Tiểu luận môn định giá doanh further development and analysis of the classical linear regression model
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GVHD: TS. Phùng Đức Nam
Chapter 4
Further development and analysis of the classical linear regression model
Phan Tuyết Trinh
Lâm Bá Du
Tô Thị Phương Thảo
Lê Chí Cang
Nguyễn Hoàng Minh Huy
Huỳnh Thái Huy
1. Generalising the simple model to multiple linear regression
2. The constant term
3. How are the parameters calculated in the generalised case?
4. Testing multiple hypotheses: the F-test
5. Sample output for multiple hypothesis tests
6. Multiple regression using an APT-style model
7. Data mining and the true size of the test
8. Goodness of fit statistics
9. Hedonic pricing models
10. Tests of non-nested hypotheses
11. Quantile regression
4.1 Generalising the simple model to multiple linear
regression
Stock returns might be purported to depend on their sensitivity to unexpected changes in:
•
•
•
•
inflation
the differences in returns on short- and long-dated bonds
industrial production
default risks
4.2 The constant term
k is defined as the number of ‘explanatory variables’ or ‘regressors’ including the constant term.
= the number of parameters that are estimated in the regression equation.
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
The elements of the β vector
•● SRF(Sample Regression Function)
, where:,
T×1
T×3
3×1
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
Ordinary least squares (OLS)
•
●
(: an estimate of the variance of the errors - )
●
var
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
Example
1
0
-1
2
-2
-2
-1
2
-1
-2
-1
1
1
-1
0
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
Example
•
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
Example
•
var
Dependent
Dependent Variable:
Variable: Y
Y
Method: Least Squares
Method: Least Squares
Date: 03/02/17 Time: 22:03
Date: 03/02/17 Time: 22:03
Sample: 1 5
Sample: 1 5
Included observations: 5
Included observations: 5
Variable
Coefficient
Std. Error
t-Statistic
Prob.
Variable
Coefficient
Std. Error
t-Statistic
Prob.
X2
0.294118
0.294118
-1.294118
-1.294118
C
0.235294
X1
0.630812
0.630812
1.036530
1.036530
0.466252
0.466252
-1.248510
-1.248510
0.892103
0.263752
0.8167
0.6869
0.6869
0.3382
0.3382
4.3 How are the parameters (the elements of the β vector) calculated in the generalised
case?
Summary
•
● var
4.4 F-test
●
•
Mô hình gốc/Mô hình không ràng buộc – UnRestricted
Ước lượng bằng OLS thu được tổng bình phương các phần dư URSS, có bậc tự do df (degree of freedom) =
T–k
●
Mô hình có ràng buộc (Mô hình bị thu hẹp, mất đi m hệ số hồi quy) – Restricted
Ước lượng bằng OLS thu được tổng bình phương các phần dư RRSS, có df = T – (k – m) = T – k + m
●
Khi đó: RRSS – URSS có df = T – k + m – (T – k) = m
●
Với giả thiết cho trước, ta có:
4.4 F-test
Ví dụ mô hình có ràng buộc (Restricted)
●
•
Mô hình gốc:
●
Kiểm định :
Ta có: , thay vào mô hình gốc:
Đặt , ta thu được
●
Kiểm định :
4.4 F-test
Xác định k, m thế nào?
•
●
●
●
k=2
k=3
k=4
:
m=1
: và
m=2
:
m=3
:
:
Phi tuyến nên không dùng F-test
được
4.5 Sample output for multiple hypothesis tests
View/Coefficient Diagnostics/Wald Test – Coefficient Restriction
=> C(1)=1, C(2)=1
F-version: small sample bias
- version
4.6 Multiple regression using an APT-style model
•
Whether the monthly returns on Microsoft stock can be explained bay
reference to unexpected changes in a set of macroeconomic and
financial variables.
=> Arbitrage pricing theory (APT)
4.6 Multiple regression using an APT-style model
The steps to take regression model
•
•
•
Step 1: Open a new Eviews workfile
Step 2: Import the data
Step 3: Generate variables:
The APT posits that the stock return can be explained by reference to the unexpected
changes in the macroeconomic varibles rather their levels
Unexpected value = Actual value – expected value
4.6 Multiple regression using an APT-style model
Generate variables
•
Genr
Dspread = baa_aaa_spread – baa_aaa_spread(-1)
Dcredit = consumer_credit – consumer_credit (-1)
Rmsoft = 100*dlog(microsoft)
Rsandp = 100*dlog(sandp)
Dmoney = m1money_supply – m1money_supply(-1)
Inflation = 100*dlog(cpi)
Term = ustb10y – ustb3m
Dinflation = inflation – inflation(-1)
Mustb3m = ustb3m/12
Rterm = term – term(-1)
Ermsoft = rmsoft – mustb3m
Ersandp = rsandp – mustb3m
4.6 Multiple regression using an APT-style model
The steps to take regression model
•
Step 4: Object/New Object/ Equation msoftreg: ERMSOFT C ERSANDP DPROD
DCREDIT DINFLATION DMONEY DSPREAD RTERM
•
Method: Least Squares.
4.6 Multiple regression using an APT-style model
The steps to take regression model
•
•
View/Coefficient Diagnostics/Wald Test – Coefficient Restrictions
C(3) = 0, C(4) = 0, C(5) = 0, C(6) = 0, C(7) = 0
The results
Wald Tes t:
Equation: Untitled
Tes t Statis tic
F-s tatis tic
Chi-s quare
Value
df
Probability
0.852936
4.264679
(5, 316)
5
0.5131
0.5120
Null Hypothes is : C(3)=0, C(4)=0, C(5)=0, C(6)=0,C(7)=0
Null Hypothes is Sum m ary:
Norm alized Res triction (= 0)
C(3)
C(4)
C(5)
C(6)
C(7)
Value
Std. Err.
-1.425779
-4.05E-05
2.959910
-0.011087
5.366629
1.324467
7.64E-05
2.166209
0.035175
6.913915
Res trictions are linear in coefficients .
4.6 Multiple regression using an APT-style model
Stepwise regression
•
Stepwise regression is an automatic variable selection produre which
chooses the jointly most important’s explanatory variables from a set of
candidate variables.
•
•
The simplest is the uni-directional forwards method.
No variables => first variable(the lowest p-value) =>the next lowest pvalue....
4.6 Multiple regression using an APT-style model
Stepwise regression
•
•
•
•
•
Object/New Object
•
Option: Forward, p-value: 0.2
Equation: Msoftstepwise
Method: STEPLS- Stepwise Least Square
Dependent variable: ERMSOFT C
Explanatory variables: ERSANDP DPROD DCREDIT DINFLATION DMONEY
DSPREAD RTERM
