AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t

Size: px
Start display at page:

Download "AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t"

Transcription

1 AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t 2, V(y t y t 1, y t 2, ) = σ 2 3. Thus, y t y t 1, y t 2, N(0, σ 2 ). = Conditional distribution of y t given y t 1, y t 2, 4. The stationarity condition is: the solution of φ(x) = 1 φx = 0, i.e., x = 1/φ, is greater than one in absolute value, or equivalently, φ < 1.

2 88 5. Rewriting the AR(1) model, y t = φy t 1 + ɛ t = φ 2 y t 2 + ɛ t + φɛ t 1 = φ 3 y t 3 + ɛ t + φɛ t 1 + φ 2 ɛ t 2. = φ s y t s + ɛ t + φɛ t φ s 1 ɛ t s+1. As s is large, φ s approaches zero. = Stationarity condition 6. For stationarity, y t = φy t 1 + ɛ t is rewritten as: y t = ɛ t + φɛ t 1 + φ 2 ɛ t Mean of y t E(y t ) = E(ɛ t + φɛ t 1 + φ 2 ɛ t 2 + )

3 89 = E(ɛ t ) + φe(ɛ t 1 ) + φ 2 E(ɛ t 2 ) + = 0 8. Variance of y t 9. Thus, y t N ( 0, 10. Estimation of AR(1) model: (a) Log-likelihood function V(y t ) = V(ɛ t + φɛ t 1 + φ 2 ɛ t 2 + ) = V(ɛ t ) + V(φɛ t 1 ) + V(φ 2 ɛ t 2 ) + = σ 2 (1 + φ 2 + φ 4 + ) = σ2 1 φ 2 σ 2 1 ρ 2 ). = Unconditional distribution of yt log f (y T,, y 1 ) = log f (y 1 ) + log f (y t y t 1,, y 1 ) t=1

4 90 = 1 2 log(2π) 1 ( ) 2 log σ φ 2 σ 2 /(1 φ 2 ) y2 1 T 1 2 log(2π) T 1 2 log(σ 2 ) 1 σ 2 (y t φy t 1 ) 2 = T 2 log(2π) T 2 log(σ2 ) 1 ( ) 2 log 1 1 φ 2 1 2σ 2 /(1 φ 2 ) y2 1 1 (y 2σ 2 t φy t 1 ) 2 Note as follows: ) 1 f (y 1 ) = ( 2πσ2 /(1 φ 2 ) exp 1 2σ 2 /(1 φ 2 ) y2 1 ( 1 f (y t y t 1,, y 1 ) = exp 1 ) 2πσ 2 2σ (y 2 t φy t 1 ) 2

5 91 log f (y T,, y 1 ) = T 1 σ 2 2 σ σ 4 /(1 φ 2 ) y σ 4 (y t φy t 1 ) 2 = 0 log f (y T,, y 1 ) φ = φ 1 φ 2 + φ σ 2 y σ 2 (y t φy t 1 )y t 1 = 0 The MLE of φ and σ 2 satisfies the above two equation.

6 y t = X t β + u t, u t = ρu t 1 + ɛ, ɛ t N(0, σ 2 ) Log of distribution function of u t log f (u T,, u 1 ) = log f (u 1 ) + log f (u t u t 1,, y 1 ) t=1 = 1 2 log(2π) 1 ( ) 2 log σ ρ 2 σ 2 /(1 ρ 2 ) u2 1 T 1 2 log(2π) T 1 2 log(σ 2 ) 1 σ 2 (u t ρu t 1 ) 2 = T 2 log(2π) T 2 log(σ2 ) 1 ( ) 2 log 1 1 ρ 2 1 2σ 2 /(1 ρ 2 ) u2 1 1 (u 2σ 2 t ρu t 1 ) 2

7 93 Log of distribution function of y t log f (y T,, y 1 ) = log f (y 1 ) + log f (y t y t 1,, y 1 ) t=1 = 1 2 log(2π) 1 ( ) 2 log σ ρ 2 σ 2 /(1 ρ 2 ) (y 1 X 1 β) 2 T 1 2 log(2π) T 1 2 log(σ 2 ) 1 σ 2 = T 2 log(2π) T 2 log(σ2 ) 1 ( ) 2 log 1 1 ρ 2 ( (yt X t β) ρ(y t 1 X t 1 β) ) 2 1 2σ 2 (y t Xt β) 2, where 1 ρ2 y y t, for t = 1, t = y t ρy t 1, for t = 2, 3,, T, 1 ρ2 X Xt t, for t = 1, = X t ρx t 1, for t = 2, 3,, T,

8 94 log f (y T,, y 1 ) is maximized with respect to β, ρ and σ 2. OLS, AR(1), AR(1)+X StataSE Data Data Editor Excel 123, var1, var2, var3,... command Y= + X+ Z reg Y X Z results Y, X, Z

9 95 gen t=_n tsset t t reg Y X Z dwstat scatter Y X X Y line Y X time time X Y Stata ( ) \2,940 (1995) t x y

10 96. gen t=_n. tsset t. reg y x Source SS df MS Number of obs = F( 1, 2) = 7.35 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = y Coef. Std. Err. t P> t [95% Conf. Interval] x _cons arima y, ar(1) nocons (setting optimization to BHHH) Iteration 0: log likelihood =

11 97 Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Iteration 4: log likelihood = (switching optimization to BFGS) Iteration 5: log likelihood = Iteration 6: log likelihood = Iteration 7: log likelihood = Iteration 8: log likelihood = Iteration 9: log likelihood = ARIMA regression Sample: 1-4 Number of obs = 4 Wald chi2(1) = Log likelihood = Prob > chi2 = OPG y Coef. Std. Err. z P> z [95% Conf. Interval] ARMA ar L /sigma Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero.

12 98. arima y x,ar(1) (setting optimization to BHHH) Iteration 0: log likelihood = Iteration 1: log likelihood = (backed up) Iteration 2: log likelihood = (backed up) Iteration 3: log likelihood = (backed up) Iteration 4: log likelihood = (backed up) (switching optimization to BFGS) Iteration 5: log likelihood = (backed up) Iteration 6: log likelihood = Iteration 7: log likelihood = Iteration 8: log likelihood = Iteration 9: log likelihood = Iteration 10: log likelihood = Iteration 11: log likelihood = Iteration 12: log likelihood = ARIMA regression Sample: 1-4 Number of obs = 4 Wald chi2(2) = Log likelihood = Prob > chi2 = OPG y Coef. Std. Err. z P> z [95% Conf. Interval]

13 y x _cons ARMA ar L /sigma Note: The test of the variance against zero is one sided, and the two-sided confidence interval is truncated at zero. 99

80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x

80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x 80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =

More information

Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestim

Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestim TS001 Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestimation 49 mwp-055 corrgram/ac/pac 56 mwp-009 dfgls

More information

卒業論文

卒業論文 Y = ax 1 b1 X 2 b2...x k bk e u InY = Ina + b 1 InX 1 + b 2 InX 2 +...+ b k InX k + u X 1 Y b = ab 1 X 1 1 b 1 X 2 2...X bk k e u = b 1 (ax b1 1 X b2 2...X bk k e u ) / X 1 = b 1 Y / X 1 X 1 X 1 q YX1

More information

s = 1.15 (s = 1.07), R = 0.786, R = 0.679, DW =.03 5 Y = 0.3 (0.095) (.708) X, R = 0.786, R = 0.679, s = 1.07, DW =.03, t û Y = 0.3 (3.163) + 0

s = 1.15 (s = 1.07), R = 0.786, R = 0.679, DW =.03 5 Y = 0.3 (0.095) (.708) X, R = 0.786, R = 0.679, s = 1.07, DW =.03, t û Y = 0.3 (3.163) + 0 7 DW 7.1 DW u 1, u,, u (DW ) u u 1 = u 1, u,, u + + + - - - - + + - - - + + u 1, u,, u + - + - + - + - + u 1, u,, u u 1, u,, u u +1 = u 1, u,, u Y = α + βx + u, u = ρu 1 + ɛ, H 0 : ρ = 0, H 1 : ρ 0 ɛ 1,

More information

% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr

% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr 1 1. 2014 6 2014 6 10 10% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti 1029 0.35 0.40 One-sample test of proportion x: Number of obs = 1029 Variable Mean Std.

More information

こんにちは由美子です

こんにちは由美子です Analysis of Variance 2 two sample t test analysis of variance (ANOVA) CO 3 3 1 EFV1 µ 1 µ 2 µ 3 H 0 H 0 : µ 1 = µ 2 = µ 3 H A : Group 1 Group 2.. Group k population mean µ 1 µ µ κ SD σ 1 σ σ κ sample mean

More information

Stata11 whitepapers mwp-037 regress - regress regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F(

Stata11 whitepapers mwp-037 regress - regress regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F( mwp-037 regress - regress 1. 1.1 1.2 1.3 2. 3. 4. 5. 1. regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F( 2, 71) = 69.75 Model 1619.2877 2 809.643849 Prob > F = 0.0000 Residual

More information

こんにちは由美子です

こんにちは由美子です 1 2 . sum Variable Obs Mean Std. Dev. Min Max ---------+----------------------------------------------------- var1 13.4923077.3545926.05 1.1 3 3 3 0.71 3 x 3 C 3 = 0.3579 2 1 0.71 2 x 0.29 x 3 C 2 = 0.4386

More information

1 Stata SEM LightStone 3 2 SEM. 2., 2,. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press.

1 Stata SEM LightStone 3 2 SEM. 2., 2,. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. 1 Stata SEM LightStone 3 2 SEM. 2., 2,. Alan C. Acock, 2013. Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. 2 3 2 Conservative Depress. 3.1 2. SEM. 1. x SEM. Depress.

More information

第11回:線形回帰モデルのOLS推定

第11回:線形回帰モデルのOLS推定 11 OLS 2018 7 13 1 / 45 1. 2. 3. 2 / 45 n 2 ((y 1, x 1 ), (y 2, x 2 ),, (y n, x n )) linear regression model y i = β 0 + β 1 x i + u i, E(u i x i ) = 0, E(u i u j x i ) = 0 (i j), V(u i x i ) = σ 2, i

More information

こんにちは由美子です

こんにちは由美子です 1 2 λ 3 λ λ. correlate father mother first second (obs=20) father mother first second ---------+------------------------------------ father 1.0000 mother 0.2254 1.0000 first 0.7919 0.5841 1.0000 second

More information

ECCS. ECCS,. ( 2. Mac Do-file Editor. Mac Do-file Editor Windows Do-file Editor Top Do-file e

ECCS. ECCS,. (  2. Mac Do-file Editor. Mac Do-file Editor Windows Do-file Editor Top Do-file e 1 1 2015 4 6 1. ECCS. ECCS,. (https://ras.ecc.u-tokyo.ac.jp/guacamole/) 2. Mac Do-file Editor. Mac Do-file Editor Windows Do-file Editor Top Do-file editor, Do View Do-file Editor Execute(do). 3. Mac System

More information

1 Stata SEM LightStone 4 SEM 4.. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press 3.

1 Stata SEM LightStone 4 SEM 4.. Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press 3. 1 Stata SEM LightStone 4 SEM 4.. Alan C. Acock, 2013. Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press 3. 2 4, 2. 1 2 2 Depress Conservative. 3., 3,. SES66 Alien67 Alien71,

More information

28

28 y i = Z i δ i +ε i ε i δ X y i = X Z i δ i + X ε i [ ] 1 δ ˆ i = Z i X( X X) 1 X Z i [ ] 1 σ ˆ 2 Z i X( X X) 1 X Z i Z i X( X X) 1 X y i σ ˆ 2 ˆ σ 2 = [ ] y i Z ˆ [ i δ i ] 1 y N p i Z i δ ˆ i i RSTAT

More information

.. est table TwoSLS1 TwoSLS2 GMM het,b(%9.5f) se Variable TwoSLS1 TwoSLS2 GMM_het hi_empunion totchr

.. est table TwoSLS1 TwoSLS2 GMM het,b(%9.5f) se Variable TwoSLS1 TwoSLS2 GMM_het hi_empunion totchr 3,. Cameron and Trivedi (2010) Microeconometrics Using Stata, Revised Edition, Stata Press 6 Linear instrumentalvariables regression 9 Linear panel-data models: Extensions.. GMM xtabond., GMM(Generalized

More information

10

10 z c j = N 1 N t= j1 [ ( z t z ) ( )] z t j z q 2 1 2 r j /N j=1 1/ N J Q = N(N 2) 1 N j j=1 r j 2 2 χ J B d z t = z t d (1 B) 2 z t = (z t z t 1 ) (z t 1 z t 2 ) (1 B s )z t = z t z t s _ARIMA CONSUME

More information

最小2乗法

最小2乗法 2 2012 4 ( ) 2 2012 4 1 / 42 X Y Y = f (X ; Z) linear regression model X Y slope X 1 Y (X, Y ) 1 (X, Y ) ( ) 2 2012 4 2 / 42 1 β = β = β (4.2) = β 0 + β (4.3) ( ) 2 2012 4 3 / 42 = β 0 + β + (4.4) ( )

More information

y i OLS [0, 1] OLS x i = (1, x 1,i,, x k,i ) β = (β 0, β 1,, β k ) G ( x i β) 1 G i 1 π i π i P {y i = 1 x i } = G (

y i OLS [0, 1] OLS x i = (1, x 1,i,, x k,i ) β = (β 0, β 1,, β k ) G ( x i β) 1 G i 1 π i π i P {y i = 1 x i } = G ( 7 2 2008 7 10 1 2 2 1.1 2............................................. 2 1.2 2.......................................... 2 1.3 2........................................ 3 1.4................................................

More information

4 OLS 4 OLS 4.1 nurseries dual c dual i = c + βnurseries i + ε i (1) 1. OLS Workfile Quick - Estimate Equation OK Equation specification dual c nurser

4 OLS 4 OLS 4.1 nurseries dual c dual i = c + βnurseries i + ε i (1) 1. OLS Workfile Quick - Estimate Equation OK Equation specification dual c nurser 1 EViews 2 2007/5/17 2007/5/21 4 OLS 2 4.1.............................................. 2 4.2................................................ 9 4.3.............................................. 11 4.4

More information

こんにちは由美子です

こんにちは由美子です Sample size power calculation Sample Size Estimation AZTPIAIDS AIDSAZT AIDSPI AIDSRNA AZTPr (S A ) = π A, PIPr (S B ) = π B AIDS (sampling)(inference) π A, π B π A - π B = 0.20 PI 20 20AZT, PI 10 6 8 HIV-RNA

More information

k2 ( :35 ) ( k2) (GLM) web web 1 :

k2 ( :35 ) ( k2) (GLM) web   web   1 : 2012 11 01 k2 (2012-10-26 16:35 ) 1 6 2 (2012 11 01 k2) (GLM) kubo@ees.hokudai.ac.jp web http://goo.gl/wijx2 web http://goo.gl/ufq2 1 : 2 2 4 3 7 4 9 5 : 11 5.1................... 13 6 14 6.1......................

More information

untitled

untitled 2 : n =1, 2,, 10000 0.5125 0.51 0.5075 0.505 0.5025 0.5 0.4975 0.495 0 2000 4000 6000 8000 10000 2 weak law of large numbers 1. X 1,X 2,,X n 2. µ = E(X i ),i=1, 2,,n 3. σi 2 = V (X i ) σ 2,i=1, 2,,n ɛ>0

More information

BR001

BR001 BR001 Stata 11 Stata Stata11 whitepaper mwp 3 mwp-027 22 mwp-028 / 40 mwp-001 logistic/logit 50 mwp-039 logistic/logit postestimation 60 mwp-040 margins 74 mwp-029 regress 90 mwp-037 regress postestimation

More information

Stata 11 Stata ROC whitepaper mwp anova/oneway 3 mwp-042 kwallis Kruskal Wallis 28 mwp-045 ranksum/median / 31 mwp-047 roctab/roccomp ROC 34 mwp-050 s

Stata 11 Stata ROC whitepaper mwp anova/oneway 3 mwp-042 kwallis Kruskal Wallis 28 mwp-045 ranksum/median / 31 mwp-047 roctab/roccomp ROC 34 mwp-050 s BR003 Stata 11 Stata ROC whitepaper mwp anova/oneway 3 mwp-042 kwallis Kruskal Wallis 28 mwp-045 ranksum/median / 31 mwp-047 roctab/roccomp ROC 34 mwp-050 sampsi 47 mwp-044 sdtest 54 mwp-043 signrank/signtest

More information

2 Tobin (1958) 2 limited dependent variables: LDV 2 corner solution 2 truncated censored x top coding censor from above censor from below 2 Heck

2 Tobin (1958) 2 limited dependent variables: LDV 2 corner solution 2 truncated censored x top coding censor from above censor from below 2 Heck 10 2 1 2007 4 6 25-44 57% 2017 71% 2 Heckit 6 1 2 Tobin (1958) 2 limited dependent variables: LDV 2 corner solution 2 truncated 50 50 censored x top coding censor from above censor from below 2 Heckit

More information

事例研究(ミクロ経済政策・問題分析III) -規制産業と料金・価格制度-

事例研究(ミクロ経済政策・問題分析III) -規制産業と料金・価格制度- 事例研究 ( ミクロ経済政策 問題分析 III) - 規制産業と料金 価格制度 - ( 第 7 回 手法 (3) 応用データ解析 / 基礎的手法 ) 2010 年 6 月 2 日 戒能一成 0. 本講の目的 ( 手法面 ) - 応用データ解析の手順や基本的な作業の流れ (Strategy) を理解する - 特にグラフ化や統計検定などの手法を用いた データ解析手法の選択と検定 確認について理解する (

More information

( 30 ) 30 4 5 1 4 1.1............................................... 4 1.............................................. 4 1..1.................................. 4 1.......................................

More information

II (2011 ) ( ) α β û i R

II (2011 ) ( ) α β û i R II 3 9 9 α β 3 û i 4 R 3 5 4 4 3 6 3 6 3 6 4 6 5 3 6 F 5 7 F 6 8 GLS 8 8 heil and Goldberger Model 9 MLE 9 9 I 3 93 II 3 94 AR 4 95 5 96 6 6 8 3 3 3 3 3 i 3 33 3 Wald, LM, LR 33 3 34 4 38 5 39 6 43 7 44

More information

Isogai, T., Building a dynamic correlation network for fat-tailed financial asset returns, Applied Network Science (7):-24, 206,

Isogai, T., Building a dynamic correlation network for fat-tailed financial asset returns, Applied Network Science (7):-24, 206, H28. (TMU) 206 8 29 / 34 2 3 4 5 6 Isogai, T., Building a dynamic correlation network for fat-tailed financial asset returns, Applied Network Science (7):-24, 206, http://link.springer.com/article/0.007/s409-06-0008-x

More information

TS002

TS002 TS002 Stata 12 Stata VAR VEC whitepaper mwp 4 mwp-084 var VAR 14 mwp-004 varbasic VAR 26 mwp-005 svar VAR 33 mwp-007 vec intro VEC 51 mwp-008 vec VEC 80 mwp-063 VAR vargranger Granger 93 mwp-062 varlmar

More information

Stata 11 Stata VAR VEC whitepaper mwp 4 mwp-084 var VAR 14 mwp-004 varbasic VAR 25 mwp-005 svar VAR 31 mwp-007 vec intro VEC 47 mwp-008 vec VEC 75 mwp

Stata 11 Stata VAR VEC whitepaper mwp 4 mwp-084 var VAR 14 mwp-004 varbasic VAR 25 mwp-005 svar VAR 31 mwp-007 vec intro VEC 47 mwp-008 vec VEC 75 mwp TS002 Stata 11 Stata VAR VEC whitepaper mwp 4 mwp-084 var VAR 14 mwp-004 varbasic VAR 25 mwp-005 svar VAR 31 mwp-007 vec intro VEC 47 mwp-008 vec VEC 75 mwp-063 VAR postestimation vargranger Granger 86

More information

Stata User Group Meeting in Kyoto / ( / ) Stata User Group Meeting in Kyoto / 21

Stata User Group Meeting in Kyoto / ( / ) Stata User Group Meeting in Kyoto / 21 Stata User Group Meeting in Kyoto / 2017 9 16 ( / ) Stata User Group Meeting in Kyoto 2017 9 16 1 / 21 Rosenbaum and Rubin (1983) logit/probit, ATE = E [Y 1 Y 0 ] ( / ) Stata User Group Meeting in Kyoto

More information

Microsoft Word - 計量研修テキスト_第5版).doc

Microsoft Word - 計量研修テキスト_第5版).doc Q10-2 テキスト P191 1. 記述統計量 ( 変数 :YY95) 表示変数として 平均 中央値 最大値 最小値 標準偏差 観測値 を選択 A. 都道府県別 Descriptive Statistics for YY95 Categorized by values of PREFNUM Date: 05/11/06 Time: 14:36 Sample: 1990 2002 Included

More information

Vol. 42 No pp Headcount ratio p p A B pp.29

Vol. 42 No pp Headcount ratio p p A B pp.29 1990 2003 2005 2000 1998 2004 2001 2 2000 2001 2000 1 Vol. 42 No. 2 2005 pp.21-22 25 25-29 30-34 1999 1 Headcount ratio 2 1995 20-25 25-30 2005 p.25 2005 2000 2 15 34 2003 p.3 15 34 A B 3 4 3 3 2003 pp.29-332001

More information

CVaR

CVaR CVaR 20 4 24 3 24 1 31 ,.,.,. Markowitz,., (Value-at-Risk, VaR) (Conditional Value-at-Risk, CVaR). VaR, CVaR VaR. CVaR, CVaR. CVaR,,.,.,,,.,,. 1 5 2 VaR CVaR 6 2.1................................................

More information

σ t σ t σt nikkei HP nikkei4csv H R nikkei4<-readcsv("h:=y=ynikkei4csv",header=t) (1) nikkei header=t nikkei4csv 4 4 nikkei nikkei4<-dataframe(n

σ t σ t σt nikkei HP nikkei4csv H R nikkei4<-readcsv(h:=y=ynikkei4csv,header=t) (1) nikkei header=t nikkei4csv 4 4 nikkei nikkei4<-dataframe(n R 1 R R R tseries fseries 1 tseries fseries R Japan(Tokyo) R library(tseries) library(fseries) 2 t r t t 1 Ω t 1 E[r t Ω t 1 ] ɛ t r t = E[r t Ω t 1 ] + ɛ t ɛ t 2 iid (independently, identically distributed)

More information

1 Stata SEM LightStone 1 5 SEM Stata Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. Introduc

1 Stata SEM LightStone 1 5 SEM Stata Alan C. Acock, Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. Introduc 1 Stata SEM LightStone 1 5 SEM Stata Alan C. Acock, 2013. Discovering Structural Equation Modeling Using Stata, Revised Edition, Stata Press. Introduction to confirmatory factor analysis 9 Stata14 2 1

More information

,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i

,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i Armitage.? SAS.2 µ, µ 2, µ 3 a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 µ, µ 2, µ 3 log a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 * 2 2. y t y y y Poisson y * ,, Poisson 3 3. t t y,, y n Nµ,

More information

kubostat2017b p.1 agenda I 2017 (b) probability distribution and maximum likelihood estimation :

kubostat2017b p.1 agenda I 2017 (b) probability distribution and maximum likelihood estimation : kubostat2017b p.1 agenda I 2017 (b) probabilit distribution and maimum likelihood estimation kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2017 11 14 : 2017 11 07 15:43 1 : 2 3? 4 kubostat2017b (http://goo.gl/76c4i)

More information

1 y x y = α + x β+ε (1) x y (2) x y (1) (2) (1) y (2) x y (1) (2) y x y ε x 12 x y 3 3 β x β x 1 1 β 3 1

1 y x y = α + x β+ε (1) x y (2) x y (1) (2) (1) y (2) x y (1) (2) y x y ε x 12 x y 3 3 β x β x 1 1 β 3 1 1 y x y = α + x β+ε (1) x y (2) x y (1) (2) (1) y (2) x y (1) (2) y x y ε x 12 x y 3 3 β x β x 1 1 β 3 1 2 2 N y(n 1 ) x(n K ) y = E(y x) + u E(y x) y u(n 1 ) y = x β + u β Ordinary Least Squares:OLS (min

More information

seminar0220a.dvi

seminar0220a.dvi 1 Hi-Stat 2 16 2 20 16:30-18:00 2 2 217 1 COE 4 COE RA E-MAIL: ged0104@srv.cc.hit-u.ac.jp 2004 2 25 S-PLUS S-PLUS S-PLUS S-code 2 [8] [8] [8] 1 2 ARFIMA(p, d, q) FI(d) φ(l)(1 L) d x t = θ(l)ε t ({ε t }

More information

I L01( Wed) : Time-stamp: Wed 07:38 JST hig e, ( ) L01 I(2017) 1 / 19

I L01( Wed) : Time-stamp: Wed 07:38 JST hig e,   ( ) L01 I(2017) 1 / 19 I L01(2017-09-20 Wed) : Time-stamp: 2017-09-20 Wed 07:38 JST hig e, http://hig3.net ( ) L01 I(2017) 1 / 19 ? 1? 2? ( ) L01 I(2017) 2 / 19 ?,,.,., 1..,. 1,2,.,.,. ( ) L01 I(2017) 3 / 19 ? I. M (3 ) II,

More information

Microsoft Word - 計量研修テキスト_第5版).doc

Microsoft Word - 計量研修テキスト_第5版).doc Q9-1 テキスト P166 2)VAR の推定 注 ) 各変数について ADF 検定を行った結果 和文の次数はすべて 1 である 作業手順 4 情報量基準 (AIC) によるラグ次数の選択 VAR Lag Order Selection Criteria Endogenous variables: D(IG9S) D(IP9S) D(CP9S) Exogenous variables: C Date:

More information

7 ( 7 ( Workfile Excel hatuden 1000kWh kion_average kion_max kion_min date holiday *1 obon 7.1 Workfile 1. Workfile File - New -

7 ( 7 ( Workfile Excel hatuden 1000kWh kion_average kion_max kion_min date holiday *1 obon 7.1 Workfile 1. Workfile File - New - 1 EViews 4 2007 7 4 7 ( 2 7.1 Workfile............................................ 2 7.2........................................... 4 8 6 8.1................................................. 6 8.2................................................

More information

untitled

untitled WinLD R (16) WinLD https://www.biostat.wisc.edu/content/lan-demets-method-statistical-programs-clinical-trials WinLD.zip 2 2 1 α = 5% Type I error rate 1 5.0 % 2 9.8 % 3 14.3 % 5 22.6 % 10 40.1 % 3 Type

More information

Microsoft Word - 計量研修テキスト_第5版).doc

Microsoft Word - 計量研修テキスト_第5版).doc Q4-1 テキスト P83 多重共線性が発生する回帰 320000 280000 240000 200000 6000 4000 160000 120000 2000 0-2000 -4000 74 76 78 80 82 84 86 88 90 92 94 96 98 R e s i dual A c tual Fi tted Dependent Variable: C90 Date: 10/27/05

More information

kubostat7f p GLM! logistic regression as usual? N? GLM GLM doesn t work! GLM!! probabilit distribution binomial distribution : : β + β x i link functi

kubostat7f p GLM! logistic regression as usual? N? GLM GLM doesn t work! GLM!! probabilit distribution binomial distribution : : β + β x i link functi kubostat7f p statistaical models appeared in the class 7 (f) kubo@eeshokudaiacjp https://googl/z9cjy 7 : 7 : The development of linear models Hierarchical Baesian Model Be more flexible Generalized Linear

More information

GLM PROC GLM y = Xβ + ε y X β ε ε σ 2 E[ε] = 0 var[ε] = σ 2 I σ 2 0 σ 2 =... 0 σ 2 σ 2 I ε σ 2 y E[y] =Xβ var[y] =σ 2 I PROC GLM

GLM PROC GLM y = Xβ + ε y X β ε ε σ 2 E[ε] = 0 var[ε] = σ 2 I σ 2 0 σ 2 =... 0 σ 2 σ 2 I ε σ 2 y E[y] =Xβ var[y] =σ 2 I PROC GLM PROC MIXED ( ) An Introdunction to PROC MIXED Junji Kishimoto SAS Institute Japan / Keio Univ. SFC / Univ. of Tokyo e-mail address: jpnjak@jpn.sas.com PROC MIXED PROC GLM PROC MIXED,,,, 1 1.1 PROC MIXED

More information

分布

分布 (normal distribution) 30 2 Skewed graph 1 2 (variance) s 2 = 1/(n-1) (xi x) 2 x = mean, s = variance (variance) (standard deviation) SD = SQR (var) or 8 8 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 8 0 1 8 (probability

More information

DVIOUT-ar

DVIOUT-ar 1 4 μ=0, σ=1 5 μ=2, σ=1 5 μ=0, σ=2 3 2 1 0-1 -2-3 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 -2-3 -4-5 0 10 20 30 40 50 60 70 80 90 8 μ=2, σ=2 5 μ=1, θ 1 =0.5, σ=1

More information

untitled

untitled 146,650 168,577 116,665 122,915 22,420 23,100 7,564 22,562 140,317 166,252 133,581 158,677 186 376 204 257 5,594 6,167 750 775 6,333 2,325 298 88 5,358 756 1,273 1,657 - - 23,905 23,923 1,749 489 1,309

More information

kubostat2017c p (c) Poisson regression, a generalized linear model (GLM) : :

kubostat2017c p (c) Poisson regression, a generalized linear model (GLM) : : kubostat2017c p.1 2017 (c), a generalized linear model (GLM) : kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2017 11 14 : 2017 11 07 15:43 kubostat2017c (http://goo.gl/76c4i) 2017 (c) 2017 11 14 1 / 47 agenda

More information

k3 ( :07 ) 2 (A) k = 1 (B) k = 7 y x x 1 (k2)?? x y (A) GLM (k

k3 ( :07 ) 2 (A) k = 1 (B) k = 7 y x x 1 (k2)?? x y (A) GLM (k 2012 11 01 k3 (2012-10-24 14:07 ) 1 6 3 (2012 11 01 k3) kubo@ees.hokudai.ac.jp web http://goo.gl/wijx2 web http://goo.gl/ufq2 1 3 2 : 4 3 AIC 6 4 7 5 8 6 : 9 7 11 8 12 8.1 (1)........ 13 8.2 (2) χ 2....................

More information

Microsoft Word - 計量研修テキスト_第5版).doc

Microsoft Word - 計量研修テキスト_第5版).doc Q8-1 テキスト P131 Engle-Granger 検定 Dependent Variable: RM2 Date: 11/04/05 Time: 15:15 Sample: 1967Q1 1999Q1 Included observations: 129 RGDP 0.012792 0.000194 65.92203 0.0000 R -95.45715 11.33648-8.420349

More information

一般化線形 (混合) モデル (2) - ロジスティック回帰と GLMM

一般化線形 (混合) モデル (2) - ロジスティック回帰と GLMM .. ( ) (2) GLMM kubo@ees.hokudai.ac.jp I http://goo.gl/rrhzey 2013 08 27 : 2013 08 27 08:29 kubostat2013ou2 (http://goo.gl/rrhzey) ( ) (2) 2013 08 27 1 / 74 I.1 N k.2 binomial distribution logit link function.3.4!

More information

1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1

1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1 2005 1 1991 1996 5 i 1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1 2 13 *3 *4 200 1 14 2 250m :64.3km 457mm :76.4km 200 1 548mm 16 9 12 589 13 8 50m

More information

yamadaiR(cEFA).pdf

yamadaiR(cEFA).pdf R 2012/10/05 Kosugi,E.Koji (Yamadai.R) Categorical Factor Analysis by using R 2012/10/05 1 / 9 Why we use... 3 5 Kosugi,E.Koji (Yamadai.R) Categorical Factor Analysis by using R 2012/10/05 2 / 9 FA vs

More information

4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model

4.9 Hausman Test Time Fixed Effects Model vs Time Random Effects Model Two-way Fixed Effects Model 1 EViews 5 2007 7 11 2010 5 17 1 ( ) 3 1.1........................................... 4 1.2................................... 9 2 11 3 14 3.1 Pooled OLS.............................................. 14

More information

151021slide.dvi

151021slide.dvi : Mac I 1 ( 5 Windows (Mac Excel : Excel 2007 9 10 1 4 http://asakura.co.jp/ books/isbn/978-4-254-12172-8/ (1 1 9 1/29 (,,... (,,,... (,,, (3 3/29 (, (F7, Ctrl + i, (Shift +, Shift + Ctrl (, a i (, Enter,

More information

201711grade1ouyou.pdf

201711grade1ouyou.pdf 2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2

More information

講義のーと : データ解析のための統計モデリング. 第2回

講義のーと :  データ解析のための統計モデリング. 第2回 Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20

More information

自由集会時系列part2web.key

自由集会時系列part2web.key spurious correlation spurious regression xt=xt-1+n(0,σ^2) yt=yt-1+n(0,σ^2) n=20 type1error(5%)=0.4703 no trend 0 1000 2000 3000 4000 p for r xt=xt-1+n(0,σ^2) random walk random walk variable -5 0 5 variable

More information

kubostat2015e p.2 how to specify Poisson regression model, a GLM GLM how to specify model, a GLM GLM logistic probability distribution Poisson distrib

kubostat2015e p.2 how to specify Poisson regression model, a GLM GLM how to specify model, a GLM GLM logistic probability distribution Poisson distrib kubostat2015e p.1 I 2015 (e) GLM kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2015 07 22 2015 07 21 16:26 kubostat2015e (http://goo.gl/76c4i) 2015 (e) 2015 07 22 1 / 42 1 N k 2 binomial distribution logit

More information

日本統計学会誌, 第44巻, 第2号, 251頁-270頁

日本統計学会誌, 第44巻, 第2号, 251頁-270頁 44, 2, 205 3 25 270 Multiple Comparison Procedures for Checking Differences among Sequence of Normal Means with Ordered Restriction Tsunehisa Imada Lee and Spurrier (995) Lee and Spurrier (995) (204) (2006)

More information

H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I

H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I H BioS (i) I treat II treat data d; input group patno treat treat; cards; 8 7 4 8 8 5 5 6 ; run; I II sum data d; set d; sum treat + treat; run; sum proc gplot data d; plot sum * group ; symbol c black

More information

DAA12

DAA12 Observed Data (Total variance) Predicted Data (prediction variance) Errors in Prediction (error variance) Shoesize 23 24 25 26 27 male female male mean female mean overall mean Shoesize 23 24 25 26 27

More information

tokei01.dvi

tokei01.dvi 2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN

More information

THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE.

THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. E-mail: {ytamura,takai,tkato,tm}@vision.kuee.kyoto-u.ac.jp Abstract Current Wave Pattern Analysis for Anomaly

More information

n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i

n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i 15 Comparison and Evaluation of Dynamic Programming and Genetic Algorithm for a Knapsack Problem 1040277 2004 2 25 n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i Abstract Comparison and

More information

2011 8 26 3 I 5 1 7 1.1 Markov................................ 7 2 Gau 13 2.1.................................. 13 2.2............................... 18 2.3............................ 23 3 Gau (Le vy

More information

オーストラリア研究紀要 36号(P)☆/3.橋本

オーストラリア研究紀要 36号(P)☆/3.橋本 36 p.9 202010 Tourism Demand and the per capita GDP : Evidence from Australia Keiji Hashimoto Otemon Gakuin University Abstract Using Australian quarterly data1981: 2 2009: 4some time-series econometrics

More information

Microsoft Word - 計量研修テキスト_第5版).doc

Microsoft Word - 計量研修テキスト_第5版).doc Q3-1-1 テキスト P59 10.8.3.2.1.0 -.1 -.2 10.4 10.0 9.6 9.2 8.8 -.3 76 78 80 82 84 86 88 90 92 94 96 98 R e s i d u al A c tual Fi tte d Dependent Variable: LOG(TAXH) Date: 10/26/05 Time: 15:42 Sample: 1975

More information

(pdf) (cdf) Matlab χ ( ) F t

(pdf) (cdf) Matlab χ ( ) F t (, ) (univariate) (bivariate) (multi-variate) Matlab Octave Matlab Matlab/Octave --...............3. (pdf) (cdf)...3.4....4.5....4.6....7.7. Matlab...8.7.....9.7.. χ ( )...0.7.3.....7.4. F....7.5. t-...3.8....4.8.....4.8.....5.8.3....6.8.4....8.8.5....8.8.6....8.9....9.9.....9.9.....0.9.3....0.9.4.....9.5.....0....3

More information

Microsoft Word - StatsDirectMA Web ver. 2.0.doc

Microsoft Word - StatsDirectMA Web ver. 2.0.doc Web version. 2.0 15 May 2006 StatsDirect ver. 2.0 15 May 2006 2 2 2 Meta-Analysis for Beginners by using the StatsDirect ver. 2.0 15 May 2006 Yukari KAMIJIMA 1), Ataru IGARASHI 2), Kiichiro TSUTANI 2)

More information

広報さがみはら第1242号

広報さがみはら第1242号 LINE UP 3 1 5 6 1 NO.1242 S A G A M I H A R A 1 1 1 16 16 1 6 1 6 1 6 1 1 1 1 1 11 1 1 1 1 1 1 6 1 6 1 1 1 1 1 1 1 1 11 1 1 16 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 16 1 16 1 6 1 1 1 1 1 1

More information

²¾ÁÛ¾õ¶·É¾²ÁË¡¤Î¤¿¤á¤Î¥Ñ¥Ã¥±¡¼¥¸DCchoice ¡Ê»ÃÄêÈÇ¡Ë

²¾ÁÛ¾õ¶·É¾²ÁË¡¤Î¤¿¤á¤Î¥Ñ¥Ã¥±¡¼¥¸DCchoice ¡Ê»ÃÄêÈÇ¡Ë DCchoice ( ) R 2013 2013 11 30 DCchoice package R 2013/11/30 1 / 19 1 (CV) CV 2 DCchoice WTP 3 DCchoice package R 2013/11/30 2 / 19 (Contingent Valuation; CV) WTP CV WTP WTP 1 1989 2 DCchoice package R

More information

kubostat2018d p.2 :? bod size x and fertilization f change seed number? : a statistical model for this example? i response variable seed number : { i

kubostat2018d p.2 :? bod size x and fertilization f change seed number? : a statistical model for this example? i response variable seed number : { i kubostat2018d p.1 I 2018 (d) model selection and kubo@ees.hokudai.ac.jp http://goo.gl/76c4i 2018 06 25 : 2018 06 21 17:45 1 2 3 4 :? AIC : deviance model selection misunderstanding kubostat2018d (http://goo.gl/76c4i)

More information

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó

¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó 2 212 4 13 1 (4/6) : ruby 2 / 35 ( ) : gnuplot 3 / 35 ( ) 4 / 35 (summary statistics) : (mean) (median) (mode) : (range) (variance) (standard deviation) 5 / 35 (mean): x = 1 n (median): { xr+1 m, m = 2r

More information

9 1 (1) (2) (3) (4) (5) (1)-(5) (i) (i + 1) 4 (1) (2) (3) (4) (5) (1)-(2) (1)-(5) (5) 1

9 1 (1) (2) (3) (4) (5) (1)-(5) (i) (i + 1) 4 (1) (2) (3) (4) (5) (1)-(2) (1)-(5) (5) 1 9 1 (1) (2) (3) (4) (5) (1)-(5) (i) (i + 1) 4 (1) (2) (3) (4) (5) (1)-(2) (1)-(5) (5) 1 2 2 y i = 1, 2, 3,...J (1 < 2 < 3

More information

2009 5 1...1 2...3 2.1...3 2.2...3 3...10 3.1...10 3.1.1...10 3.1.2... 11 3.2...14 3.2.1...14 3.2.2...16 3.3...18 3.4...19 3.4.1...19 3.4.2...20 3.4.3...21 4...24 4.1...24 4.2...24 4.3 WinBUGS...25 4.4...28

More information

II III II 1 III ( ) [2] [3] [1] 1 1:

II III II 1 III ( ) [2] [3] [1] 1 1: 2015 4 16 1. II III II 1 III () [2] [3] 2013 11 18 [1] 1 1: [5] [6] () [7] [1] [1] 1998 4 2008 8 2014 8 6 [1] [1] 2 3 4 5 2. 2.1. t Dt L DF t A t (2.1) A t = Dt L + Dt F (2.1) 3 2 1 2008 9 2008 8 2008

More information

橡表紙参照.PDF

橡表紙参照.PDF CIRJE-J-58 X-12-ARIMA 2000 : 2001 6 How to use X-12-ARIMA2000 when you must: A Case Study of Hojinkigyo-Tokei Naoto Kunitomo Faculty of Economics, The University of Tokyo Abstract: We illustrate how to

More information

H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =

H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat = H BioS t (i) treat treat data d; input patno treat treat; cards; 3 8 7 4 8 8 5 5 6 3 ; run; (i) treat treat data d; input group patno period treat y; label group patno period ; cards; 3 8 3 7 4 8 4 8 5

More information

α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β *3 2.3 * *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P + 10) 15 (µ A = µ P +

α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β *3 2.3 * *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P + 10) 15 (µ A = µ P + Armitage 1 1.1 2 t *1 α β 1.2 µ x µ 2 2 2 α β 2.1 1 α β α ( ) β *1 t t 1 α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β 1 0 0 1 1 5 2.5 *3 2.3 *4 3 3.1 1 1 1 *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P

More information

A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P

A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P 1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A

More information

時系列解析

時系列解析 B L12(2016-07-11 Mon) : Time-stamp: 2016-07-11 Mon 17:25 JST hig,, Excel,. http://hig3.net ( ) L12 B(2016) 1 / 24 L11-Q1 Quiz : 1 E[R] = 1 2, V[R] = 9 12 = 3 4. R(t), E[X(30)] = E[X(0)] + 30 1 2 = 115,

More information

Dependent Variable: LOG(GDP00/(E*HOUR)) Date: 02/27/06 Time: 16:39 Sample (adjusted): 1994Q1 2005Q3 Included observations: 47 after adjustments C -1.5

Dependent Variable: LOG(GDP00/(E*HOUR)) Date: 02/27/06 Time: 16:39 Sample (adjusted): 1994Q1 2005Q3 Included observations: 47 after adjustments C -1.5 第 4 章 この章では 最小二乗法をベースにして 推計上のさまざまなテクニックを検討する 変数のバリエーション 係数の制約係数にあらかじめ制約がある場合がある たとえばマクロの生産関数は 次のように表すことができる 生産要素は資本と労働である 稼動資本は資本ストックに稼働率をかけることで計算でき 労働投入量は 就業者数に総労働時間をかけることで計算できる 制約を掛けずに 推計すると次の結果が得られる

More information

Studies of Foot Form for Footwear Design (Part 9) : Characteristics of the Foot Form of Young and Elder Women Based on their Sizes of Ball Joint Girth

Studies of Foot Form for Footwear Design (Part 9) : Characteristics of the Foot Form of Young and Elder Women Based on their Sizes of Ball Joint Girth Studies of Foot Form for Footwear Design (Part 9) : Characteristics of the Foot Form of Young and Elder Women Based on their Sizes of Ball Joint Girth and Foot Breadth Akiko Yamamoto Fukuoka Women's University,

More information

10:30 12:00 P.G. vs vs vs 2

10:30 12:00 P.G. vs vs vs 2 1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B

More information

2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 1, 2 1, 3? , 2 2, 3? k, l m, n k, l m, n kn > ml...? 2 m, n n m

2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 1, 2 1, 3? , 2 2, 3? k, l m, n k, l m, n kn > ml...? 2 m, n n m 2009 IA I 22, 23, 24, 25, 26, 27 4 21 1 1 2 1! 4, 5 1? 50 1 2 1 1 2 1 4 2 2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 1, 2 1, 3? 2 1 3 1 2 1 1, 2 2, 3? 2 1 3 2 3 2 k, l m, n k, l m, n kn > ml...? 2 m, n n m 3 2

More information

Rによる計量分析:データ解析と可視化 - 第3回 Rの基礎とデータ操作・管理

Rによる計量分析:データ解析と可視化 - 第3回  Rの基礎とデータ操作・管理 R 3 R 2017 Email: gito@eco.u-toyama.ac.jp October 23, 2017 (Toyama/NIHU) R ( 3 ) October 23, 2017 1 / 34 Agenda 1 2 3 4 R 5 RStudio (Toyama/NIHU) R ( 3 ) October 23, 2017 2 / 34 10/30 (Mon.) 12/11 (Mon.)

More information

Part 1 GARCH () ( ) /24, p.2/93

Part 1 GARCH () ( ) /24, p.2/93 基盤研究 A 統計科学における数理的手法の理論と応用 ( 研究代表者 : 谷口正信 ) によるシンポジウム 計量ファイナンスと時系列解析法の新たな展開 平成 20 年 1 月 24 日 ~26 日香川大学 Realized Volatility の長期記憶性について 1 研究代表者 : 前川功一 ( 広島経済大学 ) 共同研究者 : 得津康義 ( 広島経済大学 ) 河合研一 ( 統計数理研究所リスク解析戦略研究センター

More information

2007-Kanai-paper.dvi

2007-Kanai-paper.dvi 19 Estimation of Sound Source Zone using The Arrival Time Interval 1080351 2008 3 7 S/N 2 2 2 i Abstract Estimation of Sound Source Zone using The Arrival Time Interval Koichiro Kanai The microphone array

More information

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H 1 1 1.1 *1 1. 1.3.1 n x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ H 0, H 1 * σ σ 0, σ 1 *1 * H 0 H 0, H 1 H 1 1 H 0 µ, σ 0 H 1 µ 1, µ, σ 1 L 0 µ, σ x L 1 µ 1, µ, σ x x H 0 L 0 µ, σ 0

More information

12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? ( :51 ) 2/ 71

12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? ( :51 ) 2/ 71 2010-12-02 (2010 12 02 10 :51 ) 1/ 71 GCOE 2010-12-02 WinBUGS kubo@ees.hokudai.ac.jp http://goo.gl/bukrb 12/1 ( ) GLM, R MCMC, WinBUGS 12/2 ( ) WinBUGS WinBUGS 12/2 ( ) : 12/3 ( ) :? 2010-12-02 (2010 12

More information

²�ËÜËܤǻþ·ÏÎó²òÀÏÊÙ¶¯²ñ - Â裱¾Ï¤ÈÂ裲¾ÏÁ°È¾

²�ËÜËܤǻþ·ÏÎó²òÀÏÊÙ¶¯²ñ - Â裱¾Ï¤ÈÂ裲¾ÏÁ°È¾ Kano Lab. Yuchi MATSUOKA December 22, 2016 1 / 32 1 1.1 1.2 1.3 1.4 2 ARMA 2.1 ARMA 2 / 32 1 1.1 1.2 1.3 1.4 2 ARMA 2.1 ARMA 3 / 32 1.1.1 - - - 4 / 32 1.1.2 - - - - - 5 / 32 1.1.3 y t µ t = E(y t ), V

More information

読めば必ずわかる 分散分析の基礎 第2版

読めば必ずわかる 分散分析の基礎 第2版 2 2003 12 5 ( ) ( ) 2 I 3 1 3 2 2? 6 3 11 4? 12 II 14 5 15 6 16 7 17 8 19 9 21 10 22 11 F 25 12 : 1 26 3 I 1 17 11 x 1, x 2,, x n x( ) x = 1 n n i=1 x i 12 (SD ) x 1, x 2,, x n s 2 s 2 = 1 n n (x i x)

More information

LA-VAR Toda- Yamamoto(1995) VAR (Lag Augmented vector autoregressive model LA-VAR ) 2 2 Nordhaus(1975) 3 1 (D2)

LA-VAR Toda- Yamamoto(1995) VAR (Lag Augmented vector autoregressive model LA-VAR ) 2 2 Nordhaus(1975) 3 1 (D2) LA-VAR 1 1 1973 4 2000 4 Toda- Yamamoto(1995) VAR (Lag Augmented vector autoregressive model LA-VAR ) 2 2 Nordhaus(1975) 3 1 (D2) E-mail b1215@yamaguchi-u.ac.jp 2 Toda, Hiro Y. and Yamamoto,T.(1995) 3

More information

研究シリーズ第40号

研究シリーズ第40号 165 PEN WPI CPI WAGE IIP Feige and Pearce 166 167 168 169 Vector Autoregression n (z) z z p p p zt = φ1zt 1 + φ2zt 2 + + φ pzt p + t Cov( 0 ε t, ε t j )= Σ for for j 0 j = 0 Cov( ε t, zt j ) = 0 j = >

More information