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  1. MN nnbbb Time series analysis using Box-Jenkins New Home Sales- U.S Bureau of Census 2008-2013 By Dalila Talbi Professor Liqiang Ni Time Series Class 2. Introduction:…
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  • 1. MN nnbbb Time series analysis using Box-Jenkins New Home Sales- U.S Bureau of Census 2008-2013 By Dalila Talbi Professor Liqiang Ni Time Series Class
  • 2. Introduction: The US economy was hit by a severe recession in 2008. The housing market had a direct impact on mortgage markets, construction companies, and home builders, banking sectors and other areas as well. The consequence of this crisis was an increase of default mortgages by home owners, and therefore a large increase of existing homes for sale. In 2009, the Bush administration provided financial support to Fannie Mae and Freddie Mac to rescue the housing market. (1) This initiative and other measures as well helped to correct the housing market in 2010. This project is about new home family houses data analysis from January 2008 until February 2014. The analysis is done using Box Jenkins models, a total of 74 observations. Using R code and Minitab, I first I identify the models inferred from the original data using Box Jenkins models, second I make a quick diagnosis to show which model is the best. Finally use the best model to predict the new home sales value for next 10 years. Model Identification 70635649423528211471 500 400 300 200 100 Index Sales Time Series Plot of Sales  This first model show data not stationary; the data seem to follow a negative trend. Thus I cannot use it for Box Jenkins models and proceed to first difference model. Page 2 of 9
  • 3. 70635649423528211471 10 5 0 -5 -10 -15 -20 Index FirstDifference Time Series Plot of First Difference  This plot does not show exactly stationary data. There is also a trend. These signs violate Jenkins models, thus I proceed to second difference analysis. 70635649423528211471 15 10 5 0 -5 -10 Index Seconddifference Time Series Plot of Second difference  The data is stationary. Few outliers are noticed, but in general, the plot can be used in Box- Jenkins forecasting models. Page 3 of 9
  • 4.  Next I need to examine the behavior of the sample autocorrelation function (SAC) and sample partial autocorrelation function (SPAC) ACF of Original data: 18161412108642 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag Autocorrelation Autocorrelation Function for Sales (with 5% significance limits for the autocorrelations) ACF of first Difference: 18161412108642 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag Autocorrelation Autocorrelation Function for First Difference (with 5% significance limits for the autocorrelations)  Both graphs show the original data and first differences are non-stationary. Thus we proceed to graph SAC and SPAC for the second difference of the sales values. Page 4 of 9
  • 5. 18161412108642 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag Autocorrelation Autocorrelation Function for Second difference (with 5% significance limits for the autocorrelations) 18161412108642 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag PartialAutocorrelation Partial Autocorrelation Function for Second difference (with 5% significance limits for the partial autocorrelations)  Both ACF and SPAC can be interpreted in two ways: 1. TAC dies down and the TPAC cuts off after lag 1 and 4. Thus I can use model autoregressive model : AR (4) 2. TPAC dies down and the TAC cuts off after lag 1, which suggests I use model moving average of order 1 (MA1) Page 5 of 9
  • 6. Diagnostic of possible two models First Model: Autoregressive model: AR (4) c(4,2,0) From above p values for Ljung-Box, not all pvalues > α=.05 thus we reject the adequacy of the model. Second model: model moving average (MA1) Page 6 of 9
  • 7. From above p values for Ljung-Box, all pvalues > α=.05 thus we cannot reject the adequacy of the model , however the ACF spikes at lag 6 [June 2008] , 28 [April 2010] , 67 [August 2013] ACF Lag 6 and 28 analysis: The trough or a negative spike in June 2008 is a reaction of the recession I mentioned earlier in 2008. The existing homes for sale exceed the new home sales offered at that time. It is also important to mention that existing homes follow a seasonal peak in summer starting April and ending in August. Thus the trough seen in June 2008 and April 2010 happen when the housing market was already saturated with exiting homes for sale. Bill McBride analysed existing home sales in summer 2008 and writed “June is an important month for existing home sales; existing home sales usually peak in the June through August period. This is usually about as good as it gets for sales on a NSA basis.” (4) ACF Lag 67 analysis: In 2013, after Bush administration took some measures to correct the housing market, like financing Fannie Mae and Freddie Mac, lowering mortgage rate, … the demand of new homes for sales increased, thus their inventory increased. This allowed a spike in the new homes sales in summer 2013, especially the month of August. “August 2013: “Inventories of new homes for sales rose by 4.3% to 171,000, as demand appears to have waned while home building has been fairly strong. The result of the rise in supply and drop in sales was a jump in the months supply to 5.2 months from 4.3 months in June. The months’ supply is the highest since 5.3 months in January 2012.” According to (https://mninews.marketnews.com/content/analysis-us-july-new-home-sales-plunge- 394000-saar) (5) Forecast 95% Prediction interval Page 7 of 9
  • 8. Based on the table below, I predicted the new home sales forecast for the next 10 years using model 2. For example March 2014 new home sales values show prediction interval [182.3693; 194.6592] Predict2<- predict(fit2, n.ahead = 10); > cbind(predict3$pred, predict3$pred-1.96*predict3$se, predict2$pred+1.96*predict3$se); Time Series: Start = 75 End = 84 Frequency = 1 Predict2$pred predict3$pred - 1.96 * predict2$se Forecast Lower 95% percent Limit 75 188.5143 182.3693 76 189.5757 178.8715 77 190.4885 174.8574 78 191.8498 170.8545 79 192.8347 166.6035 80 193.8878 162.0968 81 194.9631 157.2998 82 195.9713 152.1350 83 197.0359 146.6700 84 198.0902 140.8993 Predict2$pred + 1.96 * predict$se Upper 95 % Limit 75 194.6592 76 200.2799 77 206.1195 78 212.8452 79 219.0658 80 225.6789 81 232.6264 82 239.8076 83 247.4018 84 255.2811 Conclusion: Based on the two models MA(1) and AR(4), the diagnosis show that model MA (1) is the best. Thus we can use it to forecast the values of new home sales values. The SPAC show three spikes that can be explained, but in general, this model could be helpful for forecasting this data. Sources Page 8 of 9
  • 9. (1) http://online.wsj.com/news/articles/SB118851742988914064?mod=googlenews_wsj&mg=reno64- (2) http://www.census.gov/econ/currentdata/dbsearch? program=RESSALES&startYear=2008&endYear=2014&categories=FORSALE&dataType=TOTAL&geoLevel=US &adjusted=1&notAdjusted=1&submit=GET+DATA (3) Excel from (US Department of Commerce Census) (4) Graphs: Existing Home Sales by Bill McBride on 7/26/2008 (5) https://mninews.marketnews.com/content/analysis-us-july-new-home-sales-plunge-394000-saar R Code homes<-read.table("C:tesla stockshomes.csv",header=T,sep=",") str (homes); objects(homes) [1] "Date" "Sales" zt<-homes$Sales zt [1] 488 475 465 458 451 435 421 411 398 384 369 352 340 324 311 300 290 282 272 [20] 263 254 243 235 232 231 229 227 216 215 213 210 209 204 199 195 188 185 181 [39] 179 172 168 167 165 164 163 159 156 150 148 146 144 143 144 145 142 145 146 [58] 149 150 148 148 150 152 159 162 161 172 177 185 187 185 186 188 187 First Model: fit1<- arima(homes$Sales, order=c(4,2,0), fixed=c(NA, 0, 0, NA), include.mean=F); tsdiag(fit1); Second model; fit2<- arima(homes$Sales, order=c(0,2,1), fixed=c(NA, 0, 0, 0), include.mean=F); tsdiag(fit2); Page 9 of 9
  • 10. (1) http://online.wsj.com/news/articles/SB118851742988914064?mod=googlenews_wsj&mg=reno64- (2) http://www.census.gov/econ/currentdata/dbsearch? program=RESSALES&startYear=2008&endYear=2014&categories=FORSALE&dataType=TOTAL&geoLevel=US &adjusted=1&notAdjusted=1&submit=GET+DATA (3) Excel from (US Department of Commerce Census) (4) Graphs: Existing Home Sales by Bill McBride on 7/26/2008 (5) https://mninews.marketnews.com/content/analysis-us-july-new-home-sales-plunge-394000-saar R Code homes<-read.table("C:tesla stockshomes.csv",header=T,sep=",") str (homes); objects(homes) [1] "Date" "Sales" zt<-homes$Sales zt [1] 488 475 465 458 451 435 421 411 398 384 369 352 340 324 311 300 290 282 272 [20] 263 254 243 235 232 231 229 227 216 215 213 210 209 204 199 195 188 185 181 [39] 179 172 168 167 165 164 163 159 156 150 148 146 144 143 144 145 142 145 146 [58] 149 150 148 148 150 152 159 162 161 172 177 185 187 185 186 188 187 First Model: fit1<- arima(homes$Sales, order=c(4,2,0), fixed=c(NA, 0, 0, NA), include.mean=F); tsdiag(fit1); Second model; fit2<- arima(homes$Sales, order=c(0,2,1), fixed=c(NA, 0, 0, 0), include.mean=F); tsdiag(fit2); Page 9 of 9
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