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Data and Management Strategies for Recreational Fisheries with Annual Catch Limits (2021) / Chapter Skim
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Appendix C: Contemporaneous Correlation SUR Model
Pages 179-184

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From page 179...
... on dependent variable variable i, a matrix of nonstochastic independent variables Xi, a column vector of parameters βi yii, a matrix of nonstochastic to be estimated, independent and a column of errors eXi.ii,Each vector variables a column vector Xi matrix hasofKparameters βii to be estimated, i independent variables and a (columns)
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From page 180...
... . The TheMMmodels models 180 can canbebewritten writtentogether togetherinin"stacked" matrix "stacked" matrixform form RECREATIONAL as:as: FISHERIES WITH ANNUAL CATCH LIMITS Alternatively, Alternatively,the thesetset Alternatively, ofofM the setMmodels can ofmodels canbe M models bewritten can writtenmore compactly more be written compactly more asasas compactly simply: simply: simply: yyy===Xβ Xβ++ + Xβ e,e, e, where where where and andwhere where and where ●● inina in • afisheries fisheries a fisheries application,yiy application, application, yis isthe thecatch catchofofspecies andy yisisa arandom speciesi, i,and randomvector theyiy; i; vectorofofthe ii is the catch of species i, and y is a random vector of the yi; ●● β is the • βi βisi is i column thethecolumn vector columnvector of vector of parameters of parameters parameters forfor equation forequation i, and equationi, i,and β is the andβ βis is thethe concatenated concatenated concatenated vector vector of ofofallallofof vector the β vectors; thealliβiofvectors; the βi vectors; 167 ● ● • E(y)
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From page 181...
... . If the autoregressive specification is extended still further such that the error in a given domain is allowed to depend on the errors in previous time periods in all domains included in the model, the vector autoregressive model results (Judge et al., 1985, p.
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From page 182...
... . Autocorrelation Autocorrelation Autocorrelation Autocorrelation Autocorrelation Autocorrelation coefficients coefficients coefficients coefficients coefficients coefficients can can can can can can then then then then then be thenbe bebe be obtained beobtained obtained obtained obtained obtained by by by by by taking taking taking taking taking ratios ratios ratios ratios ratios ratios of of of of the the the the appropriate ofappropriate of theappropriate the appropriate appropriate appropriate elements elements elements elements elements of of of the ofthe the the Autocorrelation coefficients can then be obtained by taking ratios of the appropriate elements of the variance-covariance variance-covariance variance-covariance variance-covariance the variance-covariance variance-covariance matrix, matrix, matrix, matrix, matrix, variance-covariance forfor for for matrix, for matrix, example: example: example: example: for example: for example: example: VECTOR AUTOREGRESSIVE (VAR)
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From page 183...
... If the error within a domain is affected by the error within that same domain from the previous point in time, but it is not affected by at one point the error in the other domaintoatbe in time is allowed theaffected by the previous point error in time. within If the that same error within domain a domain frominthe at one point timeprevious is allowed point in time andtothebe affected error in by the the error otherwithin that same domain at domain from the point the previous previousinpoint time, the and in time VARthespecification error in the other domain at the previous point in time, the VAR specification for the variance-covariance matrix for the variance-covariance results: matrix results in: Again, thethe Again, above aboveexample example isisfor forthethe casecase of domains of two two domains and two and time two time periods.
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From page 184...
... 1980. Estimation of seemingly unrelated regression with lagged dependent variables and autocorrelated errors.
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Key Terms

  • basic sur
  • sur method
  • seemingly unrelated
  • vector autoregressive
  • contemporaneous correlation

  • autocorrelation specification
  • identity matrix
  • kronecker product
  • vector vector
  • efficiency gains

  • linear unbiased
  • joint fish
  • autoregressive specification
  • sur methods
  • catch distribution

  • fish catch
  • independent variables
  • autocorrelation coefficient
  • autocorrelation autocorrelation
  • specification specification

  • forecasting models
  • unrelated regression
  • catch estimate
  • autoregressive model
  • unbiased estimator

  • definite matrix
  • product operator
  • fishing modes
  • autocorrelation coefficients
  • catch forecasts


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