Car Sales 12-2014

Overall car sales are lower than expected.

	Predicted Values 2014-12-01 Uni-DLM	Actual Values 2014-12-01	log(Predicted DLM /Actual)	Predicted Values 2014-12-01 RF-VAR	log(Predicted RFVAR /Actual)
Acura	667.614	571.423	-0.156	638.471	-0.111
Audi	748.881	640	-0.157	714.237	-0.110
BMW	1,231.561	1,193.038	-0.032	1,347.554	-0.122
Buick	763.555	736.269	-0.036	782.536	-0.061
Cadillac	655.731	505.692	-0.260	580.159	-0.137
Chevrolet	6,835.125	5,756.654	-0.172	6,122.498	-0.062
Chrysler	1,120.799	1,047.808	-0.067	1,088.584	-0.038
Dodge	1,931.639	1,619.538	-0.176	1,796.103	-0.103
Ford	7,970.101	6,854.654	-0.151	7,841.763	-0.135
GMC	1,982.801	1,686.692	-0.162	1,898.404	-0.118
Honda	4,761.918	4,113.731	-0.146	4,646.172	-0.122
Hyundai	2,573.571	2,064.308	-0.220	2,195.227	-0.061
Infiniti	481.029	438.385	-0.093	498.734	-0.129
Jaguar	51.756	48.192	-0.071	49.113	-0.019
Jeep	2,570.222	2,211.115	-0.150	2,445.042	-0.101
Kia	1,691.116	1,728.308	0.022	1,695.402	0.019
Land.Rover	186.583	140.154	-0.286	153.189	-0.089
Lexus	1,401.406	1,056.615	-0.282	1,261.509	-0.177
Lincoln	379.194	312.038	-0.195	359.453	-0.141
Mazda	934.056	817	-0.134	900.577	-0.097
Mercedes.Benz	1,182.489	1,427.308	0.188	1,530.815	-0.070
Mini	201.142	192.654	-0.043	214.853	-0.109
Mitsubishi	236.740	251.308	0.060	263.551	-0.048
Nissan	3,842.358	3,530.385	-0.085	3,752.873	-0.061
Porsche	150.558	180.731	0.183	178.117	0.015
Subaru	1,937.090	1,740.115	-0.107	2,012.891	-0.146
Toyota	6,542.211	5,995.154	-0.087	6,486.288	-0.079
Volkswagen	1,310.049	1,220.192	-0.071	1,307.579	-0.069
Volvo	153.500	139.346	-0.097	144.812	-0.038

Above are barplots for both the univariate DLM model and the RFVAR model I made last time. On the whole, the RFVAR performed better than DLM model. The success of the new technique shouldn't come as a huge surprise since it includes MANY explanatory variables and combines them in a nonlinear manner.  However, the old model predicted 5/29 car company sales better (in terms of sqrd residuals); BMW, Subaru, Infiniti, Mini, and Buick.

However, the success of the DLM predicted Mini compared to RFVAR is probably due to the fact that DLM's are much more susceptible to new data. This can be seen by viewing November's car predictions where the Mini Prediction was 22% off! This of course, was due the fact that Mini updated its main car, the Cooper. The DLM 'learned' from that error much better than an RFVAR did b/c an RFVAR weights all observations equally while DLM's heavily favor the most recent observation.  There are two ways I think I can improve the new technique: 1. introduce some sort of error term in regressors to make it a moving average model (RFVARMA anyone?) or 2. include new car updates as regressors... Stay tuned.

	Predicted Values for DLM 2015-01-01	Predicted Values for RFVAR 2015-01-01
Acura	507.466	482.503
Audi	493.058	534.796
BMW	537.307	942.241
Buick	663.501	662.867
Cadillac	426.117	422.310
Chevrolet	5,354.776	5,933.536
Chrysler	982.456	974.300
Dodge	1,401.967	1,485.997
Ford	6,380.988	5,864.732
GMC	1,491.437	1,401.825
Honda	3,535.973	3,607.157
Hyundai	1,780.659	1,998.811
Infiniti	338.773	339.410
Jaguar	53.041	54.888
Jeep	2,055.684	2,063.373
Kia	1,734.471	1,701.986
Land.Rover	158.073	175.358
Lexus	778.053	870.991
Lincoln	287.213	285.119
Mazda	877.112	839.224
Mercedes.Benz	914.966	1,070.583
Mini	194.780	156.332
Mitsubishi	253.650	251.183
Nissan	3,359.422	3,640.657
Porsche	153.518	124.497
Subaru	1,671.166	1,399.720
Toyota	5,623.714	5,806.384
Volkswagen	1,050.926	1,039.737
Volvo	144.025	165.600

Vector Autoregression with Random Forests: New Technqiue

My previous predictions were fairly naive in that it only took previous values from each car make separately. However, other variables should be of importance (economic mostly) and could increase accuracy of predictions.

I've made new predictions based on a vector auto random forests. Like vector auto regressions, it models each time series with lagged values of itself and lag values of all other variables. The nice thing about using random forests, is that you don't necessarily need to worry about model specifications as the algorithm generally gives good predictions.

Below are predictions for December 2014 car sales.

Code

	Predicted Values for 2014-12-01
Acura	638.471
Audi	714.237
BMW	1,347.554
Buick	782.536
Cadillac	580.159
Chevrolet	6,122.498
Chrysler	1,088.584
Dodge	1,796.103
Ford	7,841.763
GMC	1,898.404
Honda	4,646.172
Hyundai	2,195.227
Infiniti	498.734
Jaguar	49.113
Jeep	2,445.042
Kia	1,695.402
Land.Rover	153.189
Lexus	1,261.509
Lincoln	359.453
Mazda	900.577
Mercedes.Benz	1,530.815
Mini	214.853
Mitsubishi	263.551
Nissan	3,752.873
Porsche	178.117
Subaru	2,012.891
Toyota	6,486.288
Volkswagen	1,307.579
Volvo	144.812