# VAR.Pope: Bias-correction for VAR parameter estimators based on Pope's... In VAR.etp: VAR modelling: estimation, testing, and prediction

## Description

The function returns bias-corrected parmater estimators and Bias estimators based on Pope's asymptotic formula

## Usage

 `1` ```VAR.Pope(x, p, type = "const") ```

## Arguments

 `x` data matrix in column `p` AR order `type` "const" for the AR model with intercept only, "const+trend" for the AR model with intercept and trend

## Details

Kilian's (1998) stationarity-correction is used for bias-correction

## Value

 `coef ` Bias-corrected coefficient matrix `resid ` matrix of residuals `sigu ` residual covariance matrix `Bias` Bias Estimate

Jae H. Kim

## References

Kim, J. H. 2004, Bias-corrected bootstrap prediction regions for Vector Autoregression, Journal of FOrecasting 23, 141-154.

Kilian, L. (1998). Small sample confidence intervals for impulse response functions, The Review of Economics and Statistics, 80, 218 - 230.

Nicholls DF, Pope AL. 1988, Bias in estimation of multivariate autoregression. Australian Journal of Statistics, 30A, 296-309.

Pope AL. 1990. Biases of estimators in multivariate non-Gaussian autoregression, Journal of Time Series Analysis 11, 249-258.

## Examples

 ```1 2``` ```data(dat) VAR.Pope(dat,p=2,type="const") ```

### Example output

```\$coef
inv(-1)    inc(-1)    con(-1)     inv(-2)    inc(-2)      con(-2)
inv -0.317014888  0.1402669  0.9526036 -0.13869135 0.12301901  0.928924128
inc  0.045371133 -0.1596940  0.2822543  0.05186441 0.03233458 -0.007794895
con -0.001134822  0.2195725 -0.2688171  0.03584184 0.35447058 -0.010087125
const
inv -0.01672199
inc  0.01576719
con  0.01292586

\$resid
inv           inc           con
[1,]  0.011777651 -0.0032376492  0.0073843429
[2,]  0.061670486  0.0054151165  0.0006005142
[3,] -0.050686422 -0.0025100142 -0.0222149905
[4,]  0.013266922 -0.0134642761  0.0122034694
[5,]  0.008313364  0.0082596033  0.0093436605
[6,]  0.044622533 -0.0023941329  0.0030074297
[7,] -0.004137380 -0.0071826355  0.0015818813
[8,] -0.001448860  0.0043276131 -0.0059298510
[9,] -0.006006271  0.0002031905 -0.0044240229
[10,] -0.149215936 -0.0069439590 -0.0146791093
[11,]  0.140723332  0.0031554753 -0.0028767648
[12,]  0.067540960 -0.0019667703  0.0039940816
[13,]  0.036378654 -0.0013761854 -0.0080115526
[14,] -0.004890340  0.0047582262  0.0116302107
[15,]  0.025149238 -0.0061207102 -0.0191046934
[16,]  0.006667678 -0.0056483550 -0.0039886111
[17,]  0.038899112  0.0265154372  0.0091967240
[18,] -0.045035578  0.0040128697  0.0041981078
[19,]  0.011969941  0.0131865133  0.0053108685
[20,] -0.025819861  0.0009935936  0.0041174663
[21,] -0.024272464 -0.0062340358 -0.0032029593
[22,]  0.006206093 -0.0169694488 -0.0020043891
[23,] -0.020210782 -0.0051092214 -0.0047589739
[24,] -0.035231741  0.0194574073 -0.0002548705
[25,] -0.031005477 -0.0419870326 -0.0351349564
[26,] -0.031843670 -0.0046209767  0.0011197599
[27,] -0.064602389 -0.0110466286 -0.0059946711
[28,] -0.031818304 -0.0080203885 -0.0043618702
[29,]  0.096253320 -0.0003418848 -0.0007486809
[30,] -0.048936073  0.0109263399 -0.0010925959
[31,]  0.013199753  0.0023529300  0.0045822807
[32,]  0.017714356  0.0069583019 -0.0009864940
[33,]  0.048064466  0.0036128916  0.0054462411
[34,] -0.026658828  0.0019547617  0.0025065703
[35,]  0.036714669  0.0080861974 -0.0004174963
[36,]  0.057250101  0.0108881810  0.0035995213
[37,]  0.015877419 -0.0165023578 -0.0006191545
[38,] -0.008759913  0.0102139048  0.0049623022
[39,]  0.109970537  0.0175743035  0.0094127667
[40,]  0.050936380  0.0124575736  0.0049457500
[41,]  0.002137305 -0.0048123563  0.0054359067
[42,] -0.010941996 -0.0207335209 -0.0079359242
[43,]  0.020913953  0.0135203008  0.0114781868
[44,] -0.017486399  0.0054664904  0.0051613831
[45,] -0.025990681  0.0164792072  0.0014022323
[46,]  0.018806271  0.0079187561  0.0115893464
[47,] -0.045373154 -0.0064617249 -0.0214781214
[48,] -0.024017176  0.0082668975  0.0105367834
[49,] -0.001059645  0.0063146205  0.0102763380
[50,]  0.035795955  0.0027433153  0.0154838603
[51,] -0.057470934 -0.0139321157 -0.0082087568
[52,] -0.057063083 -0.0010802647 -0.0127937483
[53,] -0.031427402  0.0079654566  0.0024905489
[54,]  0.023870202 -0.0013930740  0.0043588090
[55,] -0.076426301  0.0051953610 -0.0002541556
[56,] -0.036451132  0.0192398227  0.0072951880
[57,] -0.053662827  0.0022202428 -0.0082457237
[58,] -0.017503598  0.0121920631 -0.0035559396
[59,] -0.049744729  0.0221553504  0.0161165540
[60,] -0.036819904 -0.0209135117 -0.0002357952
[61,] -0.004495903 -0.0089086566  0.0015333652
[62,]  0.008743910 -0.0065727795  0.0115143660
[63,]  0.022384237 -0.0091962399 -0.0046713158
[64,] -0.022561270  0.0027978837 -0.0051197029
[65,]  0.031492793 -0.0044583261  0.0065501528
[66,]  0.030900160 -0.0159378968 -0.0040268736
[67,] -0.024229657 -0.0052271847  0.0040048596
[68,] -0.008146402 -0.0034260610  0.0068131553
[69,] -0.001585236  0.0022936950  0.0015557257
[70,]  0.010487402 -0.0084109616 -0.0064144359
[71,]  0.032193107 -0.0059089309 -0.0016246326
[72,]  0.024726067  0.0026214241 -0.0024872561
[73,]  0.031419389 -0.0136510505 -0.0148816208

\$sigu
inv          inc          con
inv 2.130747e-03 7.174158e-05 1.233737e-04
inc 7.174158e-05 1.373937e-04 6.149446e-05
con 1.233737e-04 6.149446e-05 8.924426e-05

\$Bias
inv(-1)     inc(-1)     con(-1)      inv(-2)       inc(-2)
inv -0.002616084 0.005721886 0.008615387 -0.021859755 -0.0084140318
inc -0.001440071 0.006962115 0.006247383 -0.001833569 -0.0131688213
con -0.001287845 0.005240167 0.004849595 -0.001961429  0.0004417811
con(-2)
inv  0.005469630
inc -0.002409978
con -0.012143000
```

VAR.etp documentation built on May 1, 2019, 8:02 p.m.