Problem 1 Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question, we use three equations to forecast the monthly change in the number of new one-family houses sold in the United States. In the first equation, the monthly change in the number of houses DHOMES is regressed against two lags of the monthly change in the 30-year conventional mortgage rate DIRATE. In the second equation, DHOMES is regressed against two lags of itself, and in the third equation, two lags of both DHOMES and DIRATE are included as regressors. DHOMES = Bo +8₁DIRATEt-1 +8₂DIRATEt-2+ e₁t DHOMES, = Bo + B₁DHOMESt-1+B₂DHOMES-2 +8₁DIRATEt-1 +8₂DIRATEt-2 + €3t DHOMES, Bo + B₁DHOMESt-1+B₂DHOMESt-2 + ezt The data used are from January, 1992 (1992M1) to September, 2016 (2016M9). The units of measurement are thousands of new houses for DHOMES and percentage points for DIRATE. After differencing and allowing for two lags, three observations are lost, resulting in a total of 294 observations that were used to produce the least squares estimates in the table below. Note that SSE denotes the sum of squared residuals. (feel free to ignore the results on columns pertaining to e₁t, ezt, and e3t). C Dependent variable DHOMES ₁, t -0.03 €1,1-1 e1.1-2 SSE DHOMES-1 DHOMES-2 DIRATE-1 DIRATET-2 -0.92 -46.1 -13.2 634312 -0.31 -1.17 -0.39 -0.14 DHOMESte2, t 0.05 0.05 -0.32 -0.10 550482 599720 0.04 0.16 -0.05 -0.17 DHOMES €3, t 0.65 0.53 -1.39 -0.37 -0.11 -45.6 -35.3 597568 555967 0.14 -0.003 30.8 -0.54 0.03 550770 a. Given DHOMES 2016M8 = -54, DHOMES 2016M9 = 18, DIRATE 2016M8 = 0.00, DIRATE 2016M9 = 0.02, and DIRATE 2016M10 = -0.01, use each of the three estimated equations to first obtain the point forecast and then find the 95% forecast intervals for DHOMES2016M10 and DHOMES2016M11. Comment on the results. b. Using a 5% significance level, test whether DIRATE Granger causes DHOMES. You can assume errors are homeskedastic and use the usual F-test formula you learned in class to carry out this test, adjusted to use the sum of squared residuals instead of the R-squared.
Problem 1 Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question, we use three equations to forecast the monthly change in the number of new one-family houses sold in the United States. In the first equation, the monthly change in the number of houses DHOMES is regressed against two lags of the monthly change in the 30-year conventional mortgage rate DIRATE. In the second equation, DHOMES is regressed against two lags of itself, and in the third equation, two lags of both DHOMES and DIRATE are included as regressors. DHOMES = Bo +8₁DIRATEt-1 +8₂DIRATEt-2+ e₁t DHOMES, = Bo + B₁DHOMESt-1+B₂DHOMES-2 +8₁DIRATEt-1 +8₂DIRATEt-2 + €3t DHOMES, Bo + B₁DHOMESt-1+B₂DHOMESt-2 + ezt The data used are from January, 1992 (1992M1) to September, 2016 (2016M9). The units of measurement are thousands of new houses for DHOMES and percentage points for DIRATE. After differencing and allowing for two lags, three observations are lost, resulting in a total of 294 observations that were used to produce the least squares estimates in the table below. Note that SSE denotes the sum of squared residuals. (feel free to ignore the results on columns pertaining to e₁t, ezt, and e3t). C Dependent variable DHOMES ₁, t -0.03 €1,1-1 e1.1-2 SSE DHOMES-1 DHOMES-2 DIRATE-1 DIRATET-2 -0.92 -46.1 -13.2 634312 -0.31 -1.17 -0.39 -0.14 DHOMESte2, t 0.05 0.05 -0.32 -0.10 550482 599720 0.04 0.16 -0.05 -0.17 DHOMES €3, t 0.65 0.53 -1.39 -0.37 -0.11 -45.6 -35.3 597568 555967 0.14 -0.003 30.8 -0.54 0.03 550770 a. Given DHOMES 2016M8 = -54, DHOMES 2016M9 = 18, DIRATE 2016M8 = 0.00, DIRATE 2016M9 = 0.02, and DIRATE 2016M10 = -0.01, use each of the three estimated equations to first obtain the point forecast and then find the 95% forecast intervals for DHOMES2016M10 and DHOMES2016M11. Comment on the results. b. Using a 5% significance level, test whether DIRATE Granger causes DHOMES. You can assume errors are homeskedastic and use the usual F-test formula you learned in class to carry out this test, adjusted to use the sum of squared residuals instead of the R-squared.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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Transcribed Image Text:Problem 1
Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for
houses. In this question, we use three equations to forecast the monthly change in the number of new
one-family houses sold in the United States. In the first equation, the monthly change in the number of
houses DHOMES is regressed against two lags of the monthly change in the 30-year conventional
mortgage rate DIRATE. In the second equation, DHOMES is regressed against two lags of itself, and in
the third equation, two lags of both DHOMES and DIRATE are included as regressors.
DHOMES = Bo +8₁ DIRATEt-1 +8₂DIRATEt-2 + e₁t
DHOMES = Bo + B₁DHOMESt-1 + ß₂DHOMESt-2 +§₁DIRATEt-1 +8₂DIRATEt-2 +€3t
DHOMES = Bo + B₁DHOMESt-1 + B₂DHOMESt-2 + €2t
The data used are from January, 1992 (1992M1) to September, 2016 (2016M9). The units of
measurement are thousands of new houses for DHOMES and percentage points for DIRATE. After
differencing and allowing for two lags, three observations are lost, resulting in a total of 294
observations that were used to produce the least squares estimates in the table below. Note that SSE
denotes the sum of squared residuals. (feel free to ignore the results on columns pertaining to e₁t, ezt,
and e3t).
C
Dependent variable DHOMESte1, t
-0.03
€1,1-1
€1,1-2
SSE
DHOMESt-1
DHOMESt-2
DIRATET-1
DIRATET-2
-0.92
-46.1
-13.2
634312
-0.31
-1.17
-0.39
-0.14
DHOMESte2, t
0.05
0.04
0.05
-0.32
-0.10
0.16
-0.05
-0.17
DHOMESte3, t
0.65
0.53
-1.39
-0.37
-0.11
-45.6
-35.3
550482 599720 597568 555967
0.14
-0.003
30.8
-0.54
0.03
550770
a. Given DHOMES2016M8 = -54, DHOMES2016M9 = 18, DIRATE 2016M8 = 0.00, DIRATE2016M9 = 0.02, and
DIRATE 2016M10 = -0.01, use each of the three estimated equations to first obtain the point
forecast and then find the 95% forecast intervals for DHOMES2016M10 and DHOMES 2016M11.
Comment on the results.
b. Using a 5% significance level, test whether DIRATE Granger causes DHOMES. You can assume
errors are homeskedastic and use the usual F-test formula you learned in class to carry out this
test, adjusted to use the sum of squared residuals instead of the R-squared.
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