1 . Introduction

Your vehicle Quota Program (VQS) was implemented in May ‘90 by Land Transport Authority of Singapore (LTA) to curb the swiftly increasing car population expansion. The VQS allocates a set number of Certificates of Entitlement (COE) readily available for competitive bidding process during the bidding exercises executed bi-monthly3. This kind of report studies the factors affecting the monthly rates of COE in Category B and considers the best model to forecast long term COE rates. (1-Feb-09, $689)

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(1-Feb-09, $689)

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Fig 1 ) 1 shows a gentle decline in prices from 15 Mar ‘02 to 15 Jan '09, and an increasing craze afterwards. Irregularities in the overall trend happen to be due to external factors like the consumer demand for cars plus the overall state of the economy. | Fig 1 . 3|

Date| COE Price| Lag1

1-Jan-09| $3, 089| $2, 656

15-Jan-09| $200|

1-Feb-09| $689|

15-Feb-09| $4, 889| $3, 089

(15-Jan-09, $200)

(15-Jan-09, $200)

After a regression research of COE Prices against Time, the percentage error among actual and fitted ideals in Fig 1 . a couple of reveals a couple of outliers in the dataset (as circled) that occur upon 15 By and one particular Feb ‘09. Corresponding principles falling on these schedules were taken off the data started ensure prediction accuracy. This results in a discrepancy in Lag1 prices as proven in Fig 1 . a few. By classification, the Lag1 Price of the current period should be the genuine Price of its instant previous period. However , the first Lag1 Price on 12-15 Feb ‘09 is now $3089 instead of $689, due to the omission of the outliers. To avoid this, we may exchange the 2 outlying prices using a centered going average model, which is depending on the existing prices before 15 January 2009 and after you February 2009. However , this approach is biased in assuming that the prices for those details are going to the actual same trend. 2 . Analysis and Forecasts of EXPLANATORY Variables

Running a Multiple Regression (MR) of Price against Bids, Sampling, Bid Proportion, and Lag1 (of Price), Quota and Bids were found being insignificant with a t-test. All of us suspect that the insignificance of Quota and Bids demonstrates the Omitted Variable Bias phenomenon, which in turn occurs every time a regression evaluation incorrectly omits one or more important independent variables2. This is because Quota and Bids are the basic variables in Bid Percentage and thus determinants of COE price. Hence, we made a decision to exclude Wager Ratio as being a variable and consider Subgroup and Prices for bids instead. The MR version obtained is usually Price=2203. 41+0. 97Lag1+9. 30Bids-13. 55Quota, as well as the adjusted R2 value mentioned that the version accounted for 98. 35% of the variation in Price. Furthermore, the F-statistic for the MR model of 4955. 96 was large, indicating that we may easily deny the null hypothesis. The 3 remaining impartial variables were significant his or her p-values of 6. 54E–156, 2 . 05E–15, and some. 80E–14 for Lag1, Subspecies, and Bids respectively were all lower than 0. 05. The scatter plot of residuals against predicted principles (Fig 2 . 1) shows moderately constant variance which will hints which the residuals are random. Furthermore, the Autocorrelation Function (ACF) output stand of the commissions fails to decline 17 away of twenty values as well as the remaining three or more rejected values are not drastically far away in the Upper Sure (UB) worth. This implies a large amount of the commissions are in fact unique, and the MR style is robust enough to conduct long term forecasts. The variables Subgroup and Bids will initial be predicted separately after which input back in the MR model explained above to derive foreseeable future COE rates. 3. 1 . Quota

a couple of Gelpi (2002). Intermediate Record Methods: Disregarded Variable Prejudice. Retrieved coming from http://www.duke.edu/~gelpi/ps233.lecture12.ppt

2 Gelpi (2002). Intermediate Statistical Methods: Omitted Variable Bias. Retrieved from http://www.duke.edu/~gelpi/ps233.lecture12.ppt

Subspecies is a completely independent variable determined by the LTA. The amount of Subgroup made available during each bidding process exercise...