\/li>\n<li><span>3342 rows by 555 cols<\/span><\/li>\n<\/ul>\n<h2>Data Cleaning and Feature Engineering<\/h2>\n<h3><strong>ZORI Data:<\/strong><\/h3>\n<p><strong>Missing Value Interpolation<\/strong><\/p>\n<ul>\n<li><span>Interpolated linearly from Jan. 2014 (start) to June 2021 (end)<\/span><\/li>\n<li><span>Any ZORIs missing at the time period\u2019s start or end were calculated using that year\u2019s mean change in ZORI\u00a0<\/span><\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<p><strong>Outliers<\/strong><\/p>\n<ul>\n<li><span>Each ZIP code was checked for any ZORI that was &gt;3 stddevs away from that year\u2019s mean rent price<\/span><\/li>\n<li><span>No outliers were found, and no ZIP codes were removed<\/span><\/li>\n<\/ul>\n<h3>Census Data:<\/h3>\n<p><strong>Raw Data<\/strong><\/p>\n<ul>\n<li><span>2014-2018 data comes from 5 BigQuery Census Datasets<\/span><\/li>\n<li><span>165,600 observations (33,120 ZIP codes x 5 years of data)<\/span><\/li>\n<li><span>232 Features<\/span><\/li>\n<\/ul>\n<p><strong>Missing Data<\/strong><\/p>\n<ul>\n<li><span>Removed 4 Features that had 5,000+ null values and little to no correlation with the target feature.<\/span><\/li>\n<\/ul>\n<p><strong>Combining Census Years: 2014-2018 and 2019<\/strong><\/p>\n<ul>\n<li><span>Could only pull 47 matching features between the datasets<\/span><\/li>\n<li><span>2019 census data is duplicated for 2020, will be replaced with actual data in 9\/2021<\/span><\/li>\n<\/ul>\n<p><strong>Feature Selection<\/strong><\/p>\n<ul>\n<li>Reduced to 36 Features using a Forward Stepwise function<\/li>\n<\/ul>\n<p><span>Ended with 13,920 observations (1740 zip codes*8 Years) and 36 Features<\/span><\/p>\n<h3>Covid-19 Data:<\/h3>\n<p><strong>Cleaning<\/strong><\/p>\n<p>The JHCSSE provides a daily count of global COVID-19 cases and deaths from 01\/22\/2020 to present day<\/p>\n<ul>\n<li><span>Removed all observations in non-US counties<\/span><\/li>\n<li><span>Capped data to be from 01\/22\/2020 to 06\/30\/2021<\/span><\/li>\n<li><span>Cumulative numbers of cases and deaths were the only metrics kept alongside location &amp; time attributes<\/span><\/li>\n<\/ul>\n<p><span>The count of cases and deaths on the last day of each month was used as that entire month\u2019s case and death count.\u00a0<\/span><\/p>\n<p><strong>Feature Engineering<\/strong><\/p>\n<p><span>After cleaning &amp; filtering the data, we engineered features for \u2018New Cases\u2019 and \u2018New Deaths\u2019, which were defined as the current month\u2019s cases &amp; deaths subtracted from the previous month\u2019s. We then had to convert county-level COVID cases and death metrics to the corresponding ZIP codes within each county. To do that, we assumed that the COVID cases and deaths were proportional to each ZIP Code\u2019s population within the county, using ZIP Code and county information from the Census data.<\/span><\/p>\n<p><span>This \u2018New Case Rate\u2019 feature would be the exogenous variable we will use later in our SARIMAX model, which is a seasonal time-series model with exogenous inputs.<\/span><\/p>\n<h3><b>Combining Datasets:<\/b><\/h3>\n<p>To combine all three datasets, first we <span>joined COVID-19 data with the Census data on the county &amp; state, then\u00a0<\/span><span>COVID-19 case\/deaths were split to the ZIP Code level based on the (population of ZIP code) \/ (total county population), and finally, this data was combined with the ZORI <\/span>dataset. After matching all datasets together, <span>103 ZIP codes were not included in the SARIMA and SARIMAX models due to the lack of available corresponding Census\/COVID data<\/span><\/p>\n<h2><strong>Models and Methods<\/strong><\/h2>\n<p>The following models were implemented to achieve our objective:<\/p>\n<ol>\n<li>Multiple Linear Regression (<b>MLR<\/b>) to predict the yearly and semiannual ZORI in 2021<\/li>\n<li>Vector AutoRegression (<b>VAR<\/b>) to forecast the ZORI from 2020 to mid-2021<\/li>\n<li>Seasonal Autoregressive Integrated Moving Average (<b>SARIMA<\/b>) to forecast ZORI in the first half of 202<\/li>\n<li>Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors (<b>SARIMAX<\/b>), using COVID-19 data as the exogenous variables, to forecast ZORI in the first half of 2021<\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td>\n<p><b>Model<\/b><\/p>\n<\/td>\n<td>\n<p><b>Features Used<\/b><\/p>\n<\/td>\n<td><b>Target<\/b><\/td>\n<\/tr>\n<tr>\n<td>MLR<\/td>\n<td>\n<p>ZORI (yearly, semiannually), Census 2014-20<\/p>\n<\/td>\n<td>\n<p>ZORI (semiannually) from<\/p>\n<p>01\/2021 to 06\/2021<\/p>\n<p>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>VAR<\/td>\n<td>\n<p>ZORI (monthly) from 01\/2014 to 12\/2019<\/p>\n<\/td>\n<td>\n<p>ZORI (monthly) from<\/p>\n<p>01\/2020 to 06\/2021<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p>SARIMA<\/p>\n<\/td>\n<td>\n<p>ZORI (monthly) from 01\/2014 to 12\/2020<\/p>\n<\/td>\n<td>\n<p>ZORI (monthly) from<\/p>\n<p>01\/2021 to 06\/2021<\/p>\n<p>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\n<p>SARIMAX<\/p>\n<\/td>\n<td>\n<p>ZORI (monthly) from 01\/2014 to 12\/2020;\u00a0 COVID-19 (monthly) from 1\/2020-12\/2020<\/p>\n<\/td>\n<td>\n<p>ZORI (monthly) from<\/p>\n<p>01\/2021 to 06\/2021<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong>MLR Model<\/strong><\/p>\n<p><span>Using the available data, we created models to predict:<\/span><\/p>\n<ul>\n<li><span>The current rent price<\/span><\/li>\n<li><span>The rent price in 1 year while including the current rent price as a feature<\/span><\/li>\n<li><span>The rent price in first 6 months of 2021 with the last 6 months of 2020 as the test set, using a biannual aggregation; t<\/span><span>raining on the full data for the full time period, and data for only the pandemic time period<\/span><\/li>\n<\/ul>\n<p><b>MLR Results<\/b><\/p>\n<p><span>The first 2 models were used to gauge how well MLR could predict the ZORI. This give us a basis to compare the pandemic models to.<\/span><\/p>\n<p><span>We, then, included the current ZORI and forecasted for the ZORI in one year. This gave us a much worse score, as expected. The model was trained on a time period without Covid-19 to predict on a period with Covid-19.<\/span><\/p>\n<p><span>It would obviously result in a bad model.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Model Attributes (Yearly)<\/b><\/td>\n<td><b>Test Scores<\/b><\/td>\n<\/tr>\n<tr>\n<td>Current Rent Price w\/ PCA &#8211; 2019 (Non-Pandemic)<\/td>\n<td><span>0.7304<\/span><\/td>\n<\/tr>\n<tr>\n<td>Rent Price in 1 Year w\/ PCA &#8211; 2020 (Includes Pandemic)<\/td>\n<td><span>0.6602<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><span>For the next 2 models, the\u00a0 data was redone to aggregate and interpolate semiannually. This was done to utilize the ZORI from 1\/2021 &#8211; 6\/2021, as the pandemic data was limited to the past 18 months.<\/span><\/p>\n<p><span>When training on 2014-2020 data, we got a decent score, but it improved much more when only training on 2019-2020 data<\/span><\/p>\n<p><span>Non-pandemic data seemed to skew the data away from the actual values.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Model Attributes (biannually)<\/b><\/td>\n<td><b>Test Scores<\/b><\/td>\n<\/tr>\n<tr>\n<td><span>Rent Price in 6 months w\/ PCA &#8211; 2020 (Pandemic)<\/span><\/td>\n<td><span>0.9593\u00a0 (train on 1\/2014-6\/2020)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span>Rent Price in 6 months w\/ PCA &#8211; 2020 (Pandemic)<\/span><\/td>\n<td><span>0.9966 (train on 1\/2019-6\/2020)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76446 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/act-pred-rent-6mo-part-513282-pxmbUPY3.png\" alt=\"\" width=\"817\" height=\"554\"><\/p>\n<p><b>VAR Model<\/b><\/p>\n<ul>\n<li><span>VAR Model was run on all 1743 ZORI ZIP codes as a \u2018baseline\u2019 time series forecast<\/span><\/li>\n<li><span>VAR Model proved to not be a great predictor based on RMSE scores<\/span><\/li>\n<li><span>However, it was a better model overall than ARIMA, ARMA, and VARMAX<\/span><\/li>\n<\/ul>\n<p><b>VAR Results<\/b><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76447 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-9-772536-73gcbAug.png\" alt=\"\" width=\"270\" height=\"194\"> <img loading=\"lazy\" class=\"size-full wp-image-76448 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-8-739213-nDDVmt2P.png\" alt=\"\" width=\"414\" height=\"512\"><\/p>\n<p><span>Looking at the best RMSE\u2019s and 5 worst RMSE\u2019s\u00a0 gave us a list of ZIP codes to highlight in later models&#8211; can SARIMA and SARIMAX yield accurate predictions were VAR cannot?<\/span><\/p>\n<p><b>SARIMA Parameter Tuning<\/b><\/p>\n<p><span>Grid search was performed to determine the optimal order, seasonal order, and trend parameters for SARIMA models <\/span><span>on a monthly mean of ZORI inputs. <\/span><span>The optimal parameters yielded an AIC of 8.0:<\/span><\/p>\n<ul>\n<li><span>Order (p, d, q) = (0, 0, 1)<\/span><\/li>\n<li><span>Seasonal (P, D, Q, seasonality) = (0, 1, 0, 12)<\/span><\/li>\n<li><span>Trend =\u00a0 \u2018t\u2019\u00a0<\/span>\n<ul>\n<li><span>(linear parameter controlling the deterministic trend polynomial)<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span>The same parameters were used when modeling with SARIMAX.\u00a0<\/span><\/p>\n<p><strong>SARIMA Results<\/strong><\/p>\n<p>We created seasonal 6 month forecasts for each of the 1640 available ZIP Codes, at first with no exogenous COVID features, for our first model. A summary table is below, with the Root Mean Square Errors the metric we were most interested in minimizing.\u00a0<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76417 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-3-844995-EFDVEG4U.png\" alt=\"\" width=\"284\" height=\"192\"><img loading=\"lazy\" class=\"size-full wp-image-76414 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-595067-JT6BH4n1.png\" alt=\"\" width=\"540\" height=\"638\"><\/p>\n<p>From our initial VAR model we were able to get a list of five ZIP Codes that VAR performed well and was able to predict rent indices accurately, and five other ZIP Codes that had very high root mean squared errors, and we wanted to get a sense of how predictions looked from the SARIMA model. The SARIMA model results of those ZIP Codes are below.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76421 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-7-326374-nNEVkIXk.png\" alt=\"\" width=\"554\" height=\"588\"><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76419 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-5-335459-8yBaH8Ko.png\" alt=\"\" width=\"1568\" height=\"1412\"><\/p>\n<p><strong>SARIMAX Results<\/strong><\/p>\n<p>Next we created models for each ZIP Code with exogenous factor data from the COVID &amp; Census data&#8211;we used &#8216;Monthly New Cases&#8217; as\u00a0 a percent to total ZIP Code population as the outside variable, with the target variable still being the rent index. We could then compare this model with the previous SARIMA model, because inputs and target variables were the same for the two seasonal models. Summaries of the full SARIMAX model are below.<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76416 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-2-990020-UfHyOa3i.png\" alt=\"\" width=\"328\" height=\"194\"><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76414 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-595067-JT6BH4n1.png\" alt=\"\" width=\"540\" height=\"638\"><\/p>\n<p>Just as with the SARIMA model, we further looked into the SARIMAX forecasts for previous models&#8217; good and bad predictions&#8211;that table and graph are below (we are still mainly interested in minimizing the RMSE for our forecasts).<\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76420 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-6-819806-0nxKzh0x.png\" alt=\"\" width=\"558\" height=\"570\"><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76418 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-4-045858-CGykH1tm.png\" alt=\"\" width=\"1422\" height=\"1362\"><\/p>\n<p><b>Results Summary<\/b><\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p><b>Model<\/b><\/p>\n<\/td>\n<td>\n<p><b>Target<\/b><\/p>\n<\/td>\n<td>\n<p><b>Results<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p><span>MLR<\/span><\/p>\n<\/td>\n<td>\n<p><span>ZORI (semiannually) in 2021<\/span><\/p>\n<\/td>\n<td>\n<p><span>R^2: 0.9966 test on 7\/2020 &#8211; 12\/2020<\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p><span>VAR<\/span><\/p>\n<\/td>\n<td>\n<p><span>ZORI (monthly) from<\/span><\/p>\n<p><span>01\/2020 to 06\/2021\u00a0<\/span><\/p>\n<\/td>\n<td>\n<p><span>RMSE Mean (all predictions, 18 months): $102.83<\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p><span>SARIMA*<\/span><\/p>\n<\/td>\n<td>\n<p><span>ZORI (monthly) from<\/span><\/p>\n<p><span>01\/2021 to 06\/2021<\/span><\/p>\n<\/td>\n<td>\n<p><span>RMSE Mean (all predictions, 6 months): $66.66<\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p><span>SARIMAX*<\/span><\/p>\n<\/td>\n<td>\n<p><span>ZORI (monthly) from<\/span><\/p>\n<p><span>01\/2021 to 06\/2021<\/span><\/p>\n<\/td>\n<td>\n<p><span>RMSE Mean (all predictions, 6 months): $69.56<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Comparing Models<\/b><\/p>\n<p><span>Overall, MLR seems promising for predicting the ZORI during the pandemic at the yearly and semiannual level, only when limited to time periods where Covid-19 was a factor. The trends in 2014 to 2018 influence the model too much when included, worsening the score.<\/span><\/p>\n<p><span>SARIMA proved to be our best time-series model, yielding a lower overall RMSE for 55% of ZIP Codes compared to SARIMAX (45% with lower RMSE)<\/span><\/p>\n<p><span>Both of these models had a lower RMSE than VAR, but that may be because they were both trained on 2020 data (VAR was not).<\/span><\/p>\n<p><b>SARIMAX versus SARIMA<\/b><\/p>\n<p><span>One major downside of SARIMAX is that it requires COVID-19 and Census exogenous actual inputs in order to forecast.\u00a0<\/span><\/p>\n<p><span>Future Census and COVID data can be forecasted separately and then passed as the exogenous variable. However, the accuracy lost to forecasting on top of forecasts would likely increase the RMSE of SARIMAX models, as compared to SARIMA.<\/span><\/p>\n<p><span>The mean of SARIMAX\u2019s RMSE predictions was slightly higher than that of SARIMA, <\/span><span>but it forecasted with a lower RMSE for almost half (45%) of the data.\u00a0<\/span><\/p>\n<p><span>Further work needs to be done to determine qualitative aspects of the ZIP codes whose better predictor was SARIMAX versus SARIMA.<\/span><\/p>\n<p><b>Comparing SARIMA and SARIMAX RMSE<\/b><\/p>\n<p><span>SARIMAX yielded an improved (lower) RMSE for 741 ZIP codes (45%, out of 1640):<\/span><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76458 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/xs-rmse-stats-992375-MFki0rWT.png\" alt=\"\" width=\"324\" height=\"120\"><\/p>\n<p><b>rmse_diff = x_rmse &#8211; s_rmse (<\/b><b>Where x_rmse is SARIMAX RMSE <\/b><b>and s_rmse is SARIMA RMSE)<\/b><\/p>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76457 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-10-538490-in0qnbZg.png\" alt=\"\" width=\"512\" height=\"152\"><\/p>\n<p>\u00a0<\/p>\n<h3>Conclusion<\/h3>\n<p><b>SARIMA and SARIMAX <\/b><\/p>\n<p><span>Models were created to accurately predict ZORI by ZIP code. Each modeled provided a different insight into where ZORI are increasing and decreasing the most.<\/span><\/p>\n<p><span>SARIMA and SARIMAX models each performed better on about half of the dataset each. We would follow-up to determine what about those ZIP codes led to better predictions with one models vs the other.<\/span><\/p>\n<p><span>Including COVID-19 as exogenous was not as useful as we had hoped. The pandemic influenced many markets; pinpointing the best data to use for exogenous is required. Furthermore, it is reasonable to infer that as populations moved out of highly-populated ZIP codes, they further tipped rent prices more favorably for the less-populated ZIP codes.<\/span><\/p>\n<p><b>Multiple Linear Regression<\/b><\/p>\n<p><span>We used our final model on features from the 1\/2021 &#8211; 6\/2021 to\u00a0 predict the ZORI in the 7\/2021-12\/2021. We calculated the percent change between the 2 to create the chart you see on the right.<\/span><\/p>\n<p><span>It shows the largest increases and decreases in rent. From this, you can find:<\/span><\/p>\n<ul>\n<li><span>areas for investment<\/span><\/li>\n<li><span>areas that need more government assistance<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"size-full wp-image-76461 aligncenter\" src=\"https:\/\/nycdsa-blog-files.s3.us-east-2.amazonaws.com\/2021\/07\/alexander-pinkerton\/unnamed-11-225836-FwwJQnVf.png\" alt=\"\" width=\"397\" height=\"512\"><\/p>\n<h3><b>Future<\/b> Work<\/h3>\n<p><span>SARIMAX showed an improved RMSE for many ZIP codes, leading us to believe that improving our exogenous variables we can improve our forecasts:<\/span><\/p>\n<ul>\n<li><span>Find recent\/accurate population data (monthly, by ZIP would be optimal)<\/span>\n<ul>\n<li><span>Or use 2020 census data when it becomes available<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span>Find accurate COVID-19 data by ZIP code<\/span><\/li>\n<li><span>Find other datasets that can be used for exogenous variables<\/span>\n<ul>\n<li><span>Dominant political party during the pandemic<\/span><\/li>\n<li><span>Rates of COVID-19 recovery and\/or vaccination<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span>Conditionally forecast 2021, 2022 ZORI based on whether COVID-19 diminishes or follows current ZIP code\/county trends<\/span><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/nycdatascience.com\/blog\/student-works\/predicting-zori-using-covid-19-and-census-data\/<\/p>\n","protected":false},"author":0,"featured_media":8403,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/posts\/8402"}],"collection":[{"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/comments?post=8402"}],"version-history":[{"count":0,"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/posts\/8402\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/media\/8403"}],"wp:attachment":[{"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/media?parent=8402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/categories?post=8402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wealthrevelation.com\/data-science\/wp-json\/wp\/v2\/tags?post=8402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}