# Dsc2008 Assignment

**Topics:**Regression analysis, Forecasting, Forecast error

**Pages:**8 (2626 words)

**Published:**November 11, 2012

The Vehicle Quota System (VQS) was implemented in May ‘90 by the Land Transport Authority of Singapore (LTA) to curb the rapidly increasing vehicle population growth. The VQS allocates a fixed number of Certificates of Entitlement (COE) available for competitive bidding during the bidding exercises conducted bi-monthly3. This report studies the factors affecting the monthly prices of COE in Category B and considers the best model to forecast future COE prices. (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 trend afterwards. Irregularities in the overall trend are due to external factors such as the consumer demand for cars and 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 analysis of COE Prices against Time, the percentage error between actual and fitted values in Fig 1.2 reveals 2 outliers in the dataset (as circled) that occur on 15 Jan and 1 Feb ‘09. Corresponding values falling on these dates were removed from the data set to ensure forecast accuracy. This results in a discrepancy in Lag1 prices as shown in Fig 1.3. By definition, the Lag1 Price of a current period should be the actual Price of its immediate previous period. However, the original Lag1 Price on 15 Feb ‘09 is now $3089 instead of $689, due to the omission of the outliers. To avoid this, we may replace the 2 outlying prices using a centered moving average model, which is based on the existing prices before 15 January 2009 and after 1 February 2009. However, this method is biased in assuming that the prices at those points are going to follow the same trend. 2. Analysis and Forecasts of EXPLANATORY Variables

Running a Multiple Regression (MR) of Price against Bids, Quota, Bid Ratio, and Lag1 (of Price), Quota and Bids were found to be insignificant by a t-test. We suspect that the insignificance of Quota and Bids reflects the Omitted Variable Bias phenomenon, which occurs when a regression analysis incorrectly omits one or more important independent variables2. This is because Quota and Bids are the root variables in Bid Ratio and thus determinants of COE price. Hence, we chose to exclude Bid Ratio as a variable and consider Quota and Bids instead. The MR model obtained is Price=2203.41+0.97Lag1+9.30Bids-13.55Quota, and the adjusted R2 value indicated that the model accounted for 98.35% of the variation in Price. Furthermore, the F-statistic for the MR model of 4955.96 was large, suggesting that we could easily reject the null hypothesis. The 3 remaining independent variables were significant as their p-values of 6.54E–156, 2.05E–15, and 4.80E–14 for Lag1, Quota, and Bids respectively were all less than 0.05. The scatter plot of residuals against predicted values (Fig 2.1) reveals moderately constant variance which hints that the residuals are random. Furthermore, the Autocorrelation Function (ACF) output table of the residuals fails to reject 17 out of 20 values and the remaining 3 rejected values are not significantly far away from the Upper Bound (UB) value. This implies that a large proportion of the residuals are in fact random, and our MR model is robust enough to conduct long term forecasts. The variables Quota and Bids will first be forecasted separately and then input back into the MR model stated above to derive future COE prices. 3.1. Quota

2 Gelpi (2002). Intermediate Statistical Methods: Omitted Variable Bias. Retrieved 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

Quota is an independent variable determined by the LTA. The amount of Quota made available during each bidding exercise...

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