Fit a GARCH(1,1) model to a return series

$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2.$$

Usage

morie_garch_fit(x)

Arguments

x

Numeric return series.

Value

Named list with \(omega, alpha, beta, persistence, loglik, conditional_variance, n, method\).

Details

Native Gaussian quasi-maximum-likelihood fit; no GARCH package is loaded or called. Stationarity requires \(\alpha + \beta < 1\), which the likelihood enforces by returning a large penalty outside the admissible region.

References

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.

Examples

set.seed(1)
morie_garch_fit(x = rnorm(50))
#> $omega
#> [1] 1e-08
#> 
#> $alpha
#> [1] 1e-08
#> 
#> $beta
#> [1] 0.9942084
#> 
#> $persistence
#> [1] 0.9942084
#> 
#> $loglik
#> [1] -60.92808
#> 
#> $conditional_variance
#>  [1] 0.6912159 0.6872126 0.6832326 0.6792756 0.6753415 0.6714302 0.6675416
#>  [8] 0.6636754 0.6598317 0.6560102 0.6522109 0.6484336 0.6446781 0.6409444
#> [15] 0.6372324 0.6335418 0.6298726 0.6262246 0.6225978 0.6189920 0.6154070
#> [22] 0.6118428 0.6082993 0.6047763 0.6012737 0.5977914 0.5943292 0.5908871
#> [29] 0.5874649 0.5840626 0.5806799 0.5773169 0.5739733 0.5706491 0.5673441
#> [36] 0.5640583 0.5607915 0.5575437 0.5543146 0.5511042 0.5479125 0.5447392
#> [43] 0.5415843 0.5384477 0.5353292 0.5322288 0.5291464 0.5260818 0.5230349
#> [50] 0.5200057
#> 
#> $n
#> [1] 50
#> 
#> $method
#> [1] "GARCH(1,1) Gaussian QMLE"
#>