mix_moment {mixAR}

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

Boshnakov GN (2009). “Analytic expressions for predictive distributions in mixture autoregressive models.” Stat. Probab. Lett. , 79(15), 1704-1709. doi:10.1016/j.spl.2009.04.009.

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))