tupolyn: Time-uncertain polynomial regression
In tuts: Time Uncertain Time Series Analysis

tupolyn performs estimation of parameters of N-th order polynomial regression of time-uncertain time series.

1	tupolyn(y, ti.mu, ti.sd, n.sim, polyorder, CV = FALSE, ...)

`y`	A vector of observations.
`ti.mu`	A vector of estimates of timing of observations.
`ti.sd`	A vector of standard deviations of timing.
`n.sim`	A number of simulations.
`polyorder`	Order of the polynomial regression.
`CV`	TRUE/FALSE cross-validation indicator.
`...`	optional arguments: - n.chains: number of MCMC chains, the default number of chains is set to 2. - Thin: thinning factor, the default values is set to 4. - n.cores: number of cores used in cross-validation. No value or 'MAX' applies all the available cores in computation.

# Note: Most of models included in tuts package are computationally intensive. In the example
# below I set parameters to meet CRAN's testing requirement of maximum 5 sec per example.
# A more practical example would contain N=50 in the first line of the code and n.sim=10000.

#1. Import or simulate the data (a simulation is chosen for illustrative purposes):
DATA=simtuts(N=10,Harmonics=c(4,0,0), sin.ampl=c(10,0, 0), cos.ampl=c(0,0,0),
            trend=0,y.sd=2, ti.sd=0.2)
y=DATA$observed$y.obs
ti.mu=DATA$observed$ti.obs.tnorm
ti.sd= rep(0.2, length(ti.mu))

#2. Fit the model:
polyorder=2
n.sim=1000
PN=tupolyn(y=y,ti.mu=ti.mu,ti.sd=ti.sd,polyorder=polyorder,n.sim=n.sim,CV=TRUE,n.cores=2)

#3. Generate summary results (optional parameters are listed in brackets):
summary(PN)                               # Summary results (burn, CI).

#4. Generate plots and diagnostics of the model (optional parameters are listed in brackets):
plot(PN,type='predTUTS',CI=0.95)          # One step out of salmple predictions (CI, burn).
plot(PN,type='cv',burn=0.3)               # 5 fold cross-validation (CI, burn).
plot(PN,type='GR',CI=0.95)                # Gelman-Rubin diagnostic (CI).
plot(PN,type='mcmc')                      # MCMC diagnostics.
plot(PN,type='volatility')                # Volatility realizaitons.