VARff: VGLTSM family function for the Order-p Vector...

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/VARff.R

Description

Estimates an Order(p) Vector Autoregressive Models (VAR(p)) with white noise random errors by maximum likelihood estimation using Fisher scoring.

Usage

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            VARff(VAR.order = 1,
                  zero = c("var", "cov"),
                  lmean = "identitylink",
                  lvar  = "loglink",
                  lcov  = "identitylink")
                    

Arguments

VAR.order

Length–1 (positive) integer vector. The order of the VAR to be fitted.

zero

Integer or character - string vector. Same as MVNcov. Details at zero.

lmean, lvar, lcov

Same as MVNcov.

Details

Let x[t] = (x[1, t], …, x[K, t])^T be a time dependent vector of responses, with index t = 1, …, T, and e[t] = (e[1, t], …, e[K, t])^T white noise with covariance matrix V.

VARff fits a linear model to the means of a K–variate normal distribution, where each variable, x[i, t], i = 1, …, K, is a linear function of p–past lags of itself and past p–lags of the other variables. The model has the form

x[t] = Φ[1] * x[t - 1] + … + Φ[p] * x[t - p] + e[t]

where Φ[j] are K x K matrices of coefficients, j = 1, …, K, to be estimated.

The elements of the covariance matrix are intercept–only by default.

Value

An object of class "vglmff" (see vglmff-class) to be used by VGLM/VGAM modelling functions, e.g., vglm or vgam.

Author(s)

Victor Miranda.

See Also

MVNcov, zero, Links, ECM.EngleGran, vglm.

Examples

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set.seed(20170227)
nn <- 60
var.data <- data.frame(x2 = runif(nn, -2.5, 2.5))
var.data <- transform(var.data, y1 = rnorm(nn, 1.5 - 2 * x2, sqrt(exp(1.5))),
                                y2 = rnorm(nn, 1.0 - 1 * x2, sqrt(exp(0.75))),
                                y3 = rnorm(nn, 0.5 + 1 * x2, sqrt(exp(1.0))))

fit.var <- vglm(cbind(y1, y2, y3) ~ x2, VARff(VAR.order = 2),
                trace = TRUE, data = var.data)
coef(fit.var, matrix = TRUE)

summary(fit.var)
vcov(fit.var)

Example output

Loading required package: stats4
Loading required package: VGAM
Loading required package: splines

     =====    VGAMextra 0.0-2    ===== 

Additions and extensions of the package VGAM.
For more on VGAMextra, visit
     https://www.stat.auckland.ac.nz/~vmir178/

For a short description, fixes/bugs, and new
features type vgamextraNEWS().
VGLM    linear loop  1 :  loglikelihood = -366.05629
VGLM    linear loop  2 :  loglikelihood = -346.35831
VGLM    linear loop  3 :  loglikelihood = -344.09929
VGLM    linear loop  4 :  loglikelihood = -344.05251
VGLM    linear loop  5 :  loglikelihood = -344.05248
VGLM    linear loop  6 :  loglikelihood = -344.05248
                   Mean1       Mean2       Mean3 loglink(var1) loglink(var2)
(Intercept)  0.793506515  1.24230378  0.15593749      1.388011     0.6919905
x2          -1.687137012 -0.96046974  0.87744981      0.000000     0.0000000
Y1Lag1      -0.140342495 -0.04035930  0.04630504      0.000000     0.0000000
Y1Lag2       0.010224278 -0.10864904 -0.06344463      0.000000     0.0000000
Y2Lag1       0.382952961 -0.09584133  0.01164854      0.000000     0.0000000
Y2Lag2       0.174559574  0.14781365  0.07247584      0.000000     0.0000000
Y3Lag1      -0.050557123 -0.01112331  0.13005613      0.000000     0.0000000
Y3Lag2      -0.002013108 -0.07203862 -0.05362921      0.000000     0.0000000
            loglink(var3)      cov12      cov13     cov23
(Intercept)     0.9169531 -0.3890423 -0.2288145 0.3159147
x2              0.0000000  0.0000000  0.0000000 0.0000000
Y1Lag1          0.0000000  0.0000000  0.0000000 0.0000000
Y1Lag2          0.0000000  0.0000000  0.0000000 0.0000000
Y2Lag1          0.0000000  0.0000000  0.0000000 0.0000000
Y2Lag2          0.0000000  0.0000000  0.0000000 0.0000000
Y3Lag1          0.0000000  0.0000000  0.0000000 0.0000000
Y3Lag2          0.0000000  0.0000000  0.0000000 0.0000000

Call:
vglm(formula = cbind(y1, y2, y3) ~ x2, family = VARff(VAR.order = 2), 
    data = var.data, trace = TRUE)

Coefficients: 
               Estimate Std. Error z value Pr(>|z|)    
(Intercept):1  0.793507   0.409984   1.935 0.052934 .  
(Intercept):2  1.242304   0.289486   4.291 1.78e-05 ***
(Intercept):3  0.155937   0.323950   0.481 0.630258    
(Intercept):4  1.388011   0.182574   7.602 2.91e-14 ***
(Intercept):5  0.691991   0.182574   3.790 0.000151 ***
(Intercept):6  0.916953   0.182574   5.022 5.10e-07 ***
(Intercept):7 -0.389042   0.368688  -1.055 0.291330    
(Intercept):8 -0.228814   0.409800  -0.558 0.576601    
(Intercept):9  0.315915   0.291471   1.084 0.278426    
x2:1          -1.687137   0.193833  -8.704  < 2e-16 ***
x2:2          -0.960470   0.136864  -7.018 2.26e-12 ***
x2:3           0.877450   0.153158   5.729 1.01e-08 ***
Y1Lag1:1      -0.140342   0.102180  -1.373 0.169601    
Y1Lag1:2      -0.040359   0.072148  -0.559 0.575892    
Y1Lag1:3       0.046305   0.080737   0.574 0.566289    
Y1Lag2:1       0.010224   0.100908   0.101 0.919294    
Y1Lag2:2      -0.108649   0.071250  -1.525 0.127285    
Y1Lag2:3      -0.063445   0.079733  -0.796 0.426196    
Y2Lag1:1       0.382953   0.150287   2.548 0.010830 *  
Y2Lag1:2      -0.095841   0.106117  -0.903 0.366436    
Y2Lag1:3       0.011649   0.118750   0.098 0.921858    
Y2Lag2:1       0.174560   0.154370   1.131 0.258146    
Y2Lag2:2       0.147814   0.109000   1.356 0.175069    
Y2Lag2:3       0.072476   0.121976   0.594 0.552391    
Y3Lag1:1      -0.050557   0.147983  -0.342 0.732620    
Y3Lag1:2      -0.011123   0.104489  -0.106 0.915222    
Y3Lag1:3       0.130056   0.116929   1.112 0.266023    
Y3Lag2:1      -0.002013   0.149026  -0.014 0.989222    
Y3Lag2:2      -0.072039   0.105226  -0.685 0.493590    
Y3Lag2:3      -0.053629   0.117753  -0.455 0.648794    
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1

Number of linear predictors:  9 

Names of linear predictors: Mean1, Mean2, Mean3, loglink(var1), loglink(var2), 
loglink(var3), cov12, cov13, cov23

Log-likelihood: -344.0525 on 510 degrees of freedom

Number of Fisher scoring iterations: 6 

              (Intercept):1 (Intercept):2 (Intercept):3 (Intercept):4
(Intercept):1  1.680868e-01 -1.632016e-02 -9.598671e-03  0.0000000000
(Intercept):2 -1.632016e-02  8.380218e-02  1.325249e-02  0.0000000000
(Intercept):3 -9.598671e-03  1.325249e-02  1.049434e-01  0.0000000000
(Intercept):4  0.000000e+00  0.000000e+00  0.000000e+00  0.0333333333
(Intercept):5  0.000000e+00  0.000000e+00  0.000000e+00  0.0006302874
(Intercept):6  0.000000e+00  0.000000e+00  0.000000e+00  0.0001741053
(Intercept):7  0.000000e+00  0.000000e+00  0.000000e+00 -0.0129680761
(Intercept):8  0.000000e+00  0.000000e+00  0.000000e+00 -0.0076271489
(Intercept):9  0.000000e+00  0.000000e+00  0.000000e+00  0.0007405476
x2:1           5.694783e-04 -5.529272e-05 -3.252031e-05  0.0000000000
x2:2          -5.529272e-05  2.839218e-04  4.489945e-05  0.0000000000
x2:3          -3.252031e-05  4.489945e-05  3.555485e-04  0.0000000000
Y1Lag1:1      -7.138694e-03  6.931217e-04  4.076582e-04  0.0000000000
Y1Lag1:2       6.931217e-04 -3.559102e-03 -5.628369e-04  0.0000000000
Y1Lag1:3       4.076582e-04 -5.628369e-04 -4.456977e-03  0.0000000000
Y1Lag2:1      -1.322787e-02  1.284342e-03  7.553831e-04  0.0000000000
Y1Lag2:2       1.284342e-03 -6.594949e-03 -1.042926e-03  0.0000000000
Y1Lag2:3       7.553831e-04 -1.042926e-03 -8.258695e-03  0.0000000000
Y2Lag1:1      -2.612736e-02  2.536800e-03  1.492014e-03  0.0000000000
Y2Lag1:2       2.536800e-03 -1.302618e-02 -2.059963e-03  0.0000000000
Y2Lag1:3       1.492014e-03 -2.059963e-03 -1.631237e-02  0.0000000000
Y2Lag2:1      -2.032323e-02  1.973257e-03  1.160567e-03  0.0000000000
Y2Lag2:2       1.973257e-03 -1.013245e-02 -1.602347e-03  0.0000000000
Y2Lag2:3       1.160567e-03 -1.602347e-03 -1.268862e-02  0.0000000000
Y3Lag1:1      -1.231909e-02  1.196105e-03  7.034871e-04  0.0000000000
Y3Lag1:2       1.196105e-03 -6.141866e-03 -9.712757e-04  0.0000000000
Y3Lag1:3       7.034871e-04 -9.712757e-04 -7.691310e-03  0.0000000000
Y3Lag2:1      -1.732800e-02  1.682439e-03  9.895232e-04  0.0000000000
Y3Lag2:2       1.682439e-03 -8.639133e-03 -1.366194e-03  0.0000000000
Y3Lag2:3       9.895232e-04 -1.366194e-03 -1.081858e-02  0.0000000000
              (Intercept):5 (Intercept):6 (Intercept):7 (Intercept):8
(Intercept):1  0.0000000000  0.0000000000  0.0000000000   0.000000000
(Intercept):2  0.0000000000  0.0000000000  0.0000000000   0.000000000
(Intercept):3  0.0000000000  0.0000000000  0.0000000000   0.000000000
(Intercept):4  0.0006302874  0.0001741053 -0.0129680761  -0.007627149
(Intercept):5  0.0333333333  0.0006656764 -0.0129680761  -0.002050774
(Intercept):6  0.0006656764  0.0333333333 -0.0009631733  -0.007627149
(Intercept):7 -0.0129680761 -0.0009631733  0.1359307436   0.022580834
(Intercept):8 -0.0020507738 -0.0076271489  0.0225808342   0.167936437
(Intercept):9  0.0105304909  0.0105304909 -0.0096667351  -0.017425600
x2:1           0.0000000000  0.0000000000  0.0000000000   0.000000000
x2:2           0.0000000000  0.0000000000  0.0000000000   0.000000000
x2:3           0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag1:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag1:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag1:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag2:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag2:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y1Lag2:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag1:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag1:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag1:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag2:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag2:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y2Lag2:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag1:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag1:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag1:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag2:1       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag2:2       0.0000000000  0.0000000000  0.0000000000   0.000000000
Y3Lag2:3       0.0000000000  0.0000000000  0.0000000000   0.000000000
              (Intercept):9          x2:1          x2:2          x2:3
(Intercept):1  0.0000000000  5.694783e-04 -5.529272e-05 -3.252031e-05
(Intercept):2  0.0000000000 -5.529272e-05  2.839218e-04  4.489945e-05
(Intercept):3  0.0000000000 -3.252031e-05  4.489945e-05  3.555485e-04
(Intercept):4  0.0007405476  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):5  0.0105304909  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):6  0.0105304909  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):7 -0.0096667351  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):8 -0.0174255996  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):9  0.0849555187  0.000000e+00  0.000000e+00  0.000000e+00
x2:1           0.0000000000  3.757140e-02 -3.647944e-03 -2.145531e-03
x2:2           0.0000000000 -3.647944e-03  1.873178e-02  2.962247e-03
x2:3           0.0000000000 -2.145531e-03  2.962247e-03  2.345735e-02
Y1Lag1:1       0.0000000000 -1.542368e-03  1.497541e-04  8.807759e-05
Y1Lag1:2       0.0000000000  1.497541e-04 -7.689704e-04 -1.216051e-04
Y1Lag1:3       0.0000000000  8.807759e-05 -1.216051e-04 -9.629630e-04
Y1Lag2:1       0.0000000000  3.542866e-03 -3.439898e-04 -2.023169e-04
Y1Lag2:2       0.0000000000 -3.439898e-04  1.766348e-03  2.793307e-04
Y1Lag2:3       0.0000000000 -2.023169e-04  2.793307e-04  2.211956e-03
Y2Lag1:1       0.0000000000  2.082056e-03 -2.021544e-04 -1.188967e-04
Y2Lag1:2       0.0000000000 -2.021544e-04  1.038040e-03  1.641558e-04
Y2Lag1:3       0.0000000000 -1.188967e-04  1.641558e-04  1.299912e-03
Y2Lag2:1       0.0000000000  3.278818e-03 -3.183523e-04 -1.872383e-04
Y2Lag2:2       0.0000000000 -3.183523e-04  1.634703e-03  2.585122e-04
Y2Lag2:3       0.0000000000 -1.872383e-04  2.585122e-04  2.047099e-03
Y3Lag1:1       0.0000000000 -2.111471e-03  2.050104e-04  1.205765e-04
Y3Lag1:2       0.0000000000  2.050104e-04 -1.052705e-03 -1.664750e-04
Y3Lag1:3       0.0000000000  1.205765e-04 -1.664750e-04 -1.318277e-03
Y3Lag2:1       0.0000000000  1.509235e-03 -1.465371e-04 -8.618549e-05
Y3Lag2:2       0.0000000000 -1.465371e-04  7.524512e-04  1.189928e-04
Y3Lag2:3       0.0000000000 -8.618549e-05  1.189928e-04  9.422765e-04
                   Y1Lag1:1      Y1Lag1:2      Y1Lag1:3      Y1Lag2:1
(Intercept):1 -7.138694e-03  6.931217e-04  4.076582e-04 -1.322787e-02
(Intercept):2  6.931217e-04 -3.559102e-03 -5.628369e-04  1.284342e-03
(Intercept):3  4.076582e-04 -5.628369e-04 -4.456977e-03  7.553831e-04
(Intercept):4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):5  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):6  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):7  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):8  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):9  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
x2:1          -1.542368e-03  1.497541e-04  8.807759e-05  3.542866e-03
x2:2           1.497541e-04 -7.689704e-04 -1.216051e-04 -3.439898e-04
x2:3           8.807759e-05 -1.216051e-04 -9.629630e-04 -2.023169e-04
Y1Lag1:1       1.044068e-02 -1.013724e-03 -5.962197e-04  6.974061e-04
Y1Lag1:2      -1.013724e-03  5.205357e-03  8.231761e-04 -6.771369e-05
Y1Lag1:3      -5.962197e-04  8.231761e-04  6.518543e-03 -3.982568e-05
Y1Lag2:1       6.974061e-04 -6.771369e-05 -3.982568e-05  1.018239e-02
Y1Lag2:2      -6.771369e-05  3.477021e-04  5.498568e-05 -9.886453e-04
Y1Lag2:3      -3.982568e-05  5.498568e-05  4.354190e-04 -5.814698e-04
Y2Lag1:1      -5.589581e-03  5.427127e-04  3.191954e-04  1.037581e-04
Y2Lag1:2       5.427127e-04 -2.786768e-03 -4.407000e-04 -1.007426e-05
Y2Lag1:3       3.191954e-04 -4.407000e-04 -3.489803e-03 -5.925154e-06
Y2Lag2:1      -4.542288e-03  4.410273e-04  2.593893e-04 -4.658154e-03
Y2Lag2:2       4.410273e-04 -2.264625e-03 -3.581282e-04  4.522771e-04
Y2Lag2:3       2.593893e-04 -3.581282e-04 -2.835935e-03  2.660059e-04
Y3Lag1:1       6.571954e-03 -6.380949e-04 -3.752943e-04 -9.029502e-04
Y3Lag1:2      -6.380949e-04  3.276545e-03  5.181534e-04  8.767072e-05
Y3Lag1:3      -3.752943e-04  5.181534e-04  4.103138e-03  5.156336e-05
Y3Lag2:1      -2.014596e-04  1.956045e-05  1.150444e-05  6.830750e-03
Y3Lag2:2       1.956045e-05 -1.004407e-04 -1.588371e-05 -6.632224e-04
Y3Lag2:3       1.150444e-05 -1.588371e-05 -1.257794e-04 -3.900730e-04
                   Y1Lag2:2      Y1Lag2:3      Y2Lag1:1      Y2Lag1:2
(Intercept):1  1.284342e-03  7.553831e-04 -2.612736e-02  2.536800e-03
(Intercept):2 -6.594949e-03 -1.042926e-03  2.536800e-03 -1.302618e-02
(Intercept):3 -1.042926e-03 -8.258695e-03  1.492014e-03 -2.059963e-03
(Intercept):4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):5  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):6  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):7  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):8  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
(Intercept):9  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
x2:1          -3.439898e-04 -2.023169e-04  2.082056e-03 -2.021544e-04
x2:2           1.766348e-03  2.793307e-04 -2.021544e-04  1.038040e-03
x2:3           2.793307e-04  2.211956e-03 -1.188967e-04  1.641558e-04
Y1Lag1:1      -6.771369e-05 -3.982568e-05 -5.589581e-03  5.427127e-04
Y1Lag1:2       3.477021e-04  5.498568e-05  5.427127e-04 -2.786768e-03
Y1Lag1:3       5.498568e-05  4.354190e-04  3.191954e-04 -4.407000e-04
Y1Lag2:1      -9.886453e-04 -5.814698e-04  1.037581e-04 -1.007426e-05
Y1Lag2:2       5.076582e-03  8.028115e-04 -1.007426e-05  5.173016e-05
Y1Lag2:3       8.028115e-04  6.357280e-03 -5.925154e-06  8.180616e-06
Y2Lag1:1      -1.007426e-05 -5.925154e-06  2.258629e-02 -2.192985e-03
Y2Lag1:2       5.173016e-05  8.180616e-06 -2.192985e-03  1.126073e-02
Y2Lag1:3       8.180616e-06  6.478043e-05 -1.289800e-03  1.780773e-03
Y2Lag2:1       4.522771e-04  2.660059e-04  4.517669e-03 -4.386370e-04
Y2Lag2:2      -2.322391e-03 -3.672634e-04 -4.386370e-04  2.252351e-03
Y2Lag2:3      -3.672634e-04 -2.908275e-03 -2.579835e-04  3.561872e-04
Y3Lag1:1       8.767072e-05  5.156336e-05  2.331359e-03 -2.263601e-04
Y3Lag1:2      -4.501792e-04 -7.119142e-05 -2.263601e-04  1.162334e-03
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VGAMextra documentation built on May 24, 2021, 9:07 a.m.