计量经济学英文课件(3)
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计量经济学(英文PPT)Chapter 21 Time Series Econometrics ⅠStationarity Unit roots and Cointegration
6
k
k
0
covariance at lag k variance
obviously when k 0, 1 0
1 1 k
plot against k, the graph we obtain is known as the population correlogram k
• Returning to the example given in figure 21.8,the value of the Q statistic up to lag 25 is about 793,the LB statistic is about 891,both are highly significant, the probability of obtaining such a high
• We can rewrite the functions above as,
Yt ( 1)Yt1 ut
(21.9.1)
• or,
• Yt Yt 1 ut
(-1.96*0.1066,1.96*0.1066) or (0.2089,0.2089)
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• In figure 21.8,the left two lines of dots represent the 95% confidence interval.
the joint hypothesis test of k H0 : all the k are simultaneo usly equal to zero.
• This can be done by using the Q statistic developed by Box and Pierce,
k
k
0
covariance at lag k variance
obviously when k 0, 1 0
1 1 k
plot against k, the graph we obtain is known as the population correlogram k
• Returning to the example given in figure 21.8,the value of the Q statistic up to lag 25 is about 793,the LB statistic is about 891,both are highly significant, the probability of obtaining such a high
• We can rewrite the functions above as,
Yt ( 1)Yt1 ut
(21.9.1)
• or,
• Yt Yt 1 ut
(-1.96*0.1066,1.96*0.1066) or (0.2089,0.2089)
10
• In figure 21.8,the left two lines of dots represent the 95% confidence interval.
the joint hypothesis test of k H0 : all the k are simultaneo usly equal to zero.
• This can be done by using the Q statistic developed by Box and Pierce,
计量经济学(英文版)精品PPT课件
(4.3a)
Expand and multiply top and bottom by n:
b2
=
nSxiyi - Sxi Syi nSxi2-(Sxi) 2
(4.3b)
Variance of b2
4.12
Given that both yi and ei have variance s2,
the variance of the estimator b2 is:
4. cov(ei,ej) = cov(yi,yj) = 0 5. xt c for every observation
6. et~N(0,s 2) <=> yt~N(b1+ b2xt,
The population parameters b1 and b2 4.4 are unknown population constants.
b2
+
nSxiEei - Sxi SEei nSxi2-(Sxi) 2
Since Eei = 0, then Eb2 = b2 .
An Unbiased Estimator
4.8
The result Eb2 = b2 means that the distribution of b2 is centered at b2.
4.6
The Expected Values of b1 and b2
The least squares formulas (estimators) in the simple regression case:
b2 =
nSxiyi - Sxi Syi nSxi22 -(Sxi) 2
b1 = y - b2x
计量经济学(英文PPT)Chapter 11 HETEROSCEDASTICITY
n n
X iYi
X
2 i
(
X i Yi Xi )2
(11.2.1)
under the assumption of heterscedasticity namely:
var(2 ) (
xi2
2 i
xi2 )2
(11.2.2) return
under the assumption of homoscedasticity namely:：
(11.2.2)
The Method of Generalized Least
Squares(GLS)
The usual OLS method does not make use of the information, but GLS(generalized least squares) take such information into account
Consequences of Using OLS in the Presence of Heteroscedasticity
Suppose
we
use
2
,
and
use
the
variance
formula
given
in
(11.2.2),
which takes into account heteroscedasticity explicitly.
2
ui (Yi 1 2 Xi )2
(11.3.10)
But in GLS we minimize the expression(11.3.7),
which can also be written as：
计量经济学英文课件共35页
8
One-Sided Alternatives (cont)
Having picked a significance level, a, we look up the (1 – a)th percentile in a t distribution with n – k – 1 df and call this c, the critical value We can reject the null hypothesis if the t statistic is greater than the critical value If the t statistic is less than the critical value then we fail to reject the null
Under the CLM assumptions, conditional on the sample values of the independent variable s
bˆ j ~ Normal b j ,Var bˆ j , so that
bˆ j b j sd bˆ j ~ Normal 0,1
7
t Test: One-Sided Alternatives
Besides our null, H0, we need an alternative hypothesis, H1, and a significance level H1 may be one-sided, or two-sided
because we have to estimate s 2by sˆ 2
Note the degrees of freedom : n k 1
5
The t Test (cont)
One-Sided Alternatives (cont)
Having picked a significance level, a, we look up the (1 – a)th percentile in a t distribution with n – k – 1 df and call this c, the critical value We can reject the null hypothesis if the t statistic is greater than the critical value If the t statistic is less than the critical value then we fail to reject the null
Under the CLM assumptions, conditional on the sample values of the independent variable s
bˆ j ~ Normal b j ,Var bˆ j , so that
bˆ j b j sd bˆ j ~ Normal 0,1
7
t Test: One-Sided Alternatives
Besides our null, H0, we need an alternative hypothesis, H1, and a significance level H1 may be one-sided, or two-sided
because we have to estimate s 2by sˆ 2
Note the degrees of freedom : n k 1
5
The t Test (cont)
计量经济学导论第四版英文完整教学课件
Economics 20 - Prof. Anderson
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The Question of Causality
Simply establishing a relationship between variables is rarely sufficient Want to the effect to be considered causal If we’ve truly controlled for enough other variables, then the estimated ceteris paribus effect can often be considered to be causal Can be difficult to establish causality
Need to use nonexperimental, or observational, data to make inferences
Important to be able to apply economic theory to real world data
Economics 20 - Prof. Anderson
3
Why study Econometrics?
An empirical analysis uses data to test a theory or to estimate a relationship
A formal economic model can be tested
Theory may be ambiguous as to the effect of some policy change – can use econometrics to evaluate the program
计量经济学(英文版)
●How to measure the economic growth?
(Measure GDP, Growth velocity, Fluctuation)
●Analysis the factors that impact GDP？
(Investment, Consumption, Exportation…..)
9
Contact Information
PPT download:
Public Email: econometrics_ly@ Password: fall2011
Contact Me: Email: liy@ Office：通博楼B208 Office hour：TW 1-3 pm
design the policy?
13
Case3：Share price analysis of Chinese Stocks
●How does share price change ?
（ Measure by stock index）
●What is the main effect factors
Course Arrangement and Requirement
Term mission (30 %):
10 terms are grouped by yourselves. Each term is responsible for one chapter (assign randomly).
VII. Autocorrelation (3)
5
Course Contents
VIII. IX. X. XI. Model Specification and Diagnostic testing (3) Autoregressive and distributed lag models (6) Simultaneous Equation Models (6) Time Series Econometrics (6)
(Measure GDP, Growth velocity, Fluctuation)
●Analysis the factors that impact GDP？
(Investment, Consumption, Exportation…..)
9
Contact Information
PPT download:
Public Email: econometrics_ly@ Password: fall2011
Contact Me: Email: liy@ Office：通博楼B208 Office hour：TW 1-3 pm
design the policy?
13
Case3：Share price analysis of Chinese Stocks
●How does share price change ?
（ Measure by stock index）
●What is the main effect factors
Course Arrangement and Requirement
Term mission (30 %):
10 terms are grouped by yourselves. Each term is responsible for one chapter (assign randomly).
VII. Autocorrelation (3)
5
Course Contents
VIII. IX. X. XI. Model Specification and Diagnostic testing (3) Autoregressive and distributed lag models (6) Simultaneous Equation Models (6) Time Series Econometrics (6)
计量经济学(英文版).
Chapter 4 Statistical Properties of the OLS Estimators
Xi’An Institute of Post & Telecommunication Dept of Economic & Management Prof. Long
Simple Linear Regression Model y t = b1 + b 2 x t + e t
b1 + b2 x t
Assumptions of the Simple Linear Regression Model yt = b1 + b2x t + e t 2. E(e t) = 0 <=> E(yt) = b1 + b2x t
1.
3. var(e t)
4.3
=
4.
5.
cov(e i,e j)
x t c for every observation
= cov(yi,yj)
s 2 = var(yt)
= 0
6.
e t~N(0,s 2) <=> yt~N(b1+ b2x t,
The population parameters b1 and b2 are unknown population constants.
4.2
yt = household weekly food expenditures
x t = household weekly income
For a given level of x t, the expected level of food expenditures will be: E(yt|x t) =
Xi’An Institute of Post & Telecommunication Dept of Economic & Management Prof. Long
Simple Linear Regression Model y t = b1 + b 2 x t + e t
b1 + b2 x t
Assumptions of the Simple Linear Regression Model yt = b1 + b2x t + e t 2. E(e t) = 0 <=> E(yt) = b1 + b2x t
1.
3. var(e t)
4.3
=
4.
5.
cov(e i,e j)
x t c for every observation
= cov(yi,yj)
s 2 = var(yt)
= 0
6.
e t~N(0,s 2) <=> yt~N(b1+ b2x t,
The population parameters b1 and b2 are unknown population constants.
4.2
yt = household weekly food expenditures
x t = household weekly income
For a given level of x t, the expected level of food expenditures will be: E(yt|x t) =
计量经济学(英文PPT)Chapter 2 TWO-VARIABLE REGRESSION ANALYSIS SOME BASIC IDEAS
As the X value increases, the conditional mean value of Y increases, too. The dark circled points in Figure 2.1 show the conditional mean values of Y against the various X values.
is a linear function of X i ,say, of the type
E(Y | X i ) 1 2 X i (2.2.2)
1 and 2 are known as the regression coefficients. Equation（2.2.2）itself is known as the linear population regression function or simply linear population regression.
If we want to get the relationship between weekly family consumption expenditure (Y) and weekly family income (X).
In the hypothetical community, there is a total population of 60 families. The 60 families are divided into 10 income groups (from $80 to $260) . And assume that we get the observations given in Table 2.1.
Therefore, we can express the deviation of an individual Yi around its expected value as follows:
is a linear function of X i ,say, of the type
E(Y | X i ) 1 2 X i (2.2.2)
1 and 2 are known as the regression coefficients. Equation（2.2.2）itself is known as the linear population regression function or simply linear population regression.
If we want to get the relationship between weekly family consumption expenditure (Y) and weekly family income (X).
In the hypothetical community, there is a total population of 60 families. The 60 families are divided into 10 income groups (from $80 to $260) . And assume that we get the observations given in Table 2.1.
Therefore, we can express the deviation of an individual Yi around its expected value as follows: