Goal Data

• ‘Motor Vehicle and Part Dealers’ - a report/survey from Census Bureau sent to motor vehicle and parts dealers that asks their current sales
• The preliminary sales data is released 2 weeks after the end of each month

• Nowcastic forecast on May sales with two Google Trends already available on May, 2012

Collect Data

• Target variable ‘sales’ (Survey Index from Jan. 2004 to Apr. 2012)
• Source: http://www.census.gov/retail/marts/www/timeseries.html

• Predictor ‘tss’ (Query Index - “Trucks + Sedans + SUVs” of Google Trends from Jan. 2004 to May, 2012)
• Source: http://www.google.com/insights/search/

• Predictor ‘ins’ (Query Index -“Insurance” of Google Trends from Jan. 2004 to May, 2012)
• Source: http://www.google.com/insights/search/

Analyze Data

• My data set (adt) looks like:

##            sales   tss   ins
## 2004-01-01 61146 -0.21 -0.07
## 2004-02-01 65230 -0.28 -0.11
## 2004-03-01 78662 -0.28  0.10
## 2004-04-01 73252 -0.31  0.05
## 2004-05-01 77491 -0.21  0.25
## 2004-06-01 75355 -0.42  0.16

• Verify if target variable (sales) is time-correlated:

## 
##  Box-Ljung test
## 
## data:  coredata(adt$sales)
## X-squared = 61.454, df = 1, p-value = 4.552e-15

• Yes, then plot it:
  
• Since it has large variability, log it, then plot it:
  
• Diff it and acf/pacf it:
  
• There is a seasonal component, so diff it by 12, then acf/pacf it:
• To sum up - baseline model is a seasonal AR-1 model

Model Data

• Model 1 - baseline model
• \(log(y_t) = a_1log(y_{t-1}) + a_{12}log(y_{t-12}) + e_t\)

## 
## Call:
## lm(formula = y ~ lagy.1 + lagy.12, data = d[-nrow(d), ])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.213003 -0.038462  0.003142  0.041776  0.218068 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.72587    0.75247   0.965    0.337    
## lagy.1       0.63737    0.07024   9.074 3.83e-14 ***
## lagy.12      0.29732    0.06923   4.295 4.62e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07979 on 85 degrees of freedom
##   (12 observations deleted due to missingness)
## Multiple R-squared:  0.6991, Adjusted R-squared:  0.692 
## F-statistic: 98.75 on 2 and 85 DF,  p-value: < 2.2e-16

• Model 2 - baseline model plus two Google Trends
• \(log(y_t) = a_1log(y_{t-1}) + a_{12}log(y_{t-12}) +tss+ins+ e_t\)

## 
## Call:
## lm(formula = y ~ ., data = d[-nrow(d), ])
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.166790 -0.044925 -0.002127  0.042199  0.171579 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.05232    0.89718   2.288   0.0247 *  
## lagy.1       0.54032    0.06656   8.117 3.80e-12 ***
## lagy.12      0.28402    0.06730   4.220 6.20e-05 ***
## tss          0.31692    0.06369   4.976 3.47e-06 ***
## ins          0.36442    0.08657   4.210 6.44e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.06924 on 83 degrees of freedom
##   (12 observations deleted due to missingness)
## Multiple R-squared:  0.7787, Adjusted R-squared:  0.7681 
## F-statistic: 73.03 on 4 and 83 DF,  p-value: < 2.2e-16

• Verify if Model 2 is improved significantly from Model 1:

## Analysis of Variance Table
## 
## Model 1: y ~ lagy.1 + lagy.12
## Model 2: y ~ lagy.1 + lagy.12 + tss + ins
##   Res.Df     RSS Df Sum of Sq      F    Pr(>F)    
## 1     85 0.54115                                  
## 2     83 0.39794  2    0.1432 14.934 2.883e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

• Overall fit - Out of Sample
• Evaluate models against normalized mean square errors (NMSE)

##     nmse.baseline    nmse.w.gtrends nmse.improved (%) 
##         0.3509923         0.2743213        21.8440738

• Pick Model 2 to next step

Forecast Data

• Nowcastic forecast on May sales with Google Trends data available on May, 2012

##            sales   tss   ins
## 2011-12-01 71674  0.31 -0.40
## 2012-01-01 62757  0.08 -0.27
## 2012-02-01 71103  0.15 -0.27
## 2012-03-01 82109  0.01 -0.18
## 2012-04-01 74632 -0.03 -0.21
## 2012-05-01    NA -0.04 -0.15

• Forecast with prediction intervals

##                fit      lwr      upr
## 2012-05-01 74505.7 64817.91 85641.45

• Done and Pray!