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LM Autocorrelation problem with Weight option

asked 2016-09-03 05:52:32 +0000

Shazam User gravatar image

updated 2016-09-07 15:43:40 +0000

I use the following command to calculate an LM Autocorrelation test. Without the WEIGHT option there is no problem, but the problem with WEIGHT option was that I got different results. Why?

Here is the code:

sample 1 17
read T Y X1 X2
1   99.20  96.70  101.0
2   99.00  98.10  100.1
3   100.0  100.0  100.0
4   111.6  104.9  90.60
5   122.2  104.9  86.50
6   117.6  109.5  89.70
7   121.1  110.8  90.60
8   136.0  112.3  82.80
9   154.2  109.3  70.10
10  153.6  105.3  65.40
11  158.5  101.7  61.30
12  140.6  95.40  62.50
13  136.2  96.40  63.60
14  168.0  97.60  52.60
15  154.3  102.4  59.70
16  149.0  101.6  59.50
17  165.5  103.8  61.30

set NODEL
?OLS Y X1 X2 / resid=E ut
diag / acf
gen E1=lag(E,1)
?OLS E E1 x1 x2 /   
gen1  sqrt($N*$R2)

?OLS Y X1 X2 / resid=E weight=X2 ut
diag / acf
gen E1=Lag(E,1)
?OLS E E1 x1 x2 /   
gen1  sqrt($N*$R2)

Here is the output:

|_set NODEL
 |_?OLS Y X1 X2 / resid=E ut
 |_diag / acf

 REQUIRED MEMORY IS PAR=       5 CURRENT PAR=  112400
 DEPENDENT VARIABLE = Y               17 OBSERVATIONS
 REGRESSION COEFFICIENTS
    1.06170962850      -1.38298545741       130.706587487

 RESIDUAL CORRELOGRAM
  LM-TEST FOR HJ:RHO(J)=0, STATISTIC IS STANDARD NORMAL
  LAG     RHO       STD ERR     T-STAT     LM-STAT    DW-TEST BOX-PIERCE-LJUNG
    1    -0.1455     0.2425    -0.5998     0.7014     2.0185     0.4272
    2    -0.2231     0.2425    -0.9200     1.2257     2.0359     1.4994
    3     0.1871     0.2425     0.7716     0.9975     1.1956     2.3074
    4    -0.3002     0.2425    -1.2377     1.7388     2.0133     4.5462
 LM CHI-SQUARE STATISTIC WITH   4  D.F. IS     3.333

 |_gen E1=lag(E,1)
 ...NOTE..LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO
 |_?OLS E E1 x1 x2 /
 |_gen1  sqrt($N*$R2)
 ...NOTE..CURRENT VALUE OF $N   =   17.000
 ...NOTE..CURRENT VALUE OF $R2  =  0.28942E-01
  0.70143480

 |_?OLS Y X1 X2 / resid=E weight=X2 ut 
 |_diag / acf
 REQUIRED MEMORY IS PAR=       5 CURRENT PAR=  112400
 DEPENDENT VARIABLE = Y               17 OBSERVATIONS
 REGRESSION COEFFICIENTS
   0.975798381981      -1.36603123581       138.217582873

 RESIDUAL CORRELOGRAM
  LM-TEST FOR HJ:RHO(J)=0, STATISTIC IS STANDARD NORMAL
  LAG     RHO       STD ERR     T-STAT     LM-STAT    DW-TEST BOX-PIERCE-LJUNG
    1    -0.1453     0.2425    -0.5990     0.6957     2.0257     0.4261
    2    -0.2332     0.2425    -0.9615     1.2576     2.0795     1.5972
    3     0.1883     0.2425     0.7762     1.0115     1.2232     2.4148
    4    -0.3195     0.2425    -1.3174     1.8588     2.0829     4.9515
 LM CHI-SQUARE STATISTIC WITH   4  D.F. IS     3.621

 |_gen E1=lag(E,1)
 ...NOTE..LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ...
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answered 2016-09-08 16:24:54 +0000

updated 2016-09-08 16:26:51 +0000

Weighted Least Squares is different to Ordinary Least Squares and is used when the assumption of constant variance is violated. You need to read up on the difference but your model assumes that the error variance is directly related to X2. The Weighted Least Squares estimate $\hat{\beta}_{w}$ is obtained by applying OLS to the transformed model:

$$\sqrt{N_t}Y_t=\sqrt{N_t}X^{'}_t\beta +v_t$$

The model in both cases fits poorly and you may want to think again about it.

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answered 2016-09-07 15:46:40 +0000

The WEIGHT option performs Weighted Least Squares (WLS). OLS with the WEIGHT= option is similar to a GLS regression with a diagonal Omega matrix. One application of WLS is as a correction for heteroskedasticity.

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Comments

Please I need exactly answer With solution

Now the code again

OLS Y X1 X2 / resid=E weight=X2 ut
diag / acf

gen E1=lag(E,1)
?OLS E E1 x1 x2 /   
gen1  sqrt($N*$R2)

Why I got different results? Thanks in advance

Shazam User gravatar imageShazam User ( 2016-09-08 13:00:09 +0000 )edit
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Asked: 2016-09-03 05:52:32 +0000

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Last updated: Sep 08 '16