{ From user Lonnie, Model Using_regression at Thu, May 01, 2008 10:53 AM~~
}
Softwareversion 4.1.0
{ System Variables with non-default values: }
Typechecking := 1
Checking := 1
Saveoptions := 2
Savevalues := 0
{!40000|Att_contlinestyle Graph_pdf_valdim: 1}
Model Using_regression
Title: Using Regression
Description: User Group Webinar for 1 May 2008. ~
Basically a repeat of the webinar given 30 Aug 2007.~
~
Regression analysis is a statistical technique for curve fitting, dis~~
covering relationships in data, and testing hypotheses between variab~~
les. In this webinar, I will focus on generalized linear regression, ~~
which is provided by Analytica's Regression function, and examine man~~
y ways in which is can be used, including fitting simple lines to dat~~
a, polynomial regression, use of other non-linear terms, and fitting ~~
of autoregressive models (e.g., ARMA). I'll examine how we can assess~~
how likely it is the data might have been generated from the particu~~
lar form of the regression model used. We can also determine the leve~~
l of uncertainty in our inferred parameter values, and incorporate th~~
ese uncertainties into a model that uses the result of the regression~~
. The talk will cover Analytica 4.0 functions Regression, RegressionD~~
ist, RegressionFitProb, and RegressionNoise. ~
Author: Lonnie Chrisman~
Lumina Decision Systems
Date: Thu, May 01, 2008 8:41 AM
Saveauthor: Lonnie
Savedate: Thu, May 01, 2008 10:53 AM
Defaultsize: 48,24
Diagstate: 1,1,7,550,300,17
Windstate: 2,14,17,538,378
Fontstyle: Arial, 15
Fileinfo: 0,Model Using_regression,2,2,0,0,W:\Training\User Group Webi~~
nars\Using Regression2.ANA
Index Date1
Title: Date
Definition: [37.623K,37.624K,37.625K,37.628K,37.629K,37.63K,37.631K,37~~
.632K,37.636K,37.637K,37.638K,37.639K,37.642K,37.643K,37.644K,37.645K~~
,37.646K,37.649K,37.65K,37.651K,37.652K,37.653K,37.656K,37.657K,37.65~~
8K,37.659K,37.66K,37.663K,37.664K,37.665K,37.666K,37.667K,37.671K,37.~~
672K,37.673K,37.674K,37.677K,37.678K,37.679K,37.68K,37.681K,37.684K,3~~
7.685K,37.686K,37.687K,37.688K,37.691K,37.692K,37.693K,37.694K,37.695~~
K,37.698K,37.699K,37.7K,37.701K,37.702K,37.705K,37.706K,37.707K,37.70~~
8K,37.709K,37.712K,37.713K,37.714K,37.715K,37.719K,37.72K,37.721K,37.~~
722K,37.723K,37.726K,37.727K,37.728K,37.729K,37.73K,37.733K,37.734K,3~~
7.735K,37.736K,37.737K,37.74K,37.741K,37.742K,37.743K,37.744K,37.747K~~
,37.748K,37.749K,37.75K,37.751K,37.754K,37.755K,37.756K,37.757K,37.75~~
8K,37.761K,37.762K,37.763K,37.764K,37.765K,37.769K,37.77K,37.771K,37.~~
772K,37.775K,37.776K,37.777K,37.778K,37.779K,37.782K,37.783K,37.784K,~~
37.785K,37.786K,37.789K,37.79K,37.791K,37.792K,37.793K,37.796K,37.797~~
K,37.798K,37.799K,37.8K,37.803K,37.804K,37.806K,37.807K,37.81K,37.811~~
K,37.812K,37.813K,37.814K,37.817K,37.818K,37.819K,37.82K,37.821K,37.8~~
24K,37.825K,37.826K,37.827K,37.828K,37.831K,37.832K,37.833K,37.834K,3~~
7.835K,37.838K,37.839K,37.84K,37.841K,37.842K,37.845K,37.846K,37.847K~~
,37.848K,37.849K,37.852K,37.853K,37.854K,37.855K,37.856K,37.859K,37.8~~
6K,37.861K,37.862K,37.863K,37.867K,37.868K,37.869K,37.87K,37.873K,37.~~
874K,37.875K,37.876K,37.877K,37.88K,37.881K,37.882K,37.883K,37.884K,3~~
7.887K,37.888K,37.889K,37.89K,37.891K,37.894K,37.895K,37.896K,37.897K~~
,37.898K,37.901K,37.902K,37.903K,37.904K,37.905K,37.908K,37.909K,37.9~~
1K,37.911K,37.912K,37.915K,37.916K,37.917K,37.918K,37.919K,37.922K,37~~
.923K,37.924K,37.925K,37.926K,37.929K,37.93K,37.931K,37.932K,37.933K,~~
37.936K,37.937K,37.938K,37.939K,37.94K,37.943K,37.944K,37.945K,37.947~~
K,37.95K,37.951K,37.952K,37.953K,37.954K,37.957K,37.958K,37.959K,37.9~~
6K,37.961K,37.964K,37.965K,37.966K,37.967K,37.968K,37.971K,37.972K,37~~
.973K,37.974K,37.975K,37.978K,37.98K,37.981K,37.982K,37.985K,37.987K,~~
37.988K,37.989K,37.992K,37.993K,37.994K,37.995K,37.996K,37.999K,38K,3~~
8.001K,38.002K,38.003K,38.007K,38.008K,38.009K,38.01K,38.013K,38.014K~~
,38.015K,38.016K,38.017K,38.02K,38.021K,38.022K,38.023K,38.024K,38.02~~
7K,38.028K,38.029K,38.03K,38.031K,38.035K,38.036K,38.037K,38.038K,38.~~
041K,38.042K,38.043K,38.044K,38.045K,38.048K,38.049K,38.05K,38.051K,3~~
8.052K,38.055K,38.056K,38.057K,38.058K,38.059K,38.062K,38.063K,38.064~~
K,38.065K,38.069K,38.07K,38.071K,38.072K,38.073K,38.076K,38.077K,38.0~~
78K,38.079K,38.08K,38.083K,38.084K,38.085K,38.086K,38.087K,38.09K,38.~~
091K,38.092K,38.093K,38.094K,38.097K,38.098K,38.099K,38.1K,38.101K,38~~
.104K,38.105K,38.106K]
Nodelocation: 80,56,1
Nodesize: 48,24
Aliases: Alias Date5, Alias Date3, Alias Date4
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
{!40000|Att_previndexvalue: [37.623K,37.624K,37.625K,37.628K,37.629K,37.63K~~
,37.631K,37.632K,37.636K,37.637K,37.638K,37.639K,37.642K,37.643K,37.644K~~
,37.645K,37.646K,37.649K,37.65K,37.651K,37.652K,37.653K,37.656K,37.657K~~
,37.658K,37.659K,37.66K,37.663K,37.664K,37.665K,37.666K,37.667K,37.671K~~
,37.672K,37.673K,37.674K,37.677K,37.678K,37.679K,37.68K,37.681K,37.684K~~
,37.685K,37.686K,37.687K,37.688K,37.691K,37.692K,37.693K,37.694K,37.695K~~
,37.698K,37.699K,37.7K,37.701K,37.702K,37.705K,37.706K,37.707K,37.708K~~
,37.709K,37.712K,37.713K,37.714K,37.715K,37.719K,37.72K,37.721K,37.722K~~
,37.723K,37.726K,37.727K,37.728K,37.729K,37.73K,37.733K,37.734K,37.735K~~
,37.736K,37.737K,37.74K,37.741K,37.742K,37.743K,37.744K,37.747K,37.748K~~
,37.749K,37.75K,37.751K,37.754K,37.755K,37.756K,37.757K,37.758K,37.761K~~
,37.762K,37.763K,37.764K,37.765K,37.769K,37.77K,37.771K,37.772K,37.775K~~
,37.776K,37.777K,37.778K,37.779K,37.782K,37.783K,37.784K,37.785K,37.786K~~
,37.789K,37.79K,37.791K,37.792K,37.793K,37.796K,37.797K,37.798K,37.799K~~
,37.8K,37.803K,37.804K,37.806K,37.807K,37.81K,37.811K,37.812K,37.813K~~
,37.814K,37.817K,37.818K,37.819K,37.82K,37.821K,37.824K,37.825K,37.826K~~
,37.827K,37.828K,37.831K,37.832K,37.833K,37.834K,37.835K,37.838K,37.839K~~
,37.84K,37.841K,37.842K,37.845K,37.846K,37.847K,37.848K,37.849K,37.852K~~
,37.853K,37.854K,37.855K,37.856K,37.859K,37.86K,37.861K,37.862K,37.863K~~
,37.867K,37.868K,37.869K,37.87K,37.873K,37.874K,37.875K,37.876K,37.877K~~
,37.88K,37.881K,37.882K,37.883K,37.884K,37.887K,37.888K,37.889K,37.89K~~
,37.891K,37.894K,37.895K,37.896K,37.897K,37.898K,37.901K,37.902K,37.903K~~
,37.904K,37.905K,37.908K,37.909K,37.91K,37.911K,37.912K,37.915K,37.916K~~
,37.917K,37.918K,37.919K,37.922K,37.923K,37.924K,37.925K,37.926K,37.929K~~
,37.93K,37.931K,37.932K,37.933K,37.936K,37.937K,37.938K,37.939K,37.94K~~
,37.943K,37.944K,37.945K,37.947K,37.95K,37.951K,37.952K,37.953K,37.954K~~
,37.957K,37.958K,37.959K,37.96K,37.961K,37.964K,37.965K,37.966K,37.967K~~
,37.968K,37.971K,37.972K,37.973K,37.974K,37.975K,37.978K,37.98K,37.981K~~
,37.982K,37.985K,37.987K,37.988K,37.989K,37.992K,37.993K,37.994K,37.995K~~
,37.996K,37.999K,38K,38.001K,38.002K,38.003K,38.007K,38.008K,38.009K,~~
38.01K,38.013K,38.014K,38.015K,38.016K,38.017K,38.02K,38.021K,38.022K~~
,38.023K,38.024K,38.027K,38.028K,38.029K,38.03K,38.031K,38.035K,38.036K~~
,38.037K,38.038K,38.041K,38.042K,38.043K,38.044K,38.045K,38.048K,38.049K~~
,38.05K,38.051K,38.052K,38.055K,38.056K,38.057K,38.058K,38.059K,38.062K~~
,38.063K,38.064K,38.065K,38.069K,38.07K,38.071K,38.072K,38.073K,38.076K~~
,38.077K,38.078K,38.079K,38.08K,38.083K,38.084K,38.085K,38.086K,38.087K~~
,38.09K,38.091K,38.092K,38.093K,38.094K,38.097K,38.098K,38.099K,38.1K~~
,38.101K,38.104K,38.105K,38.106K]}
Variable Stock_price
Title: Stock Price
Definition: Table(Date1)(~
83.8,85.66,85.05,85.47,92.56999999999999,97,95.8,94.62000000000001,97~~
.09999999999999,94.95,89.06999999999999,88.5,86.79000000000001,85.7,8~~
6.7,86.25,85.38,85.94,85.55,85.73,84.74,84.75,83.94,84.15000000000001~~
,86.15000000000001,86.18000000000001,83.27,84.88,84.7,85.3,85.2099999~~
9999999,84.83,85.90000000000001,89.2,89.51000000000001,89.06999999999~~
999,88.51000000000001,83.93000000000001,84.61,87.06,85.41,86.31999999~~
999999,88.19,87.72,88,87.97,89.87000000000001,88.40000000000001,90,89~~
.56999999999999,89.59,91.13,91.48,93.87000000000001,93.95999999999999~~
,93.52,95.84999999999999,95.45999999999999,93.24,93.75,92.91,93.65000~~
000000001,94.5,94.27,94.68000000000001,93.65000000000001,94.25,92.59,~~
92.19,90.24,91.43000000000001,90.34999999999999,90.40000000000001,90.~~
27,90.97,93.51000000000001,93.24,95.34999999999999,98.84,99.92,99.8,9~~
9.47,100.39,100.4,100.81,103.92,105.06,106.88,107.34,108.74,109.36,10~~
7.52,107.34,109.44,110.02,111.98,113.54,112.89,110.69,113.62,114.35,1~~
18.77,121.19,118.4,121.33,122.67,123.64,124.07,124.49,120.19,120.38,1~~
17.5,118.75,120.5,125.09,123.66,121.55,123.9,123,122.34,119.65,121.89~~
,120.56,122.04,121.26,127.17,132.75,132.3,130.33,132.35,132.39,134.07~~
,137.73,138.1,138.91,138.12,140,143.75,143.7,134.89,137.26,146,143.85~~
,141.43,131.76,135,136.49,131.85,135.25,135.03,134.01,126.39,125,127.~~
79,124.03,119.9,117.05,122.06,122.22,127.57,132.51,131.07,135.3,132.2~~
5,126.82,134.08,136.25,138.48,144.16,136.76,135.01,131.77,136.71,135.~~
49,136.85,137.2,138.81,138.41,140.92,140.77,140.31,144.15,148.28,153.~~
18,152.77,154.5,153.47,156.34,158.45,157.92,156.24,161.45,167.91,167.~~
86,166.79,162.23,167.25,166.98,169.58,172.75,173.5,170.42,174.36,186.~~
16,185.93,182.78,184.7,185.09,187,189.95,187.44,187.87,186.18,191.79,~~
186.3,175.47,165.37,153.76,169.96,166.11,164.3,166.39,163.95,168.85,1~~
68.46,171.54,172.54,174.81,180.22,184.29,182.22,178.86,179.81,185.5,1~~
89.95,194.3,194.21,188.54,190.86,191.83,190.39,184.4,182.98,183.12,18~~
7.21,193.91,198.8,198.95,198.57,199.83,198.08,194.84,194.93,180.05,17~~
7.64,171.25,179.4,178.02,172.69,178.78,169.04,159.64,160.89,161.36,15~~
5.64,139.07,135.6,130.01,130.01,131.54,132.18,135.36,133.75,131.65,12~~
9.36,122,121.24,125.48,129.45,124.86,129.4,127.46,124.63,122.18,123.8~~
2,121.54,119.46,119.74,119.15,122.96,129.91,125.02,121.73,124.62,124.~~
49,120.93,122.25,119.69,127.35,126.03,127.94,126.61,126.73,132.82,129~~
.67,133.27,139.53,140.98,145.06,140.25,143.01,143.5,149.53,147.49,151~~
.61,153.08,155.89,152.84,151.44,154.55,147.14,147.78,148.38,153.7,154~~
.49,161.04,168.16,160.2,162.89,168.94,169.73,172.24,175.05,173.95)
Nodelocation: 192,56,1
Nodesize: 48,24
Valuestate: 2,30,72,368,433,0,MIDM
Aliases: Alias Stock_price1, Alias Stock_price2, Alias Stock_price3
Module Linear_regression
Title: Linear Regression
Author: Lonnie
Date: Thu, May 01, 2008 8:51 AM
Defaultsize: 48,24
Nodelocation: 88,128,1
Nodesize: 64,28
Diagstate: 1,1,7,550,300,17
Alias Date5
Title: Date
Definition: 1
Nodelocation: 96,48,1
Nodesize: 48,24
Original: Date1
Alias Stock_price1
Title: Stock Price
Definition: 1
Nodelocation: 208,48,1
Nodesize: 48,24
Original: Stock_price
Variable Lr_basis
Title: LR Basis
Definition: Table(Self)(~
1,@Date1)
Indexvals: ['b','m']
Nodelocation: 96,120,1
Nodesize: 48,24
Reformval: [Self,Date1]
Chance Lr_c
Title: LR c
Definition: RegressionDist( Stock_price, Lr_basis, Date1, Lr_basis )
Nodelocation: 208,120,1
Nodesize: 48,24
Valuestate: 2,104,114,595,452,1,SAMP
Reformval: [Undefined,Undefined,Undefined,Undefined,1]
{!40000|Att_resultslicestate: [Lr_basis,2,Sys_localindex('STEP'),1]}
{!40000|Att_coordinateindex: Lr_basis}
Chance Lr_price
Title: LR Price
Definition: sum( Lr_c * Lr_basis, Lr_basis ) + Normal( 0, Lr_noise )
Nodelocation: 320,120,1
Nodesize: 48,24
Valuestate: 2,140,80,735,437,1,CONF
Reformval: [Date1,Undefined,2]
Variable Lr_comparison
Title: LR Comparison
Definition: [STOCK_PRICE,LR_PRICE]
Indexvals: ['Stock Price','LR Price']
Nodelocation: 448,120,1
Nodesize: 48,24
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Valuestate: 2,200,86,746,470,1,CONF
Reformval: [Date1,Self]
Att__totalsindex: Variable Self
{!40000|Att_resultslicestate: [Self,-1,Sys_localindex('PROBABILITY'),1~~
,Date1,1]}
Variable R
Title: R
Definition: Correlation(Stock_price, @Date1, Date1 )
Nodelocation: 96,192,1
Nodesize: 48,24
Variable Lr_noise
Title: LR Noise
Definition: RegressionNoise( Stock_price, Lr_basis, Date1, Lr_basis, L~~
r_c )
Nodelocation: 320,48,1
Nodesize: 48,24
Valuestate: 2,402,192,416,303,0,MIDM
Variable Lr_confidence
Title: LR Confidence
Description: The probability that the regression fit obtained would be~~
as bad or worse than what we just obtained if our assumption that th~~
e data is generated by a linear process with iid noise is correct.
Definition: RegressionFitProb( Stock_price, Lr_basis, Date1, Lr_basis,~~
LR_c, LR_Noise )
Nodelocation: 448,192,1
Nodesize: 48,24
Valuestate: 2,511,111,416,303,0,MIDM
Close Linear_regression
Module Cubic_regression
Title: Cubic Regression
Author: Lonnie
Date: Thu, May 01, 2008 8:51 AM
Defaultsize: 48,24
Nodelocation: 240,128,1
Nodesize: 64,28
Diagstate: 1,262,33,670,456,17
Alias Date3
Title: Date
Definition: 1
Nodelocation: 96,48,1
Nodesize: 48,24
Original: Date1
Alias Stock_price2
Title: Stock Price
Definition: 1
Nodelocation: 208,48,1
Nodesize: 48,24
Original: Stock_price
Index Cr_k
Title: CR K
Definition: "c" & 0..3
Nodelocation: 96,112,1
Nodesize: 48,24
Valuestate: 2,388,80,416,303,0,MIDM
Variable Cr_basis
Title: CR Basis
Definition: @Date1 ^ (@CR_K - 1)
Nodelocation: 96,168,1
Nodesize: 48,24
Valuestate: 2,72,82,816,453,0,MIDM
Reformval: [Date1,Cr_k]
Chance Cr_c
Title: CR c
Definition: RegressionDist( Stock_price, Cr_basis, Date1, Cr_k )
Nodelocation: 208,112,1
Nodesize: 48,24
Chance Cr_price
Title: CR Price
Definition: Normal( Sum( Cr_c*Cr_basis, Cr_k ), CR_Noise )
Nodelocation: 336,112,1
Nodesize: 48,24
Variable Cr_comparison
Title: CR Comparison
Definition: [STOCK_PRICE,CR_PRICE]
Indexvals: ['Stock Price','CR Price']
Nodelocation: 464,112,1
Nodesize: 48,24
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Valuestate: 2,104,114,749,419,1,CONF
Reformval: [Date1,Self]
Att__totalsindex: Variable Self
{!40000|Att_resultslicestate: [Self,-1,Sys_localindex('PROBABILITY'),1~~
,Date1,1]}
Variable Cr_noise
Title: CR Noise
Definition: RegressionNoise( Stock_price, Cr_basis, Date1, Cr_k, CR_c ~~
)
Nodelocation: 336,48,1
Nodesize: 48,24
Variable Cr_confidence
Title: CR Confidence
Definition: RegressionFitProb( Stock_price, Cr_basis, Date1, Cr_k, CR_~~
c, CR_Noise )
Nodelocation: 464,176,1
Nodesize: 48,24
Valuestate: 2,335,158,416,303,0,MIDM
Chance Cr_future_price
Title: CR Future Price
Definition: var basis := @Date2 ^ (@CR_K-1);~
Normal( Sum( Cr_c*basis, CR_K), Cr_noise )
Nodelocation: 216,248,1
Nodesize: 48,24
Alias Future_stock_price1
Title: Future stock price
Definition: 1
Nodelocation: 96,248,1
Nodesize: 48,24
Original: Future_stock_price
Variable Cr_compare_future
Title: CR Compare Future
Definition: [CR_FUTURE_PRICE,FUTURE_STOCK_PRICE]
Indexvals: ['CR Future Price','Future stock price']
Nodelocation: 344,249,0
Nodesize: 48,31
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Valuestate: 2,120,36,805,481,1,CONF
Reformval: [Date2,Self]
Att__totalsindex: Variable Self
{!40000|Att_resultslicestate: [Self,-1,Sys_localindex('PROBABILITY'),1~~
,Date2,1]}
Close Cubic_regression
Module Autoregressive_regre
Title: Autoregressive regression
Author: Lonnie
Date: Thu, May 01, 2008 8:51 AM
Defaultsize: 48,24
Nodelocation: 392,128,1
Nodesize: 64,28
Diagstate: 1,233,21,641,400,17
Alias Date4
Title: Date
Definition: 1
Nodelocation: 96,48,1
Nodesize: 48,24
Original: Date1
Alias Stock_price3
Title: Stock Price
Definition: 1
Nodelocation: 208,48,1
Nodesize: 48,24
Original: Stock_price
Constant Window_size
Title: Window size
Definition: 10
Nodelocation: 96,120,1
Nodesize: 48,24
Index Ar_k
Title: AR K
Definition: 0..Window_size
Nodelocation: 96,176,1
Nodesize: 48,24
{!40000|Att_previndexvalue: [1,2,3,4,5,6,7,8,9,10]}
Index Ar_date
Title: AR Date
Definition: subset(@date1 > window_size )
Nodelocation: 96,240,1
Nodesize: 48,24
Valuestate: 2,349,135,416,303,0,MIDM
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
Variable Ar_basis
Title: AR Basis
Definition: if Ar_k = 0 then 1~
else Stock_price[ @Date1 = @[Date1=Ar_Date] - Ar_k ]
Nodelocation: 208,120,1
Nodesize: 48,24
Valuestate: 2,530,22,416,303,0,MIDM
Reformval: [Ar_date,Ar_k]
Chance Ar_c
Title: AR c
Definition: regressionDist(Ar_stock_price, Ar_basis, Ar_date, Ar_k )
Nodelocation: 208,184,1
Nodesize: 48,24
Variable Ar_stock_price
Title: AR Stock price
Definition: Stock_price[Date1=Ar_date]
Nodelocation: 320,48,1
Nodesize: 48,24
Chance Ar_price
Title: AR Price
Definition: Normal( Sum( Ar_c * Ar_basis, Ar_k ), Ar_noise )
Nodelocation: 328,184,1
Nodesize: 48,24
Variable Ar_comparison
Title: AR Comparison
Definition: [AR_STOCK_PRICE,AR_PRICE]
Indexvals: ['AR Stock price','AR Price']
Nodelocation: 448,184,1
Nodesize: 48,24
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Valuestate: 2,40,50,892,513,1,CONF
Reformval: [Ar_date,Self]
Att__totalsindex: Variable Self
{!40000|Att_resultslicestate: [Self,-1,Sys_localindex('PROBABILITY'),1~~
,Ar_date,1]}
Variable Ar_noise
Title: AR Noise
Definition: regressionNoise(Ar_stock_price, Ar_basis, Ar_date, Ar_k, A~~
R_c )
Nodelocation: 208,240,1
Nodesize: 48,24
Variable Ar_confidence
Title: AR Confidence
Definition: regressionFitProb(Ar_stock_price, Ar_basis, Ar_date, Ar_k,~~
AR_c, AR_Noise)
Nodelocation: 448,112,1
Nodesize: 48,24
Decision Begin_forecast
Title: Begin Forecast
Definition: 1 Oct 2007
Nodelocation: 96,304,1
Nodesize: 48,24
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
Chance Ar_future_price
Title: AR Future Price
Definition: var y := IgnoreWarnings( Ar_stock_price[Ar_Date = Date2] )~~
;~
for i := @[date2 = subset( Date2>=Begin_forecast) ] do ( ~
y[@Date2=i] := 1;~
var b := y[@date2 = i - Ar_k ];~
y[@Date2 = i] := Normal( Sum( Ar_c*b, Ar_K), Ar_Noise )~
);~
y
Nodelocation: 208,304,1
Nodesize: 48,24
Valuestate: 2,24,55,831,477,1,CONF
Reformval: [Date2,Undefined,2]
Alias Future_stock_price2
Title: Future stock price
Definition: 1
Nodelocation: 208,360,1
Nodesize: 48,24
Original: Future_stock_price
Variable Compare1
Definition: [AR_FUTURE_PRICE,FUTURE_STOCK_PRICE]
Indexvals: ['AR Future Price','Future stock price']
Nodelocation: 336,128,1
Nodesize: 48,24
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Valuestate: 2,92,39,871,526,1,CONF
Reformval: [Date2,Date2,2]
Att__totalsindex: Variable Self
{!40000|Att_resultslicestate: [Self,-1,Sys_localindex('PROBABILITY'),1~~
,Date2,1]}
Close Autoregressive_regre
Library Multivariate_distrib
Title: Multivariate Distributions
Description: A library of multivariate distributions.~
~
In a multivariate distribution, each sample is a vector. This vector~~
is identified by an index, identified by the I parameter of the func~~
tions in this library. A Mid value from a distribution function will~~
therefore be indexed by I, whlie a Sample from a distribution functi~~
on is indexed by both I and Run. These distribution functions can al~~
so be used from within the Random function to generate a single monte~~
-carlo sample, which will be indexed by I.~
~
This library also contains functions for generating correlated distri~~
butions. Correlate_with, for example, allows you to generate a univa~~
rite distribution with an arbitrary marginal distribution that has a ~~
specified rank correlation with an arbitrary reference distribution. ~~
Several functions may be used for generating serial correlations, w~~
here each distribution along an index is correlated with the previous~~
point along that index.
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems~
~
With contributions by:~
John Bowers, US FDA.~
Max Henrion, Lumina Decision Systems
Date: Fri, Aug 01, 2003 7:12 PM
Saveauthor: Lonnie
Savedate: Tue, Nov 20, 2007 10:36 AM
Defaultsize: 48,24
Nodelocation: 392,56,0
Nodesize: 64,28
Nodeinfo: 1,1,1,1,1,1,0,0,0,0
Diagstate: 1,42,10,649,1009,17
Windstate: 2,401,199,483,316
Fontstyle: Arial, 15
Function Wishart( cv : Number[I,J,Run] ; n :positive ; I,J : Index ; ~
singleSampleMethod : optional hidden scalar)
Title: Wishart(cv,n,I,J)
Description: Suppose you sample N samples from a Gaussian(0,cv,I,J) di~~
stribution, X[I,R]. (R is the index that indexes each sample, R:=1..~~
N). The Wishart distribution describes the distribution of sum( X * ~~
X[I=J], R ). This matrix is dimensioned by I and J and is called the~~
scatter matrix. ~
~
A sample drawn from the Wishart is therefore a sample scatter matrix.~~
If you divide that sample by (N-1), you have a sampled covariance m~~
atrix. ~
~
If you compute a sample covariance matrix from data, and then want to~~
use this in your model, if you just use it directly, you'll be ignor~~
ing sampling error. That may be insignificant of N is large. Otherw~~
ise, you may want to use:~
Wishart( SampleCV, N, I, J) / (N-1)~
instead of just SampleCV in your model. The extended variance will ~~
account for the uncertainty from the finite sample size that was used~~
to obtain your sample CV.~
~
If you can express a prior probability on covariances in the form of ~~
an InvertedWishart distribution, then the posterior distribution, aft~~
er having computed the sample covariance matrix (assumed to be drawn,~~
by nature, from a Wishart), is also an InvertedWishart.
Definition: var T := if i0~
Each sample of a Dirichlet distribution produces a random vector whos~~
e elements sum to 1. It is commonly used to represent second order p~~
robability information.~
~
The Dirichlet distribution has a density given by ~
k * Product( X^(alpha-1), I)~
where k is a normalization factor equal to~
GammaFn( sum(alpha,I )) / Sum(GammaFn(alpha),I)~
~
The parameters, alpha, can be interpreted as observation counts. The~~
mean is given by the relative values of alpha (normalized to 1), but~~
the variance narrows as the alphas get larger, just as your confiden~~
ce in a distribution would narrow as you get more samples.~
~
The Dirichlet lends itself to easy Bayesian updating. If you have a ~~
prior of alpha0, and you observe N
Definition: var a:=Gamma(alpha,singleSampleMethod:singleSampleMethod);~~
~
a/sum(a,I)
Nodelocation: 272,120,1
Nodesize: 58,16
Windstate: 2,26,18,624,485
Paramnames: alpha,I,Over
Function Binormal(MeanVec :numeric[I,Run]; Sdeviations : positive[I,Ru~~
n]; I:IndexType; correlationCoef : numeric[Run];~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar)
Title: BiNormal (m, s, i, c )
Description: A 2-D Normal (or Bi-variate Gaussian) distribution with t~~
he indicated individual standard deviations (>0) and the indicated co~~
rrelation coefficient. The index, I, must have exactly 2 elements, S~~
deviations must be indexed by I.
Definition: if size(I)<>2 then ~
Error("Index to BiNormal must have 2 elements")~
else begin~
var s := product(Sdeviations,I) * correlationCoef;~
Index J:=CopyIndex(I);~
Gaussian( meanVec, If I<>J Then s else Sdeviations^2, I,J,~
singleSampleMethod: singleSampleMethod )~
end
Nodelocation: 288,72,1
Nodesize: 78,16
Windstate: 2,2,24,525,540
Paramnames: MeanVec,Sdeviations,I,correlationCoef,Over
Function Multinomial(N:Positive ; theta:NonNegative ; I : IndexType;~
Over : ... optional atomic ;~
singleSampleMethod : hidden optional scalar )
Title: Multinomial (n, theta, i )
Description: Returns the Multinomial Distribution.~
~
The multinomial distribution is a generalization of the Binomial dist~~
ribution to N possible outcomes. For example, if you were to roll a ~~
fair die N times, an outcome would be the number of times each of the~~
six numbers appears. Theta would be the probability of each outcome~~
, where sum(theta,I)=1, and index I is the list of possible outcome. ~~
If theta doesn't sum to 1, it is normalized.~
~
Each sample is a vector indexed by I indicating the number of times t~~
he corresponding outcome (die number) occurred during that sample poi~~
nt. Each sample will have the property that sum( result, I ) = N.
Definition: var z := n;~
var k := size(I);~
~
var j:=cumulate(1,I) in I do begin~
Index I2 := j..k;~
var theta2 := Slice(theta,I,I2); /* unnormalized sub-process */~
var p := theta2/sum(theta2, I2);~
p := if IsNan(p) then 0 else p;~
var xj := Binomial(z,p[I2=j],~
singleSampleMethod:singleSampleMethod);~~
~
z := z - xj;~
xj~
end~
Nodelocation: 117,120,1
Nodesize: 85,16
Windstate: 2,75,167,476,522
Paramnames: N,theta,I,Over
Function Correlate_dists(dists : Context[I,RunIndex] ; rankcorrs : num~~
eric array[I,J] ; ~
I,J : IndexType;~
RunIndex : optional Index = Run )
Title: Correlate Dists (d, rc, i, j )
Description: Reorders the samples in dists so as to match the desired~~
rank correlations between distributions as closely as possible. Ran~~
kCorrs must be positive definite, and the diagonal should contain all~~
ones.~
~
The result will be distributions having the same margins as the origi~~
nal input, but with rank correlations close to those of the rankcorrs~~
matrix.
Definition: if not IsSampleEvalMode and Handle(RunIndex)=Handle(Run) T~~
hen~
dists {Mid mode}~
Else begin~
var u := if Handle(RunIndex)=Handle(run) ~
Then Sample(Gaussian(0,rankcorrs,I,J))~
Else Random(Gaussian(0,rankcorrs,I,J),Over:RunIndex);~
var dsort := sortIndex(dists,RunIndex);~
var urank := Rank(u,RunIndex);~
dists[RunIndex=dsort[RunIndex=urank]]~
end
Nodelocation: 136,392,1
Nodesize: 100,16
Windstate: 2,301,193,494,399
Paramnames: dists,rankcorrs,I,J,RunIndex
Function Correlate_with( S, ref : Context[RunIndex] ; rc : scalar ; ~
RunIndex : optional Index = Run )
Title: Correlate With (s, ref, rc )
Description: Reorders the samples of S so that the result is correlate~~
d with the reference sample with a rank correlation close to rankcorr~~
. ~
~
Example: To generate a logNormal distribution that is highly correlat~~
ed with Ch1, use, e.g.,: Correlate_With( LogNormal(2,3), Ch1, 0.8 )~
~
Note: This achieves a given unweighted rank correlation. If you have~~
a non-default SampleWeighting of points, the weighted rank correlato~~
n may differ.
Definition: if IsSampleEvalMode or Handle(runIndex)<>Handle(Run) Then ~~
begin~
Index q := 1..2;~
var u := If Handle(RunIndex)=Handle(Run) ~
Then binormal( 0, 1, q, rc )~
Else Random(binormal(0,1,q,rc),Over:RunIndex);~
var rrank := Rank(ref,RunIndex);~
var u1sort := sortIndex(u[q=1],RunIndex);~
var u2rank := Rank(u[q=2],RunIndex);~
var ssort := sortIndex(S,RunIndex);~
S[RunIndex=ssort[RunIndex=u2rank[RunIndex=~
u1sort[Ru~~
nIndex=rrank]]]]~
end ~
else {mid mode}~
S
Nodelocation: 128,312,1
Nodesize: 96,16
Windstate: 2,205,170,545,485
Paramnames: S,ref,rc,RunIndex
Function Uniformspherical(I : IndexType ; R : optional Numeric[I,Run] ~~
;~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Uniform Spherical (i, r )
Description: Generates points uniformly on a sphere (or circle or hype~~
rsphere).~
Each sample generated is indexed by I -- so if I has 3 elements, the ~~
points will lie on a sphere.~
~
The mid value is a bit strange here since there isn't really a median~~
that lies on the sphere. Obviously the center of the sphere is the ~~
middle value, but that isn't in the allowable range. So, an arbitrar~~
y point on the sphere is used.
Definition: if IsNotSpecified(R) then R:=1;~
var u := Normal(0,1,over:I,~
singleSampleMethod:singleSampleMethod); ~
var d := sqrt( sum(u^2,I) );~
ifall d=0 and @I then R/sqrt(size(I)) else r*u/d
Nodelocation: 328,168,1
Nodesize: 86,16
Windstate: 2,151,227,476,424
Paramnames: I,R,Over
Function Multiuniform(corr : Numeric[I,J,Run] ; I,J : IndexType ; lb,u~~
b : optional Numeric[I,J,Run] ;~
Over : ... optional atomic ;~
singleSampleMethod : hidden optional scalar )
Title: MultiUniform ( c, i, j, lb, ub )
Description: The multi-variate uniform distribution.~
Generates vector samples (indexed by I) such that each component has ~~
a uniform marginal distribution, and such that each component have th~~
e pair-wise correlations given by corr. Indexes I and J must have th~~
e same number of elements, corr needs to be symmetric and must obey a~~
certain semidefinite condition (namely that the transformed matrix [~~
2*sin(30*cov) ] is positive semidefinite. In most cases, this rough~~
ly the same as corr being, or not being, positive semidefinite). Lb ~~
and ub can be used to specify upper and lower bounds, either for all ~~
components, or individually if these bounds are indexed by I. If lb ~~
& ub are omitted, each component will have marginal Uniform(0,1).~
~
The correlation specified in corr is true sample correlation - not ra~~
nk correlation. ~
~
The transformation here is based on:~
* Falk, M. (1999), "A simple approach to the generation of uniformly ~~
distributed random variables with prescribed correlations," Comm. in ~~
Stats - Simulation and Computation 28: 785-791.
Definition: if IsNotSpecified(lb) then lb:=0;~
if IsNotSpecified(ub) then ub := 1;~
var R := if I=J then 1 else 2*sin(30*corr);~
var g := Gaussian(0,R,I,J,~
singleSampleMethod:singleSampleMethod);~~
~
Cumnormal( g ) * (ub-lb) + lb
Nodelocation: 132,168,1
Nodesize: 100,16
Windstate: 2,67,106,608,611
Paramnames: corr,I,J,lb,ub,Over
Module Depricated_multi_var
Title: Depricated multi-variate stuff
Description: Functions found in this module are here for legacy reason~~
s. They existed in older versions of the Multivariate library, but h~~
ave been become obsolete for whatever reason.
Author: Lonnie
Date: Mon, Apr 30, 2007 3:49 PM
Defaultsize: 48,24
Nodelocation: 80,944,1
Nodesize: 56,32
Function Samplecovariance(X ; I : Index ; J : optional Index ; R : Ind~~
ex)
Title: Sample Covariance
Description: This function is obsolete. In Analytica 4.0, the builtin~~
function Variance can be used to compute a covariance matrix. The e~~
quivalent of this function would be: Variance( X, R, CoVarDim:I, CoV~~
arDim2:J ).~
~
Returns a covariance matrix based on the sampled data, X, indexed by ~~
I and R. (I is the dimensionality of X, R corresponds to the samples~~
). The result will be indexed by I and J -- supply J to be the same ~~
length as I.~
~
Note that the mean is simply Average(X,R), and doen't warrant a separ~~
ate function.
Definition: var I2 := if IsNotSpecified(J) ~
Then (Index K/((identifier of I)&"2") := I do VarTerm(K~~
)) ~
Else VarTerm(J);~
var Z:=X-Average(X,R);~
var Zt := Z[@I=@I2];~
Sum(Z*Zt,R)/(size(R)-1)
Nodelocation: 80,48,1
Nodesize: 48,24
Windstate: 2,222,299,476,297
Paramnames: X,I,J,R
Function Samplecorrelation(X : array[I,R] ; I,J,R : IndexType)
Title: sample correlation
Description: This function is obsolete. A covariance matrix can be co~~
mputed in Analytica 4.0+ using the built-in function Correlation. Th~~
e equivalent of this function is Correlation(X,X[@I=@J],R).~
~
Returns a correlation matrix based on data in X, where each data poin~~
t is a vector indexed by I, and the entries in the correlation matrix~~
are the pair-wise correlations of the columns of data. A second ind~~
ex, J, of size identical to I, is required in order to index the 2-di~~
mensional result.
Definition: var z:=x-average(x,R);~
var zt := slice(z,I,cumulate(1,J));~
sum(z*zt,R) / sqrt(sum(z^2,R) * sum(zt^2,R))~
Nodelocation: 208,48,1
Nodesize: 48,24
Windstate: 2,70,24,523,377
Paramnames: X,I,J,R
Close Depricated_multi_var
Text Multvar_te1
Description: Parametric Multivariate Distributions
Nodelocation: 160,40,-1
Nodesize: 136,12
Text Multvar_te2
Description: Creating an array of mutually correlated distributions:
Nodelocation: 232,368,-1
Nodesize: 200,16
Text Multvar_te3
Description: Creating a single univariate distribution correlated wit~~
h another existing dist:
Nodelocation: 296,280,-1
Nodesize: 268,12
Function Normal_correl(m, s, r, y: Numeric ;~
over : optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Normal_correl(m, s, r, y)
Description: Generates a normal distribution with mean m, standard dev~~
iation s, and correlation r with normally distributed value y. In a ~~
deterministic context, it will return m.~
~
If y is not normally distributed, the result will also not be normal,~~
and the correlation will be approximate. It generalizes appropriatel~~
y if any of the parameters are arrays:The result array will have the ~~
union of the indexes of the parameters.
Definition: IF r<-1 OR r>1 THEN Error('Correlation parameter r in func~~
tion Normal_correl(m, s, r, y) is outside the expected range [-1, 1].~~
');~
IFOnly IsSampleEvalMode ~
THEN m + s * (Sqrt(1-r^2) ~
* Normal(Sameindexes( 0, m ), Sameindexes( 1,~~
s ),~
singleSampleMethod:singleSampl~~
eMethod ) ~
+ r * (y - Mean(y))/Sdeviation(y))~
ELSE m
Nodelocation: 352,312,1
Nodesize: 108,16
Windstate: 2,102,90,503,416
Paramnames: m,s,r,y,over
Module Multivariate_interna
Title: Multivariate Internal Functions
Author: Lonnie
Date: Tue, May 01, 2007 9:29 PM
Defaultsize: 48,24
Nodelocation: 200,944,1
Nodesize: 52,32
Function Sameindexes(x, y)
Title: SameIndexes(x,y)
Description: Returns an array with the same indexes as y, and value x ~~
in each cell.
Definition: IF y=y THEN x ELSE x
Nodelocation: 120,64,1
Nodesize: 80,20
Paramnames: x,y
Close Multivariate_interna
Function Multinormal(m, s: Numeric; cm: ArrayType[i, j,Run]; i , j: In~~
dexType ;~
Over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Multinormal(m,s,c,i,j)
Description: A multi-variate normal (or Gaussian) distribution with me~~
an m, standard deviation s, and correlation matrix cm. m and s may ~~
be scalar or indexed by i. cm must be symmetric, positive-definite, a~~
nd indexed by i & j, which must be the same length.~
~
Multinormal uses a correlation matrix. Compare with Gaussian, which ~~
also defines a multi-variate normal but which uses a covariance matri~~
x.
Definition: Gaussian(m,cm*s*s[@i=@j],i,j,over,singleSampleMethod)
Nodelocation: 472,72,1
Nodesize: 84,16
Windstate: 2,391,248,512,343
Paramnames: m,s,cm,i,j,Over
Text Multvar_te4
Description: Reshaped distributions:
Nodelocation: 136,448,-1
Nodesize: 100,16
Function Dist_reshape(x : Numeric[R] ; newdist : all Numeric[R] ; ~
R : optional Index = Run )
Title: Dist_reshape(x, newdist)
Description: Reshapes the probability distribution of uncertain quanti~~
ty x so that it has the same marginal probability distribution (i.e, ~~
same set of sample values) as newdist, but retains the same ranks as ~~
x. Thus:~
Rank(Sample(x), Run) ~
= Rank(Sample(Reshape_dist(x, y)), Run)~
In a Mid context, it simply returns the mid value of newdist, with an~~
y indexes of x.~
~
The result retains any rank correlations that x may have with other p~~
redecessor variables. So, the rank-order correlation between a third~~
variable z and x will be the same as the rank-order correlation betw~~
een z and a reshaped version of x, i.e.~
RankCorrel(x, z) = RankCorrel(Reshape_Dist(x, y), z)~
~
The operation may optionally be applied along an index other than Run~~
.
Definition: IFOnly IsSampleEvalMode or Handle(R)<>Handle(Run) THEN BEG~~
IN~
VAR dsort := SortIndex(newdist, Run);~
VAR xranks := Rank(x, Run);~
newdist[Run = dsort[Run=xranks]]~
END~
ELSE newdist * (x=x)
Nodelocation: 152,472,1
Nodesize: 116,16
Windstate: 2,102,90,646,469
Paramnames: x,newdist,R
Text Multvar_te5
Description: Arrays with serial correlation
Nodelocation: 208,532,-1
Nodesize: 168,12
Function Normal_serial_correl(m, s, r: Numeric; i: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Normal_serial_correl(m,s,r,i)
Description: Generates an array over index i of normal distributions w~~
ith mean m, standard deviation s, and correlation r between successiv~~
e values over index i. You can give each distribution a different m~~
ean and/or standard deviation if m and/or s are arrays indexed by i. ~~
If r is indexed by i, r[i=k] specifies the correlation between result~~
[i=k] and result[i=k-1]. (Then the first correlation, slice(r, i, 1)~~
is ignored.)
Definition: Var x := Normal(0, 1,singleSampleMethod:singleSampleMethod~~
);~
(FOR j := i DO ~
x := Normal_correl( 0, 1, r[i = j],x,~
singleSampleMethod:singleSampl~~
eMethod ) ) ~
* s + m
Nodelocation: 160,560,1
Nodesize: 120,16
Windstate: 2,353,325,540,383
Paramnames: m,s,r,i,over
Function Normal_additive_gro(x, m, s, r: Numeric; i: IndexType ;~
over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Normal_additive_gro(x,m,s,r,i)
Description: Adds a normally distributed percent growth g with mean m ~~
and standard deviation s to x for each value of index i. The growth g~~
for each i has serial correlation r with g for i-1.
Definition: x *( 1 + Cumulate(Normal_serial_correl(m, s, r, i,~
singleSampleMethod:singleSampleMethod), i~~
))
Nodelocation: 159,600,1
Nodesize: 119,16
Windstate: 2,102,90,519,306
Paramnames: x,m,s,r,i,over
Function Normal_compound_gro(x, m, s, r: Numeric; t: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Normal_compound_gro(x,m,s,r,t)
Description: An array of values over time index t, starting from with ~~
value x, and with compound growth applied for each time interval, wit~~
h normal uncertainty with mean m and standard deviation s The growth~~
g for each i has correlation r with g for i-1.
Definition: x * Cumproduct(IF t = Slice(t, 1) THEN 1 ELSE Normal_seria~~
l_correl(m, s, r, t, singleSampleMethod:singleSampleMethod ) + 1, t)~~
Nodelocation: 159,640,1
Nodesize: 119,16
Windstate: 2,102,90,529,366
Paramnames: x,m,s,r,t,over
Function Dist_serial_correl(x; r; i: IndexType ;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Dist_serial_correl(x,r,i)
Description: Generates an array y over index i where each y[i] has a m~~
arginal distribution identical to x, and serial rank correlation of ~~
r with y[i-1]. If x is indexed by i, each y[i] has the same margin~~
al distribution as x[i], but with samples reordered to have the speci~~
fied rank correlation r between successive values. If r is indexed b~~
y i, r[i=k] specifies the rank correlation between y[i=k] and y[i=k-1~~
]. Then the first correlation, r[i=1], is ignored.~
~
In Mid context, it returns Mid(x).~
~
Note: The result retains no probabilistic dependence on x.
Definition: Dist_reshape(Normal_serial_correl( 0, 1, r, i, singleSampl~~
eMethod:singleSampleMethod ), x)
Nodelocation: 408,560,1
Nodesize: 120,16
Windstate: 2,302,78,477,447
Paramnames: x,r,i,over
Function Dist_additive_growth(x, g, r: Numeric; i: IndexType;~
over : ... optional atomic;~
singleSampleMethod : optional hidden scalar )
Title: Dist_additive_growth(x,g,r,i)
Description: Generates an array of values over index i, with the first~~
equal to x, and successive values adding an uncertain growth with pr~~
obability distribution g, and serial correlation r between growth[i =~~
k] and growth[i=k-1]. x, g, and r each may be indexed by i if you w~~
ant them to vary over i.
Definition: x + Cumulate(Dist_serial_correl( g, r, i, singleSampleMeth~~
od : singleSampleMethod), i)
Nodelocation: 407,600,1
Nodesize: 119,16
Windstate: 2,102,90,506,300
Paramnames: x,g,r,i,over
Function Dist_compound_growth(x, g, r; i: IndexType ;~
over : ... optional atomic ;~
singleSampleMethod : optional hidden scalar )
Title: Dist_compound_growth(x,g,r,i)
Description: Starts with x and applies a compound growth g for each va~~
lue of index i. The growth g for each i has correlation r with g for ~~
i-1.
Definition: x * Cumproduct(~
IF i = Slice(i, 1) THEN 1 ~
ELSE (Dist_serial_correl( g, r, i, ~
singleSampleMethod:singleSampleMe~~
thod ) + 1)~
, i)
Nodelocation: 407,640,1
Nodesize: 119,16
Windstate: 2,102,90,489,307
Paramnames: x,g,r,i,over
Text Multvar_te6
Description: Distributions on Linear Regression coefficients
Nodelocation: 296,688,-1
Nodesize: 256,12
Function Regressionnoise( Y : Numeric[I,Run] ; B : Numeric[I,K,Run] ; ~~
I,K : Index; C : optional Numeric[K,Run] )
Title: RegressionNoise(Y,B,I,K,C)
Description: When you have data, Y[I] and B[I,K], generated from an un~~
derlying model with unknown coefficients C[k] and S of the form:~
~
Y = Sum( C*B, I) + Normal(0,S)~
~
This function computes an estimate for S. ~
~
When using in conjunction with RegressionDist, it is most efficient t~~
o provide the optional parameter C to both routines, where C is the e~~
xpected value of the regression coefficients, obtained from calling R~~
egression(Y,B,I,K). Doing so avoids an unnecessary call to the built~~
in Regression function.
Definition: if IsNotSpecified(C) Then C := Regression(Y,B,I,K);~
Var resid := Y - Sum(C*B,K);~
sqrt( Sum(resid^2,I) / (size(I)-size(K)) );~
Nodelocation: 384,736,1
Nodesize: 104,20
Windstate: 2,332,211,498,542
Paramnames: Y,B,I,K,C
Function Regressionfitprob( Y : Numeric[I,Run] ; B : Numeric[I,K,Run] ~~
; I,K : Index; C : optional Numeric[K,Run] ; ~
S : optional Numeric[I,Run] )
Title: RegressionFitProb(Y,B,I,K,C)
Description: Once you've obtained regression coefficients C (indexed b~~
y K) by calling the Regression function, this function returns the pr~~
obability that a fit this poor would occur by chance, given the assum~~
ption that the data was generated by a process of the form:~
~
Y = Sum( C*B,K) + Normal(0,S)~
~
If this result is very close to zero, it probably indicates that the ~~
assumption of linearity is bad. If it is very close to one, then it ~~
validates the assumption of linearity.~
~
This is not a distribution function - it does not return a sample whe~~
n evaluated in Sample mode. However, it does complement the multivar~~
iate RegressionDist function also included in this library.~
~
To use, first call the Regression function, then you must either know~~
the measurement knows a priori, or obtain it using the RegressionNoi~~
se function.~
~
Var E_C := Regression(Y,B,I,K);~
Var S := RegressionNoise(Y,B,I,K,C);~
Var PrThisPoor := RegressionFitProb(Y,B,I,K,E_C,S)
Definition: var resid := Y - sum(C*B,K);~
var n := size(I);~
var chi2 := sum( resid^2 / Mean(S)^2, I);~
GammaI( n/2 - 1, chi2/2 )
Nodelocation: 152,800,1
Nodesize: 112,20
Windstate: 2,287,69,586,548
Paramnames: Y,B,I,K,C,S
Close Multivariate_distrib
Index Date2
Title: Date2
Definition: concat( CopyIndex( Date1), ~
DateAdd( Slice(Date1,size(Date1)), 1..100, "wd" ) )
Nodelocation: 80,200,1
Nodesize: 48,24
Numberformat: 2,DD,2,2,0,0,4,0,$,0,"ABBREV",0
Variable Future_stock_price
Title: Future stock price
Definition: IgnoreWarnings( Stock_price[Date1=Date2] )
Nodelocation: 200,200,1
Nodesize: 48,24
Aliases: Alias Future_stock_price1, Alias Future_stock_price2
Close Using_regression