Skip to contents

Fitting Vector Heterogeneous Autoregressive Model

Source: R/vharlse.R, R/print-vharlse.R
vhar_lm.Rd

This function fits VHAR using OLS method.

Usage

vhar_lm(
  y,
  har = c(5, 22),
  include_mean = TRUE,
  method = c("nor", "chol", "qr")
)

# S3 method for vharlse
print(x, digits = max(3L, getOption("digits") - 3L), ...)

# S3 method for vharlse
knit_print(x, ...)

Arguments

y

Time series data of which columns indicate the variables

har

Numeric vector for weekly and monthly order. By default, c(5, 22).

include_mean

Add constant term (Default: TRUE) or not (FALSE)

method

Method to solve linear equation system. ("nor": normal equation (default), "chol": Cholesky, and "qr": HouseholderQR)

x

vharlse object

digits

digit option to print

...

not used

Value

vhar_lm() returns an object named vharlse

class. It is a list with the following components:

coefficients

Coefficient Matrix

fitted.values

Fitted response values

residuals

Residuals

covmat

LS estimate for covariance matrix

df

Numer of Coefficients: 3m + 1 or 3m

p

3 (The number of terms. vharlse contains this element for usage in other functions.)

week

Order for weekly term

month

Order for monthly term

m

Dimension of the data

obs

Sample size used when training = totobs - 22

totobs

Total number of the observation

call

Matched call

process

Process: VHAR

type

include constant term ("const") or not ("none")

HARtrans

VHAR linear transformation matrix: \(C_{HAR}\)

y0

\(Y_0\)

design

\(X_0\)

y

Raw input

It is also a bvharmod class.

Details

For VHAR model $$Y_{t} = \Phi^{(d)} Y_{t - 1} + \Phi^{(w)} Y_{t - 1}^{(w)} + \Phi^{(m)} Y_{t - 1}^{(m)} + \epsilon_t$$ the function gives basic values.

References

Baek, C. and Park, M. (2021). Sparse vector heterogeneous autoregressive modeling for realized volatility. J. Korean Stat. Soc. 50, 495–510.

Bubák, V., Kočenda, E., & Žikeš, F. (2011). Volatility transmission in emerging European foreign exchange markets. Journal of Banking & Finance, 35(11), 2829–2841.

Corsi, F. (2008). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174–196.

See also

Examples

# Perform the function using etf_vix dataset
fit <- vhar_lm(y = etf_vix)
class(fit)
#> [1] "vharlse"  "bvharmod"
str(fit)
#> List of 18
#>  $ coefficients : num [1:28, 1:9] 0.8698 0.02988 -0.01632 -0.10078 0.00306 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:28] "GVZCLS_day" "OVXCLS_day" "VXFXICLS_day" "VXEEMCLS_day" ...
#>   .. ..$ : chr [1:9] "GVZCLS" "OVXCLS" "VXFXICLS" "VXEEMCLS" ...
#>  $ fitted.values: num [1:883, 1:9] 20.4 20.6 20.1 19.9 19.3 ...
#>  $ residuals    : num [1:883, 1:9] 0.3176 -0.5873 -0.3752 -0.8374 -0.0281 ...
#>  $ covmat       : num [1:9, 1:9] 1.119 0.375 0.299 0.437 1.37 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:9] "GVZCLS" "OVXCLS" "VXFXICLS" "VXEEMCLS" ...
#>   .. ..$ : chr [1:9] "GVZCLS" "OVXCLS" "VXFXICLS" "VXEEMCLS" ...
#>  $ df           : int 28
#>  $ m            : int 9
#>  $ obs          : int 883
#>  $ y0           : num [1:883, 1:9] 20.7 20 19.7 19.1 19.2 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:9] "GVZCLS" "OVXCLS" "VXFXICLS" "VXEEMCLS" ...
#>  $ p            : int 3
#>  $ week         : int 5
#>  $ month        : int 22
#>  $ totobs       : num 905
#>  $ process      : chr "VHAR"
#>  $ type         : chr "const"
#>  $ HARtrans     : num [1:28, 1:199] 1 0 0 0 0 0 0 0 0 0.2 ...
#>  $ design       : num [1:883, 1:199] 20.4 20.7 20 19.7 19.1 ...
#>  $ y            : num [1:905, 1:9] 21.5 21.5 22.3 21.6 21.2 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : NULL
#>   .. ..$ : chr [1:9] "GVZCLS" "OVXCLS" "VXFXICLS" "VXEEMCLS" ...
#>  $ call         : language vhar_lm(y = etf_vix)
#>  - attr(*, "class")= chr [1:2] "vharlse" "bvharmod"

# Extract coef, fitted values, and residuals
coef(fit)
#>                      GVZCLS      OVXCLS      VXFXICLS     VXEEMCLS
#> GVZCLS_day      0.869796005 -0.04681230 -0.0172897224  0.049002224
#> OVXCLS_day      0.029877159  0.91358257  0.0350799026  0.010047707
#> VXFXICLS_day   -0.016319909 -0.13959548  0.8575034005 -0.033709406
#> VXEEMCLS_day   -0.100780743 -0.08210474  0.0121290737  0.655662834
#> VXSLVCLS_day    0.003060357  0.03668387  0.0282158214  0.013830263
#> EVZCLS_day      0.186426595 -0.17282244  0.0494563262 -0.062064078
#> VXXLECLS_day    0.078818472  0.10515479  0.0728823779  0.279901357
#> VXGDXCLS_day   -0.039080303  0.04925811 -0.0428945531 -0.033003536
#> VXEWZCLS_day    0.032080106  0.07853175  0.0131343314  0.069517084
#> GVZCLS_week    -0.040418408 -0.07188231 -0.0938952991 -0.157648897
#> OVXCLS_week    -0.085524289 -0.06406862 -0.0701989801 -0.038293713
#> VXFXICLS_week  -0.029907441  0.12562086  0.0749857892  0.139908054
#> VXEEMCLS_week   0.230258633  0.05761231  0.0006402918  0.126209971
#> VXSLVCLS_week   0.027500102  0.02993123  0.0442818765  0.042748861
#> EVZCLS_week    -0.236308396  0.28602174 -0.0005685013  0.140233072
#> VXXLECLS_week  -0.120360477 -0.05095917 -0.1126391194 -0.332190330
#> VXGDXCLS_week   0.054947386 -0.06808223  0.0506682953  0.025319297
#> VXEWZCLS_week  -0.043554254 -0.05055300  0.0078698375 -0.007277838
#> GVZCLS_month    0.023458944  0.01754305 -0.0253911426  0.003596504
#> OVXCLS_month    0.001541434  0.07383772 -0.0059125573 -0.012132076
#> VXFXICLS_month -0.011772882 -0.02021036 -0.0587438676 -0.128208430
#> VXEEMCLS_month -0.134015581 -0.03842329 -0.0059768395  0.135807907
#> VXSLVCLS_month -0.002659358 -0.01415388 -0.0158012078  0.038533007
#> EVZCLS_month    0.185251113 -0.05458701  0.1512782039 -0.012040779
#> VXXLECLS_month  0.105997340  0.09819774  0.0508482758  0.101087018
#> VXGDXCLS_month  0.033825430  0.05583194  0.0377451676  0.024847951
#> VXEWZCLS_month  0.020348604 -0.01547358 -0.0074385193 -0.065668936
#> const           0.257508640 -0.75244225  0.7874223172  0.329901821
#>                     VXSLVCLS        EVZCLS     VXXLECLS    VXGDXCLS
#> GVZCLS_day      0.2171686933 -8.528593e-04 -0.006316449  0.14468642
#> OVXCLS_day     -0.0038224358  1.317614e-02  0.023484352  0.06339221
#> VXFXICLS_day   -0.0821022074 -2.145593e-02 -0.074931174 -0.05632922
#> VXEEMCLS_day   -0.0951773758 -1.278904e-02 -0.111052628 -0.05281887
#> VXSLVCLS_day    0.6911996371  4.988352e-03  0.009943586  0.07416401
#> EVZCLS_day      0.2247289953  8.908482e-01 -0.164489289 -0.02651442
#> VXXLECLS_day    0.1848839755  2.688135e-02  1.110417850  0.20178781
#> VXGDXCLS_day   -0.0326865958 -1.097720e-02  0.015583137  0.65845387
#> VXEWZCLS_day    0.0086576066  2.741950e-02  0.057451312  0.06060228
#> GVZCLS_week    -0.1717505332  5.820058e-03 -0.062671994 -0.07765708
#> OVXCLS_week     0.0013998157 -3.043820e-02 -0.081955633 -0.06014147
#> VXFXICLS_week   0.0351147921  4.615955e-02  0.148110845  0.14285833
#> VXEEMCLS_week   0.2351233848  5.680828e-03  0.007968589  0.02454380
#> VXSLVCLS_week   0.1788828526 -8.453363e-05  0.023363480 -0.06368503
#> EVZCLS_week    -0.4461793985  1.019828e-02  0.182684876 -0.09790030
#> VXXLECLS_week  -0.2019441922 -2.813833e-02 -0.236461970 -0.21181825
#> VXGDXCLS_week   0.0003105573 -7.379189e-03 -0.011074423  0.20755785
#> VXEWZCLS_week  -0.0240538695 -2.495159e-02  0.001237576 -0.08368461
#> GVZCLS_month   -0.0834085916 -2.856799e-02 -0.047705620 -0.12266095
#> OVXCLS_month   -0.0657907568  1.107681e-02  0.017294294 -0.05920651
#> VXFXICLS_month -0.1051804654 -1.719717e-02 -0.087376926 -0.15744156
#> VXEEMCLS_month -0.0829087351 -1.492401e-02  0.038494367 -0.02320949
#> VXSLVCLS_month  0.0325418895  1.020723e-02  0.048603609  0.05950528
#> EVZCLS_month    0.5392049317  7.115211e-02  0.002772821  0.24304619
#> VXXLECLS_month  0.0824108862  2.585456e-02  0.176619398  0.06498108
#> VXGDXCLS_month  0.1042356427  2.218512e-02  0.016276608  0.11878639
#> VXEWZCLS_month  0.0298234196 -1.661517e-05 -0.049185431  0.06065243
#> const           0.8310348716 -2.382650e-02  0.258939806  0.60556631
#>                    VXEWZCLS
#> GVZCLS_day      0.060810440
#> OVXCLS_day     -0.021328545
#> VXFXICLS_day   -0.103241781
#> VXEEMCLS_day   -0.050810494
#> VXSLVCLS_day   -0.041214628
#> EVZCLS_day     -0.044510366
#> VXXLECLS_day    0.286415660
#> VXGDXCLS_day   -0.004629846
#> VXEWZCLS_day    0.952152534
#> GVZCLS_week    -0.232659033
#> OVXCLS_week     0.029438686
#> VXFXICLS_week   0.233415007
#> VXEEMCLS_week  -0.104629279
#> VXSLVCLS_week   0.174714784
#> EVZCLS_week     0.123320940
#> VXXLECLS_week  -0.239829609
#> VXGDXCLS_week  -0.012408245
#> VXEWZCLS_week   0.018610770
#> GVZCLS_month    0.334911077
#> OVXCLS_month    0.012987518
#> VXFXICLS_month -0.111977668
#> VXEEMCLS_month  0.133305259
#> VXSLVCLS_month -0.181258940
#> EVZCLS_month   -0.129656359
#> VXXLECLS_month -0.041980863
#> VXGDXCLS_month -0.027342181
#> VXEWZCLS_month -0.009420411
#> const           1.047643911
head(residuals(fit))
#>             [,1]        [,2]       [,3]        [,4]       [,5]       [,6]
#> [1,]  0.31758364 -0.11022615 -0.5296023  0.04716717 -0.5378020 -0.4659005
#> [2,] -0.58729937 -0.02977095 -0.9556970 -0.70126942 -1.4850409 -0.5500010
#> [3,] -0.37519058  0.15466899  2.8092305  1.54460103 -0.4209523  0.4631326
#> [4,] -0.83743454  0.32276054 -1.2472184 -1.66328320 -2.0118629 -0.4732741
#> [5,] -0.02811876  0.29432487 -0.2286953  0.48869052  0.5149326  0.3606493
#> [6,] -0.14617138  1.20662142  0.3416573  1.34978100 -0.7638851  0.6622565
#>             [,7]       [,8]       [,9]
#> [1,] -0.03896889 -0.8878031  0.8547725
#> [2,] -0.01517932 -1.2314864 -0.6129635
#> [3,]  2.49685115  0.9469600  2.3957692
#> [4,] -2.00237189 -1.4008812 -1.1284324
#> [5,] -0.26141669  0.4395067  1.5021262
#> [6,]  0.71563874  0.7208909  1.7436068
head(fitted(fit))
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
#> [1,] 20.37242 32.43023 29.98960 28.28283 40.30780 12.91590 24.22897 32.12780
#> [2,] 20.61730 32.45977 29.62570 28.64127 39.48504 12.51000 24.56518 32.01149
#> [3,] 20.10519 32.67533 28.92077 28.50540 38.21095 12.07687 25.06315 31.72304
#> [4,] 19.90743 32.97724 31.71722 30.56328 38.13186 12.61327 27.88237 33.30088
#> [5,] 19.26812 33.34568 30.41870 29.20131 36.60507 12.20935 26.08142 32.38049
#> [6,] 19.42617 33.64338 30.16834 29.66022 37.24389 12.58774 25.84436 33.12911
#>          [,9]
#> [1,] 29.00523
#> [2,] 29.72296
#> [3,] 29.20423
#> [4,] 31.84843
#> [5,] 30.60787
#> [6,] 31.67639