mix_moment: Conditional moments of MixAR models

In GeoBosh/mixAR: Mixture Autoregressive Models

Conditional moments of MixAR models

Description

Conditional moments of MixAR models.

Usage

mix_location(model, x, index, xcond)
mix_variance(model, x, index, xcond)
mix_central_moment(model, x, index, xcond, k)
mix_moment(model, x, index, xcond, k)
mix_kurtosis(...)
mix_ekurtosis(...)

Arguments

model	a MixAR object.
x	a time series.
index	a vector of indices in x for which to compute the requested property. If missing, the computation is done for all indices greater than max(model@order).
xcond	a time series, the point prediction is computed for the first value after the end of the time series. Only the last max(model@order) values in xcond are used.
k	a positive integer specifying the moment to compute.
...	passed on to mix_central_moment.

Details

These functions compute conditional moments and related quantities.

kurtosis and ekurtosis compute conditional kurtosis and excess kurtosis, respectively. Effectively, they have the same parameters as mix_central_moment, since they pass "..." to it along with k = 4. It is an error to supply argument k to the kurtosis functions.

Value

when called with one argument (model), a function with argument xcond; otherwise if xcond is not missing, a single numeric value; otherwise a vector of length length(index).

Note

I wrote the above description recently from reading six years old code, it may need further verification.

Author(s)

Georgi N. Boshnakov

References

\insertRef

boshnakov2009marmixAR

See Also

mix_pdf, mix_cdf, mix_qf for the predictive distributions (pdf, cdf, quantiles);

Examples

## data(ibmclose, package = "fma") # `ibmclose'
ibmclose <- as.numeric(fma::ibmclose)
length(ibmclose) # 369
max(exampleModels$WL_ibm@order) # 2

## compute point predictions for t = 3,...,369
pred <- mix_location(exampleModels$WL_ibm, ibmclose)
plot(pred)
## compute one-step point predictions for t = 360,...369
mix_location(exampleModels$WL_ibm, ibmclose, index = 369 - 9:0 )

f <- mix_location(exampleModels$WL_ibm) # a function
## predict the value after the last
f(ibmclose)

## a different way to compute one-step point predictions for t = 360,...369
sapply(369 - 10:1, function(k) f(ibmclose[1:k]))

## the results are the same, but notice that xcond gives past values
## while index above specifies the times for which to compute the predictions.
identical(sapply(369 - 10:1, function(k) f(ibmclose[1:k])),
          mix_location(exampleModels$WL_ibm, ibmclose, index = 369 - 9:0 ))


## conditional variance
f <- mix_variance(exampleModels$WL_ibm) # a function
## predict the value after the last
f(ibmclose)

## a different way to compute one-step point predictions for t = 360,...369
sapply(369 - 10:1, function(k) f(ibmclose[1:k]))

## the results are the same, but notice that xcond gives past values
## while index above specifies the times for which to compute the predictions.
identical(sapply(369 - 10:1, function(k) f(ibmclose[1:k])),
          mix_variance(exampleModels$WL_ibm, ibmclose, index = 369 - 9:0 ))


# interesting example
# bimodal distribution, low kurtosis, 4th moment not much larger than 2nd
moWL <- exampleModels$WL_ibm

mix_location(moWL,xcond = c(500,450))
mix_kurtosis(moWL,xcond = c(500,450))

f1pdf <- mix_pdf(moWL,xcond = c(500,450))
f1cdf <- mix_cdf(moWL,xcond = c(500,450))
gbutils::plotpdf(f1pdf,cdf=f1cdf)
gbutils::plotpdf(f1cdf,cdf=f1cdf)
f1cdf(c(400,480))

mix_variance(moWL,xcond = c(500,450))
mix_central_moment(moWL,xcond = c(500,450), k=2)

sqrt(mix_variance(moWL,xcond = c(500,450)))
sqrt(mix_central_moment(moWL,xcond = c(500,450), k=2))

GeoBosh/mixAR documentation built on May 9, 2022, 7:36 a.m.