Transcript Bevezetes az Okonometriaba

Spurious regression
The stock market and daily temperature
S&P 500 daily closing value and daily maximum temperature in New York,
Sep 1 to Dec 31 2008
1400
90
1300
80
1200
70
1100
60
1000
50
900
40
800
30
700
20
2008M09
2008M10
2008M11
2008M12
S&P500 closing price
Max daily temperature, Farenheit
 negative trend
in both
stochastic trend
in S&P500
deterministic trend
in temp.
Spurious: ln(SP) and ln(Temperature)
Spurious regression:
ln(SPt) = α + βln(temperaturet) + ut
Dependent Variable: LN_SP
Method: Least Squares
Date: 02/04/11 Time: 13:11
Sample: 9/01/2008 12/31/2008
Included observations: 86
Variable
Coefficient
Std. Error
t-Statistic
Prob.
LN_TEMP
C
0.388089
5.358239
0.036664
0.144857
10.58515
36.98981
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.571528
0.566427
0.095906
0.772625
80.60056
0.649803
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
6.887661
0.145651
-1.827920
-1.770842
112.0453
0.000000
Another spurious regression would be: SPt = α + βtemperaturet + ut
Correct: Δln(SP) and Δln(Temperature)
Spurious regression:
Δln(SPt) = α + βΔln(temperaturet) + Δut
Dependent Variable: D(LN_SP)
Method: Least Squares
Date: 02/04/11 Time: 14:05
Sample: 9/01/2008 12/31/2008
Included observations: 86
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(LN_TEMP)
C
-0.044461
-0.004509
0.028390
0.004307
-1.566091
-1.046840
0.1211
0.2982
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.028370
0.016803
0.039860
0.133459
156.1084
2.263090
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-0.004079
0.040199
-3.583917
-3.526839
2.452640
0.121087
Spurious: two simulated RW series
15
Xt = Xt-1 + ωt ωt~WN
Yt = Yt-1 + εt εt~WN
ωt and εt independent
10
5
0
-5
-10
10
20
30
40
50
RW_X
60
70
80
90
00
RW_Y
Spurious regression:
Yt = α + βXt + ut
Correct regression:
ΔYt = α + βΔXt + vt
Dependent Variable: D(RW_Y)
Dependent Variable: RW_Y
Variable
Coefficient
Std. Error
t-Statistic
Prob.
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
RW_X
-3.050638
-0.394909
0.286633
0.051691
-10.64300
-7.639825
0.0000
0.0000
C
D(RW_X)
-0.059322
0.068723
0.115759
0.089802
-0.512464
0.765278
0.6095
0.4460
R-squared
0.373269
Mean dependent var
0.006001
Mean dependent var
-4.756460 R-squared
-0.051743