-- o C inter Arctic Oscillation Index Sapporo Air-Temp Matlab randn (red n
|
|
- あいと あいしま
- 5 years ago
- Views:
Transcription
1 (autoregressive process) (MA) (ARMA) (ARIMA) (persistency) (serial correlation) m amias (988) 970 SST (re-emergence) Alexander (999)
2 -- o C inter Arctic Oscillation Index Sapporo Air-Temp Matlab randn (red noise model) yt () = ryt ( ) + σε() t (.) y(t) t r ε σ (white noise) r=0 r -.
3 (.) r σ σ R σ yt () = r yt ( ) + rσ yt ( ) ε() t R = r σ + σ R + σ ε() t σ = σ σ = σ (.) ( r ) R R / ( r ) <> σ σ R (.) Allen and Smith (996) (first order Markov process)
4 tlng, nsmpl, r rtsrs=randn(tlng,nsmpl); % tlngnsmpl rtsrs(,:)=rtsrs(,:)/sqrt(-r^); % for t=:tlng rtsrs(t,:)=rtsrs(t-,:)*r+rtsrs(t,:); end - r=0.5, nsmpl=0000, tlng=0 m n (/ n) y ( t) i= m
5 (autoregressive process) (autoregressive model) p yt ( ) + φ() yt ( ) φ( pyt ) ( p) + σε( t) = 0 (.3) φ() i y y t AR(q) φ AR AR Matlab yt () = yt () yt ( ) + φ() yt ( ) φ( pyt ) ( p) = 0
6 -6- t p yt () = λ yt ( p) (.4) yt () = λ yt ( ) p p λ + φ() λ... + φ( p) = 0 λ> y λ= λ< AR AR φ () <..4. Maximum Entropy Method (MEM) Spectrum φ τ ρτ ( ) yt ( ) yt ( + τ) ρτ ( ) yt ( ) yt ( τ) { ()... ( p) p σ ε } = φ yt ( ) + + φ yt ( ) + ( t) yt ( τ) = φ() yt ( ) yt ( τ) φ( p) yt ( pyt ) ( τ) + σ ε( t) yt ( τ) (.5) ρτ ( ) + φ() yt ( ) yt ( τ) φ( p) yt ( pyt ) ( τ) + σ ε( t) yt ( τ) = 0 ρτ ( ) + φ() ρτ ( ) φ( p) ρ( t p) = 0 σ = ρ(0) r r() τ + φ()( r τ ) + φ()( r τ ) φ( p)( r t p) = 0 (.6) AR r() = φ() AR 0 (.5) yt ( ), t=,..., n yt ( + τ )
7 -7- ρ(0) + φ() yt ( ) yt ( τ) φ( p) yt ( pyt ) ( τ) + σ ε( t) yt ( ) = 0 φ() r() φ() r()... φ( p) r( p) σ / σ = (.7) (.6) (.7) r() r() r( p) σ / σ () r() r( p ) φ r() φ() r() r() r( p ) = r() φ( p) r( p ) r( p ) r( p) (.8) Toeplitz( ) r() r() r( p) σ / σ r() r() r( p ) φ() 0 r() r() r( p ) φ() = 0 r( p) r( p ) r( p ) φ ( p) 0 (.9) (Yule-alker equation) Matlab lpc, pyulear p p p p (Akaike s Information Criterion, AIC) p AIC (996) AIC AIC = + + p + (.0) ln πσ ( ) AIC = + p + (.) ln σ ( ) AIC AIC AR ) AR
8 -8- ) AR AIC 3) AIC AR φ( p) (Burg) Matlab pburg p p (.6)..5. (MA) q (moving-average process, MA process) yt ( ) + ε( t) + θ() ε( t ) + θ() ε( t ) θ( q) ε( t q), t=,..., n y y t MA(q) MA AR() MA..6. (ARMA) p,q (autoregressive-moving average process, ARMA process) y t ARMA(p,q) (,985, (.5)) yt ( ) + φ() yt ( ) φ( pyt ) ( p) + ε( t) + θ() ε( t ) θ( q) ε( t q) = 0, t =,..., T p,q ARMA AR ARMA..7. (ARIMA) (autoregressive-integrated-moving moving average) ARIMA ARIMA y(t)-y(t-)arma ARIMA..8. (correlogram).3.
9 -9- (time between effectively independent samples, Trenberth (984) Metz (99) ) (effective decorrelation time) T e (effective number of degrees of freedom) τ τ Te = rxx( τ) = + rxx( τ) τ= τ= (.) τ τ Te = rxx ( τ) = + rxx ( τ) τ= τ= (.3) τ Te = rxx( ) ryy( ) rxy( ) ryx( ) τ τ + τ τ τ = τ = + rxy (0) ryx(0) + rxx ( τ) ryy ( τ) + rxy ( τ) ryx ( τ) τ = (.4) r τ τ xtxt ( ) ( + τ) yt ( ) yt ( + τ) τ t= τ t= rx ( τ), ryy( τ), x xt () yt () t= t= τ xt () yt ( + τ ) τ t= rxy ( τ ) xt () yt () t= t= Lieth (98) Bayley and Hammersley (946) Lieth (98)Trenberth (984) Bartlett 930 Bartlett(955) Davis (976) Lieth 98 (Trenberth 984 reference ) Katz (98)Trenberth (984) AR AR
10 -0- AR Trenberth(984) (/ ) x( t) x( t+ τ ) AR AR AIC τ t=.3.. {} x x ({} ) {} {} {} v x x = x x x + x = x x (.5) () (.6) t = v= x t x x x= x ' + µ, µ= x v= x'( t) + µ x t= = = ( x'( t) + µ )( x'( s) + µ ) µ s= t= ( x'( t) x'( s) + ( x'( s) + x'( t) ) µ + µ ) µ s= t= = x'( t) x'( s) + x'( s) + x'( t) + µ s= t= µ x'( t) x'( s) = s = t = { } τ= j i σ τ v= = r τ= τ= (.7) ( τ ) ρxx ( τ) xx ( τ) (.8)
11 -- σ e / = σ T / (.9) e e Te Te = / e (.8)(.9) T e τ = rxx( τ ) τ = (.0) (.) (.7) v= x'( t) + x x t= s= t= s= t= s= t= = ( x'( t) + x)( x'( s) + x) x = ( x'( t) x'( s) + ( x'( s) + x'( t) ) x + x ) x { '( ) '( ) '( ) '( ) } = x t x s x s x t x x x (.).3.. (.4) <> {} (sample mean) q(i), i=,, {} q = (/ ) q () i x, y < xy >= V sample variance { xy} = V + v (sample variance) v= { xy} < xy > v = { xy} { xy} < xy >+< xy> v n= v = { xy} { xy} xy + xy = { xy} xy {} q = q
12 -- = x y x y xy v () t () t () s () s t= s= = xt () ytxs () () ys ( ) t= s= = xt () yt () xs ( ) ys () t= s= xy xy <> ( p.33) x, x, x, x m n p q xmxnxpxq xmxn xpxq + xmxp xnxq + xmxq xnxp v = () ( ) () () () () () ( ) () () ( ) ( ) x t x s y t y s x t y s y t x s x t x t y s y s xy + + t= s= = xt () xs ( ) yt () ys () xt () ys () yt () xs ( ) + t= s= τ= j i v τ = ρxx ( τ) ρyy ( τ) + ρxy ( τ) ρyx ( τ) τ = (.) ρxx( τ) = xtxt ( ) ( + τ), ρyy ( τ) = yt ( ) yt ( + τ), ρ ( τ) = xt ( ) yt ( + τ), ρ ( τ) = ytxt ( ) ( + τ) xy yx x, y Q = x, Q = y r ( τ) = ρ ( τ)/ Q, r ( τ) = ρ ( τ)/ Q, r ( τ) = ρ ( τ)/ Q Q xx xx x yy yy y xy xy x y (.) QQ τ ( τ) ( τ) ( τ) ( τ) (.3) x y v = τ = rxx ryy + rxy ryx x y
13 -3- xt ()', yt ()', t=,..., t= xt () yt () = QQ x y v ( the effective number of degrees of freedom (effective sample size), Metz (99)) QQ τ QQ QQ x y x y x y v = rxx ( ) ryy ( ) rxy ( ) ryx ( ) τ τ + τ τ = = τ = e t/ Te T e τ Te = t rxx( τ) ryy( τ) + rxy( τ) ryx( τ) τ = (.4) DOF = t / Te [] (.4) Te = t rxx( τ) ryy( τ) + rxy( τ) ryx( τ) τ = (, ) e.4. Finite Impulse Reponse (FIR) Infinite Impulse Response (IIR) FIRIIR Press (993) FIR IIR IIR
14 -4- Matlab fft ifft filter filtfilt butter Allen, Myles R., and Leonard A. Smith, 996: Monte Carlo SSA: Detecting irregular oscillations in the Presence of Colored oise. J. Climate, 9 (), Alexander, M. A., C. Deser, and M. S. Timlin, 999: The Reemergence of SST anomalies in the orth Pacific Ocean. J. Climate, (8), Bartlett, M. S., 955: An introduction to stochastic processes with special reference to methods and applications. Cambridge university press, pp (third edition 978) Bayley G. V. and J. M. Hammersley, 946: The 'effective' number of independent observations in autocorrelated time series. J. Roy. Statist. Soc. Suppl., 8(), Davis, R. E., 976: Predictability of sea surface temperature and sea level pressure anomalies over the orth Pacific Ocean. J. Phys. Oceanogr. 6 (3), Hanan, E. J. 970: Multiple Time Seies. iley. Katz, R.., 98: Statistical evaluation of climate experiments with genal circulation models: A parametric time series modeling approach. J. Atmos. Sci., 39, pp. 37, 989. Lieth, C. E.,98: Statistical methods for the verification of long and short range forecasts. ECMF seminar on Problems and prospects in long and medium range weather forecasting [available from ECMF] Metz,., 99 : Optimal relationship of large-scale flow patterns and the barotropic feedback due to high-frequency eddies, J. Atmos. Sci., 48, amias, J., X.,Yuan, and D. R. Cayan, 988: Persistence of orth Pacific Sea Surface Temperature and Atmospheric Flow Patterns. J. Climate,, Press,. H., B. P. Flannery, S. A. Teukolsky,. T. Vetterling, 993: umerical Recipes in C [ ],, pp Trenberth K. E., 984: Some effects of finite sample size and persistence on meteorological statistics. Part I: autocorrelations. Mon. ea. Rev.,,
-- Blackman-Tukey FFT MEM Blackman-Tukey MEM MEM MEM MEM Singular Spectrum Analysis Multi-Taper Method (Matlab pmtm) 3... y(t) (Fourier transform) t=
--... 3..... 3...... 3...... 3..3....3 3..4....4 3..5....5 3.....6 3......6 3......7 3..3....0 3..4. Matlab... 3.3....3 3.3.....3 3.3.....4 3.3.3....4 3.3.4....5 3.3.5....5 3.4. MEM...8 3.4.. MEM...8 3.4..
More information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(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 informationStata 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 informationDVIOUT-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 informationseminar0220a.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 information01.Œk’ì/“²fi¡*
AIC AIC y n r n = logy n = logy n logy n ARCHEngle r n = σ n w n logσ n 2 = α + β w n 2 () r n = σ n w n logσ n 2 = α + β logσ n 2 + v n (2) w n r n logr n 2 = logσ n 2 + logw n 2 logσ n 2 = α +β logσ
More informationII 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カルマンフィルターによるベータ推定( )
β TOPIX 1 22 β β smoothness priors (the Capital Asset Pricing Model, CAPM) CAPM 1 β β β β smoothness priors :,,. E-mail: koiti@ism.ac.jp., 104 1 TOPIX β Z i = β i Z m + α i (1) Z i Z m α i α i β i (the
More informationIsogai, 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 information10:30 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 informationRecent Developments and Perspectives of Statistical Time Series Analysis /ta) : t"i,,t Q) w (^ - p) dp *+*ffi t 1 ] Abraham, B. and Ledolter, J. (1986). Forecast functions implied by autoregressive
More informationブック
ARMA Estimation on Process of ARMA Time Series Model Sanno University Bulletin Vol.26 No. 2 February 2006 ARMA Estimation on Process of ARMA Time Series Model Many papers and books have been published
More informationimpulse_response.dvi
5 Time Time Level Level Frequency Frequency Fig. 5.1: [1] 2004. [2] P. A. Nelson, S. J. Elliott, Active Noise Control, Academic Press, 1992. [3] M. R. Schroeder, Integrated-impulse method measuring sound
More information1.7 D D 2 100m 10 9 ev f(x) xf(x) = c(s)x (s 1) (x + 1) (s 4.5) (1) s age parameter x f(x) ev 10 9 ev 2
2005 1 3 5.0 10 15 7.5 10 15 ev 300 12 40 Mrk421 Mrk421 1 3.7 4 20 [1] Grassberger-Procaccia [2] Wolf [3] 11 11 11 11 300 289 11 11 1 1.7 D D 2 100m 10 9 ev f(x) xf(x) = c(s)x (s 1) (x + 1) (s 4.5) (1)
More informationarma dvi
ARMA 007/05/0 Rev.0 007/05/ Rev.0 007/07/7 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3.3 : : : :
More informationOn model selection problems in terms of prediction mean squared error and interpretaion of AIC (slides)
Applications in Econometrics and Finance by Long Memory Processes 2007 11 6 13:30-16:10 Table of Contents PART1 PART2 PART3 PART1 1 {y t } ρ(h) = ( h ) = Cov[y t y t+h ]/ Var[y t ] (yt y)(y t+h y) ρ(h)
More informationばらつき抑制のための確率最適制御
( ) http://wwwhayanuemnagoya-uacjp/ fujimoto/ 2011 3 9 11 ( ) 2011/03/09-11 1 / 46 Outline 1 2 3 4 5 ( ) 2011/03/09-11 2 / 46 Outline 1 2 3 4 5 ( ) 2011/03/09-11 3 / 46 (1/2) r + Controller - u Plant y
More information( ) ) ) ) 5) 1 J = σe 2 6) ) 9) 1955 Statistical-Mechanical Theory of Irreversible Processes )
( 3 7 4 ) 2 2 ) 8 2 954 2) 955 3) 5) J = σe 2 6) 955 7) 9) 955 Statistical-Mechanical Theory of Irreversible Processes 957 ) 3 4 2 A B H (t) = Ae iωt B(t) = B(ω)e iωt B(ω) = [ Φ R (ω) Φ R () ] iω Φ R (t)
More informationMcCain & McCleary (1979) The Statistical Analysis of the Simple Interrupted Time-Series Quasi-Experiment
Quasi-Experimenaion Ch.6 005/8/7 ypo rep: The Saisical Analysis of he Simple Inerruped Time-Series Quasi-Experimen INTRODUCTION () THE PROBLEM WITH ORDINAR LEAST SQUARE REGRESSION OLS (Ordinary Leas Square)
More informationAR(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
87 6.1 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,
More informationmains.dvi
8 Λ MRI.COM 8.1 Mellor and Yamada (198) level.5 8. Noh and Kim (1999) 8.3 Large et al. (1994) K-profile parameterization 8.1 8.1: (MRI.COM ) Mellor and Yamada Noh and Kim KPP (avdsl) K H K B K x (avm)
More information²�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 information1 Tokyo Daily Rainfall (mm) Days (mm)
( ) r-taka@maritime.kobe-u.ac.jp 1 Tokyo Daily Rainfall (mm) 0 100 200 300 0 10000 20000 30000 40000 50000 Days (mm) 1876 1 1 2013 12 31 Tokyo, 1876 Daily Rainfall (mm) 0 50 100 150 0 100 200 300 Tokyo,
More information10
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 informationD v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco
post glacial rebound 3.1 Viscosity and Newtonian fluid f i = kx i σ ij e kl ideal fluid (1.9) irreversible process e ij u k strain rate tensor (3.1) v i u i / t e ij v F 23 D v D F v/d F v D F η v D (3.2)
More information80 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 informationdpri04.dvi
47 B 6 4 Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 47B, 24 AR AR :,, AR,. () point process Waymire et et al. (984) WGR () Over and Gupta (994, 996) Chatchai et al. (2) (23) Fig. Structure for
More informationInput image Initialize variables Loop for period of oscillation Update height map Make shade image Change property of image Output image Change time L
1,a) 1,b) 1/f β Generation Method of Animation from Pictures with Natural Flicker Abstract: Some methods to create animation automatically from one picture have been proposed. There is a method that gives
More information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ウェーブレット分数を用いた金融時系列の長期記憶性の分析
TOPIX E-mail: masakazu.inada@boj.or.jp wavelet TOPIX Baillie Gourieroux and Jasiak Elliott and Hoek TOPIX I (0) I (1) I (0) I (1) TOPIX ADFAugmented Dickey-Fuller testppphillips-perron test I (1) I (0)
More information数値計算:常微分方程式
( ) 1 / 82 1 2 3 4 5 6 ( ) 2 / 82 ( ) 3 / 82 C θ l y m O x mg λ ( ) 4 / 82 θ t C J = ml 2 C mgl sin θ θ C J θ = mgl sin θ = θ ( ) 5 / 82 ω = θ J ω = mgl sin θ ω J = ml 2 θ = ω, ω = g l sin θ = θ ω ( )
More information& 3 3 ' ' (., (Pixel), (Light Intensity) (Random Variable). (Joint Probability). V., V = {,,, V }. i x i x = (x, x,, x V ) T. x i i (State Variable),
.... Deeping and Expansion of Large-Scale Random Fields and Probabilistic Image Processing Kazuyuki Tanaka The mathematical frameworks of probabilistic image processing are formulated by means of Markov
More information2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t) = x 0 + v 0 t 1 2 gt2 v(t) = v 0 gt t x = x 0 + v2 0 2g v2 2g 1.1 (x, v) θ
1 1 1.1 (Isaac Newton, 1642 1727) 1. : 2. ( ) F = ma 3. ; F a 2 t x(t) v(t) = x (t) v (t) = x (t) F 3 3 3 3 3 3 6 1 2 6 12 1 3 1 2 m 2 1 x 1.1: v mg x (t) = v(t) mv (t) = mg 0 x(0) = x 0 v(0) = v 0 x(t)
More information画像工学特論
.? (x i, y i )? (x(t), y(t))? (x(t)) (X(ω)) Wiener-Khintchine 35/97 . : x(t) = X(ω)e jωt dω () π X(ω) = x(t)e jωt dt () X(ω) S(ω) = lim (3) ω S(ω)dω X(ω) : F of x : [X] [ = ] [x t] Power spectral density
More information通信容量制約を考慮したフィードバック制御 - 電子情報通信学会 情報理論研究会(IT) 若手研究者のための講演会
IT 1 2 1 2 27 11 24 15:20 16:05 ( ) 27 11 24 1 / 49 1 1940 Witsenhausen 2 3 ( ) 27 11 24 2 / 49 1940 2 gun director Warren Weaver, NDRC (National Defence Research Committee) Final report D-2 project #2,
More information時系列解析と自己回帰モデル
B L11(2017-07-03 Mon) : Time-stamp: 2017-07-03 Mon 11:04 JST hig,,,.,. http://hig3.net ( ) L11 B(2017) 1 / 28 L10-Q1 Quiz : 1 6 6., x[]={1,1,3,3,3,8}; (. ) 2 x = 0, 1, 2,..., 9 10, 10. u[]={0,2,0,3,0,0,0,0,1,0};
More informationtime2print4.dvi
iii 2 P. J. Brockwell and R.A. Davis, Introduction to Time Series and Forecasting, 2nd edition (Springer, 2002) 1 2 ITSM2000(version 7) 6 10 7 2 2 2 ITSM2000 student version professional version CD-ROM
More informationThe Physics of Atmospheres CAPTER :
The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(
More informationxia2.dvi
Journal of Differential Equations 96 (992), 70-84 Melnikov method and transversal homoclinic points in the restricted three-body problem Zhihong Xia Department of Mathematics, Harvard University Cambridge,
More information03.Œk’ì
HRS KG NG-HRS NG-KG AIC Fama 1965 Mandelbrot Blattberg Gonedes t t Kariya, et. al. Nagahara ARCH EngleGARCH Bollerslev EGARCH Nelson GARCH Heynen, et. al. r n r n =σ n w n logσ n =α +βlogσ n 1 + v n w
More informationSample function Re random process Flutter, Galloping, etc. ensemble (mean value) N 1 µ = lim xk( t1) N k = 1 N autocorrelation function N 1 R( t1, t1
Sample function Re random process Flutter, Galloping, etc. ensemble (mean value) µ = lim xk( k = autocorrelation function R( t, t + τ) = lim ( ) ( + τ) xk t xk t k = V p o o R p o, o V S M R realization
More informationNo δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
More informationSeptember 9, 2002 ( ) [1] K. Hukushima and Y. Iba, cond-mat/ [2] H. Takayama and K. Hukushima, cond-mat/020
mailto:hukusima@issp.u-tokyo.ac.jp September 9, 2002 ( ) [1] and Y. Iba, cond-mat/0207123. [2] H. Takayama and, cond-mat/0205276. Typeset by FoilTEX Today s Contents Against Temperature Chaos in Spin Glasses
More informationxyr x y r x y r u u
xyr x y r x y r u u y a b u a b a b c d e f g u a b c d e g u u e e f yx a b a b a b c a b c a b a b c a b a b c a b c a b c a u xy a b u a b c d a b c d u ar ar a xy u a b c a b c a b p a b a b c a
More information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鉄鋼協会プレゼン
NN :~:, 8 Nov., Adaptive H Control for Linear Slider with Friction Compensation positioning mechanism moving table stand manipulator Point to Point Control [G] Continuous Path Control ground Fig. Positoining
More informationtokei01.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 informationx T = (x 1,, x M ) x T x M K C 1,, C K 22 x w y 1: 2 2
Takio Kurita Neurosceince Research Institute, National Institute of Advanced Indastrial Science and Technology takio-kurita@aistgojp (Support Vector Machine, SVM) 1 (Support Vector Machine, SVM) ( ) 2
More information1 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 informationGNSS satellite or Quasar 10m [5] (n 1) 10 6 = K 1 ( P d T ) + K 2( P v T ) + K 3( P v T 2 ) (2) O 1 S G Earth Atmosphere [4] (ray bending) 1 S
- - ( ) A Software Package Development for Estimating Atmospheric Path Delay based on JMA Numerical Weather Prediction Model Ryuichi ICHIKAWA (KASHIMA SPACE RESEARCH CENTER, NICT) Key words: GNSS, VLBI,
More informationGo a σ(a). σ(a) = 2a, 6,28,496, = 2 (2 2 1), 28 = 2 2 (2 3 1), 496 = 2 4 (2 5 1), 8128 = 2 6 (2 7 1). 2 1 Q = 2 e+1 1 a = 2
Go 2016 8 26 28 8 29 1 a σ(a) σ(a) = 2a, 6,28,496,8128 6 = 2 (2 2 1), 28 = 2 2 (2 3 1), 496 = 2 4 (2 5 1), 8128 = 2 6 (2 7 1) 2 1 Q = 2 e+1 1 a = 2 e Q (perfect numbers ) Q = 2 e+1 1 Q 2 e+1 1 e + 1 Q
More informationQUARTERLY JOURNAL HYDROGRAPHY Establishing a JCG/UKHO cooperative framework on nautical charts -- Part. (p. ), Investigations on reproduced Ino-zu Maps, Japanese historical maps,owned by JHOD.(p. ), Various
More information2 4 (four-dimensional variational(4dvar))(talagrand and Courtier(1987), Courtier et al.(1994)) (Ensemble Kalman Filter( EnKF))(Evensen(1994), Evensen(
1,3 2,3 2,3 ; ; ; 1. (Wunsch(1996), Daley(1991), Bennett(2002), (1997)) 1 106-8569 4-6-7 2 106-8569 4-6-7 3 (JST) (CREST) 2 4 (four-dimensional variational(4dvar))(talagrand and Courtier(1987), Courtier
More informationwaseda2010a-jukaiki1-main.dvi
November, 2 Contents 6 2 8 3 3 3 32 32 33 5 34 34 6 35 35 7 4 R 2 7 4 4 9 42 42 2 43 44 2 5 : 2 5 5 23 52 52 23 53 53 23 54 24 6 24 6 6 26 62 62 26 63 t 27 7 27 7 7 28 72 72 28 73 36) 29 8 29 8 29 82 3
More informationnews
ETL NEWS 1999.9 ETL NEWS 1999.11 Establishment of an Evaluation Technique for Laser Pulse Timing Fluctuations Optoelectronics Division Hidemi Tsuchida e-mail:tsuchida@etl.go.jp A new technique has been
More informationLA-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 informationNo pp The Relationship between Southeast Asian Summer Monsoon and Upper Atmospheric Field over Eurasia Takeshi MORI and Shuji YAMAKAWA
No.42 2007 pp.159 166 The Relationship between Southeast Asian Summer Monsoon and Upper Atmospheric Field over Eurasia Takeshi MORI and Shuji YAMAKAWA Received September 30, 2006 Using Southeast Asian
More informationA
A04-164 2008 2 13 1 4 1.1.......................................... 4 1.2..................................... 4 1.3..................................... 4 1.4..................................... 5 2
More information1 5 1.1..................................... 5 1.2..................................... 5 1.3.................................... 6 2 OSPF 7 2.1 OSPF.
2011 2012 1 31 5110B036-6 1 5 1.1..................................... 5 1.2..................................... 5 1.3.................................... 6 2 OSPF 7 2.1 OSPF....................................
More informationVenkatram and Wyngaard, Lectures on Air Pollution Modeling, m km 6.2 Stull, An Introduction to Boundary Layer Meteorology,
65 6 6.1 No.4 1982 1 1981 J. C. Kaimal 1993 1994 Turbulence and Diffusion in the Atmosphere : Lectures in Environmental Sciences, by A. K. Blackadar, Springer, 1998 An Introduction to Boundary Layer Meteorology,
More informationI A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
More information重力方向に基づくコントローラの向き決定方法
( ) 2/Sep 09 1 ( ) ( ) 3 2 X w, Y w, Z w +X w = +Y w = +Z w = 1 X c, Y c, Z c X c, Y c, Z c X w, Y w, Z w Y c Z c X c 1: X c, Y c, Z c Kentaro Yamaguchi@bandainamcogames.co.jp 1 M M v 0, v 1, v 2 v 0 v
More informationk3 ( :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 information02.„o“φiflì„㙃fic†j
X-12-ARIMA Band-PassDECOMP HP X-12-ARIMADECOMP HPBeveridge and Nelson DECOMP X-12-ARIMA Band-PassHodrick and PrescottHP DECOMPBeveridge and Nelson M CD X ARIMA DECOMP HP Band-PassDECOMP Kiyotaki and Moore
More informationuntitled
* 10 100 1 ( ) ( ) 20 2 X f( ) (pdf: probability density function) F( ) X (cdf: cumulative distribution function) (2.1) X ( ) p ( ) W( ) 1 F( ) p p 1(p) W( p) ( p) X 1/T T ( ) T p T T T p 1 1/T p F( )
More information国土技術政策総合研究所資料
ISSN 1346-7328 国総研資料第 652 号平成 23 年 9 月 国土技術政策総合研究所資料 TECHNICAL NOTE of Naional Insiue for Land and Infrasrucure Managemen No.652 Sepember 2011 航空需要予測における計量時系列分析手法の適用性に関する基礎的研究 ~ 季節変動自己回帰移動平均モデル及びベクトル誤差修正モデルの適用性
More information1 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 information1. ( ) L L L Navier-Stokes η L/η η r L( ) r [1] r u r ( ) r Sq u (r) u q r r ζ(q) (1) ζ(q) u r (1) ( ) Kolmogorov, Obukov [2, 1] ɛ r r u r r 1 3
Kolmogorov Toward Large Deviation Statistical Mechanics of Strongly Correlated Fluctuations - Another Legacy of A. N. Kolmogorov - Hirokazu FUJISAKA Abstract Recently, spatially or temporally strongly
More information1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV
More informationARspec_decomp.dvi
February 8, 0 auto-regresive mode AR ) AR.. t N fx t);x t);x3 t); ;xn t)g Burg AR xt) a m xt m t)+fft) AR M Fina Prediction Error,FPE) FPEM) ^ff M +MN MN ^ff M P f) P f) ff t M a m e ißfm t AR [,,3]. AR
More informationII 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y
More information相互相関を考慮した非線形予測モデルに基づく 札幌市気温と北海道大学構内電力需要の同時推定
Title 相互相関を考慮した非線形予測モデルに基づく札幌市気温と北海道大学構内電力需要の同時推定 Author(s) 岩山, 浩将 Issue Date 212-3-22 Doc URL http://hdl.handle.net/2115/52278 Type theses (bachelor) File Information Iwayama_BachelorThesis211.pdf Instructions
More information: 1g99p038-8
16 17 : 1g99p038-8 1 3 1.1....................................... 4 1................................... 5 1.3.................................. 5 6.1..................................... 7....................................
More information9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L) du (L) = f (9.3) dx (9.) P
9 (Finite Element Method; FEM) 9. 9. P(0) P(x) u(x) (a) P(L) f P(0) P(x) (b) 9. P(L) 9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L)
More informationuntitled
. x2.0 0.5 0 0.5.0 x 2 t= 0: : x α ij β j O x2 u I = α x j ij i i= 0 y j = + exp( u ) j v J = β y j= 0 j j o = + exp( v ) 0 0 e x p e x p J j I j ij i i o x β α = = = + +.. 2 3 8 x 75 58 28 36 x2 3 3 4
More information山形大学紀要
x t IID t = b b x t t x t t = b t- AR ARMA IID AR ARMAMA TAR ARCHGARCH TARThreshold Auto Regressive Model TARTongTongLim y y X t y Self Exciting Threshold Auto Regressive, SETAR SETARTAR TsayGewekeTerui
More information1 4 1 ( ) ( ) ( ) ( ) () 1 4 2
7 1995, 2017 7 21 1 2 2 3 3 4 4 6 (1).................................... 6 (2)..................................... 6 (3) t................. 9 5 11 (1)......................................... 11 (2)
More informationuntitled
18 1 2,000,000 2,000,000 2007 2 2 2008 3 31 (1) 6 JCOSSAR 2007pp.57-642007.6. LCC (1) (2) 2 10mm 1020 14 12 10 8 6 4 40,50,60 2 0 1998 27.5 1995 1960 40 1) 2) 3) LCC LCC LCC 1 1) Vol.42No.5pp.29-322004.5.
More information082_rev2_utf8.pdf
3 1. 2. 3. 4. 5. 1 3 3 3 2008 3 2008 2008 3 2008 2008, 1 5 Lo and MacKinlay (1990a) de Jong and Nijman (1997) Cohen et al. (1983) Lo and MacKinlay (1990a b) Cohen et al. (1983) de Jong and Nijman (1997)
More information磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
More informationuntitled
1 Hitomi s English Tests 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 2 0 0 1 1 0 0 0 0 0 1 1 1 1 0 3 1 1 0 0 0 0 1 0 1 0 1 0 1 1 4 1 1 0 1 0 1 1 1 1 0 0 0 1 1 5 1 1 0 1 1 1 1 0 0 1 0
More informationPart 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 informationBlack-Scholes [1] Nelson [2] Schrödinger 1 Black Scholes [1] Black-Scholes Nelson [2][3][4] Schrödinger Nelson Parisi Wu [5] Nelson Parisi-W
003 7 14 Black-Scholes [1] Nelson [] Schrödinger 1 Black Scholes [1] Black-Scholes Nelson [][3][4] Schrödinger Nelson Parisi Wu [5] Nelson Parisi-Wu Nelson e-mail: takatoshi-tasaki@nifty.com kabutaro@mocha.freemail.ne.jp
More informationI 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変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
More informationuntitled
Stacking sequence optimization of composite wing using fractal branch and bound method Orbiting Plane : HOPE-X (JAXA) Fractal Branch and Bound Method (FBBM) Fractal structure of design space 5 y V a 9º
More information公益社団法人日本都市計画学会都市計画論文集 Vol.53 No 年 10 月 Journal of the City Planning Institute of Japan, Vol.53 No.3, October, 2018 A queueing model for goods d
A queueing model for goods delivery service by drones In many depopulated rural districts in Japan, it as been ard to run regional retail stores and many of tem ave closed down. As te result, tere as been
More information2 1,2, , 2 ( ) (1) (2) (3) (4) Cameron and Trivedi(1998) , (1987) (1982) Agresti(2003)
3 1 1 1 2 1 2 1,2,3 1 0 50 3000, 2 ( ) 1 3 1 0 4 3 (1) (2) (3) (4) 1 1 1 2 3 Cameron and Trivedi(1998) 4 1974, (1987) (1982) Agresti(2003) 3 (1)-(4) AAA, AA+,A (1) (2) (3) (4) (5) (1)-(5) 1 2 5 3 5 (DI)
More information1 (1997) (1997) 1974:Q3 1994:Q3 (i) (ii) ( ) ( ) 1 (iii) ( ( 1999 ) ( ) ( ) 1 ( ) ( 1995,pp ) 1
1 (1997) (1997) 1974:Q3 1994:Q3 (i) (ii) ( ) ( ) 1 (iii) ( ( 1999 ) ( ) ( ) 1 ( ) ( 1995,pp.218 223 ) 1 2 ) (i) (ii) / (iii) ( ) (i ii) 1 2 1 ( ) 3 ( ) 2, 3 Dunning(1979) ( ) 1 2 ( ) ( ) ( ) (,p.218) (
More information撮 影
DC cathode ray tube, 2.2 log log log + log log / / / A method determining tone conversion characteristics of digital still camera from two pictorial images Tone conversion characteristic Luminance
More informationR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 informationCOE-RES Discussion Paper Series Center of Excellence Project The Normative Evaluation and Social Choice of Contemporary Economic Systems Graduate Scho
COE-RES Discussion Paper Series Center of Excellence Project The Normative Evaluation and Social Choice of Contemporary Economic Systems Graduate School of Economics and Institute of Economic Research
More informationX X X Y R Y R Y R MCAR MAR MNAR Figure 1: MCAR, MAR, MNAR Y R X 1.2 Missing At Random (MAR) MAR MCAR MCAR Y X X Y MCAR 2 1 R X Y Table 1 3 IQ MCAR Y I
(missing data analysis) - - 1/16/2011 (missing data, missing value) (list-wise deletion) (pair-wise deletion) (full information maximum likelihood method, FIML) (multiple imputation method) 1 missing completely
More informationIPSJ SIG Technical Report 1, Instrument Separation in Reverberant Environments Using Crystal Microphone Arrays Nobutaka ITO, 1, 2 Yu KITANO, 1
1, 2 1 1 1 Instrument Separation in Reverberant Environments Using Crystal Microphone Arrays Nobutaka ITO, 1, 2 Yu KITANO, 1 Nobutaka ONO 1 and Shigeki SAGAYAMA 1 This paper deals with instrument separation
More information<4D F736F F D20939D8C7689F090CD985F93C18EEA8D758B E646F63>
Gretl OLS omitted variable omitted variable AIC,BIC a) gretl gretl sample file Greene greene8_3 Add Define new variable l_g_percapita=log(g/pop) Pg,Y,Pnc,Puc,Ppt,Pd,Pn,Ps Add logs of selected variables
More informationsp2.dvi
2 4 27 2 2 2 2 5 3 8 4 9 2 2 2 2 22 9 23 2 24 EM 23 3 28 3 28 32 29 33 3 4 33 4 33 42 33 43 35 44 37 5 43 5 43 52 46 53 AR 49 54 52 55 55 6 AR 58 6 Levinson Durbin 58 62 AR 6 63 Burg 62 z x x (sample)
More information