View source: R/ARMA.studentt.ff.R

ARMA.studentt.ff | R Documentation |

For an ARMA model, estimates a 3–parameter
Student-`t`

distribution characterizing the errors
plus the ARMA coefficients by MLE usign Fisher
scoring. Central Student–t handled currently.

```
ARMA.studentt.ff(order = c(1, 0),
zero = c("scale", "df"),
cov.Reg = FALSE,
llocation = "identitylink",
lscale = "loglink",
ldf = "logloglink",
ilocation = NULL,
iscale = NULL,
idf = NULL)
```

`order` |
Two–entries vector, non–negative. The order $u$ and $v$ of the ARMA model. |

`zero` |
Same as |

`cov.Reg` |
Logical. If covariates are entered, Should these be
included in the ARMA model as a |

```
llocation, lscale, ldf, ilocation,
iscale, idf
``` |
Same as |

The normality assumption for time series analysis is relaxed to handle
heavy–tailed data, giving place to the ARMA model with shift-scaled
Student-`t`

errors, another subclass of VGLTSMs.

For a univariate time series, say `y_t`

,
the model described by this VGLTSM family function is

```
\theta(B)y_t = \phi(B) \varepsilon_t,
```

where `\varepsilon_t`

are distributed as
a shift-scaled Student–`t`

with `\nu`

degrees of freedom, i.e.,
`\varepsilon_t \sim t(\nu_t, \mu_t, \sigma_t)`

.
This family functions estimates the location (`\mu_t`

),
scale (`\sigma_t`

) and degrees of freedom (`\nu_t`

)
parameters, plus the ARMA coefficients by MLE.

Currently only centered Student–t distributions are handled. Hence, the non–centrality parameter is set to zero.

The linear/additive predictors are
`\boldsymbol{\eta} = (\mu, \log \sigma, \log \log \nu)^T,`

where `\log \sigma`

and `\nu`

are intercept–only
by default.

An object of class `"vglmff"`

(see `vglmff-class`

)
to be used by VGLM/VGAM modelling functions, e.g.,
`vglm`

or `vgam`

.

If `order = 0`

, then `AR.studentt.ff`

fits a usual 3–parameter Student–`t`

, as with
`studentt3`

.

If covariates are incorporated in the analysis,
these are embedded in the location–parameter model.
Modify this through `zero`

.
See `CommonVGAMffArguments`

for details on `zero`

.

Victor Miranda

`ARIMAXff`

,
`studentt`

,
`vglm`

.

```
### Estimate the parameters of the errors distribution for an
## AR(1) model. Sample size = 50
set.seed(20180218)
nn <- 250
y <- numeric(nn)
ncp <- 0 # Non--centrality parameter
nu <- 3.5 # Degrees of freedom.
theta <- 0.45 # AR coefficient
res <- numeric(250) # Vector of residuals.
y[1] <- rt(1, df = nu, ncp = ncp)
for (ii in 2:nn) {
res[ii] <- rt(1, df = nu, ncp = ncp)
y[ii] <- theta * y[ii - 1] + res[ii]
}
# Remove warm up values.
y <- y[-c(1:200)]
res <- res[-c(1:200)]
### Fitting an ARMA(1, 0) with Student-t errors.
AR.stut.er.fit <- vglm(y ~ 1, ARMA.studentt.ff(order = c(1, 0)),
data = data.frame(y = y), trace = TRUE)
summary(AR.stut.er.fit)
Coef(AR.stut.er.fit)
plot(ts(y), col = "red", lty = 1, ylim = c(-6, 6), main = "Plot of series Y with Student-t errors")
lines(ts(fitted.values(AR.stut.er.fit)), col = "blue", lty = 2)
abline( h = 0, lty = 2)
```

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