DEM/USD Exchange Rate Returns
MarkDollar.RdA time series of intra-day percentage returns of Deutsche mark/US dollar (DEM/USD) exchange rates, consisting of two observations per day from 1992-10-01 through 1993-09-29.
Usage
data("MarkDollar")Source
Journal of Business & Economic Statistics Data Archive.
http://www.amstat.org/publications/jbes/upload/index.cfm?fuseaction=ViewArticles&pub=JBES&issue=96-2-APR
References
Bollerslev, T., and Ghysels, E. (1996). Periodic Autoregressive Conditional Heteroskedasticity. Journal of Business & Economic Statistics, 14, 139–151.
Examples
library("tseries")
data("MarkDollar")
## GARCH(1,1)
fm <- garch(MarkDollar, grad = "numerical")
#>
#> ***** ESTIMATION WITH NUMERICAL GRADIENT *****
#>
#>
#> I INITIAL X(I) D(I)
#>
#> 1 2.303489e-01 1.000e+00
#> 2 5.000000e-02 1.000e+00
#> 3 5.000000e-02 1.000e+00
#>
#> IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
#> 0 1 -9.291e+01
#> 1 4 -9.309e+01 1.90e-03 2.48e-03 1.8e-02 2.3e+03 1.0e-02 2.87e+00
#> 2 5 -9.322e+01 1.38e-03 1.99e-03 2.0e-02 6.2e+00 1.0e-02 6.66e+00
#> 3 6 -9.328e+01 6.91e-04 1.36e-03 1.7e-02 2.4e+00 1.0e-02 1.28e+00
#> 4 7 -9.337e+01 9.48e-04 1.43e-03 1.8e-02 2.0e+00 1.0e-02 5.04e-01
#> 5 8 -9.342e+01 4.63e-04 9.69e-04 1.5e-02 2.0e+00 1.0e-02 1.30e-01
#> 6 10 -9.342e+01 9.17e-05 2.26e-04 6.3e-03 2.0e+00 3.7e-03 1.05e-02
#> 7 11 -9.343e+01 5.39e-05 6.37e-05 7.5e-03 1.9e+00 3.7e-03 6.11e-04
#> 8 13 -9.343e+01 3.39e-05 4.55e-05 3.0e-02 1.7e+00 1.5e-02 4.33e-04
#> 9 17 -9.363e+01 2.07e-03 6.22e-04 5.6e-01 5.7e-01 2.4e-01 2.45e-03
#> 10 19 -9.790e+01 4.36e-02 8.76e-03 4.3e-01 1.9e+00 4.8e-01 1.44e+00
#> 11 21 -9.958e+01 1.69e-02 2.05e-02 5.7e-02 2.0e+00 9.5e-02 1.72e+04
#> 12 25 -9.993e+01 3.49e-03 6.12e-03 1.0e-03 3.6e+00 1.8e-03 1.31e+03
#> 13 26 -9.997e+01 4.35e-04 4.02e-04 9.0e-04 2.0e+00 1.8e-03 8.01e+02
#> 14 29 -1.003e+02 3.30e-03 5.23e-03 1.7e-02 2.0e+00 3.1e-02 1.00e+03
#> 15 31 -1.006e+02 2.65e-03 2.77e-03 2.4e-03 4.6e+00 4.2e-03 7.06e-01
#> 16 32 -1.006e+02 1.99e-04 3.15e-03 1.9e-03 2.0e+00 4.2e-03 7.19e+01
#> 17 33 -1.008e+02 2.23e-03 2.62e-03 1.0e-03 2.0e+00 2.1e-03 1.35e+01
#> 18 34 -1.009e+02 4.32e-04 5.82e-04 1.0e-03 2.0e+00 2.1e-03 3.35e+00
#> 19 36 -1.009e+02 5.21e-05 3.91e-04 8.4e-04 2.0e+00 1.6e-03 4.70e-01
#> 20 37 -1.009e+02 2.96e-04 4.77e-04 7.5e-04 2.0e+00 1.6e-03 6.26e-02
#> 21 39 -1.009e+02 5.25e-04 6.57e-04 2.1e-03 2.0e+00 4.4e-03 4.89e-02
#> 22 41 -1.010e+02 7.85e-05 1.78e-04 1.9e-04 4.0e+01 4.4e-04 1.33e-01
#> 23 42 -1.010e+02 1.71e-04 1.73e-04 2.2e-04 2.0e+00 4.4e-04 8.03e-02
#> 24 43 -1.010e+02 2.28e-04 2.29e-04 3.8e-04 2.0e+00 8.9e-04 7.99e-02
#> 25 47 -1.017e+02 7.05e-03 7.25e-03 1.4e-02 1.1e+00 2.6e-02 7.85e-02
#> 26 49 -1.021e+02 4.00e-03 4.53e-03 1.0e-02 1.5e+00 2.0e-02 2.05e-02
#> 27 51 -1.022e+02 3.81e-04 8.76e-04 1.9e-03 1.6e+00 4.0e-03 3.66e-03
#> 28 52 -1.022e+02 6.70e-04 7.31e-04 1.9e-03 1.4e+00 4.0e-03 1.67e-03
#> 29 53 -1.022e+02 2.12e-04 3.93e-04 4.0e-03 3.4e-01 8.0e-03 4.22e-04
#> 30 55 -1.023e+02 5.39e-05 8.97e-05 3.7e-04 8.5e-01 9.0e-04 1.57e-04
#> 31 56 -1.023e+02 1.32e-05 2.52e-05 8.5e-04 1.7e-01 1.8e-03 2.55e-05
#> 32 57 -1.023e+02 2.92e-06 2.95e-06 1.6e-04 0.0e+00 3.5e-04 2.95e-06
#> 33 58 -1.023e+02 3.75e-08 5.20e-08 3.6e-05 0.0e+00 7.5e-05 5.20e-08
#> 34 59 -1.023e+02 3.24e-09 3.24e-09 8.3e-06 0.0e+00 1.8e-05 3.24e-09
#> 35 60 -1.023e+02 5.00e-14 4.85e-14 3.3e-08 0.0e+00 6.3e-08 4.85e-14
#>
#> ***** RELATIVE FUNCTION CONVERGENCE *****
#>
#> FUNCTION -1.022536e+02 RELDX 3.282e-08
#> FUNC. EVALS 60 GRAD. EVALS 118
#> PRELDF 4.849e-14 NPRELDF 4.849e-14
#>
#> I FINAL X(I) D(I) G(I)
#>
#> 1 7.196360e-03 1.000e+00 -8.915e-06
#> 2 2.890741e-02 1.000e+00 -1.574e-05
#> 3 9.411625e-01 1.000e+00 -7.970e-06
#>
summary(fm)
#>
#> Call:
#> garch(x = MarkDollar, grad = "numerical")
#>
#> Model:
#> GARCH(1,1)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.59574 -0.60031 0.01855 0.67733 3.88521
#>
#> Coefficient(s):
#> Estimate Std. Error t value Pr(>|t|)
#> a0 0.007196 0.005511 1.306 0.1916
#> a1 0.028907 0.013832 2.090 0.0366 *
#> b1 0.941162 0.032770 28.721 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Diagnostic Tests:
#> Jarque Bera Test
#>
#> data: Residuals
#> X-squared = 20.32, df = 2, p-value = 3.868e-05
#>
#>
#> Box-Ljung test
#>
#> data: Squared.Residuals
#> X-squared = 0.76798, df = 1, p-value = 0.3808
#>
logLik(fm)
#> 'log Lik.' -372.8376 (df=3)