| Version: | 1.2 |
| Title: | Random Coefficient Minification Time Series Models |
| Author: | L. Han [aut, cre] |
| Maintainer: | L. Han <lengyi.han@ubc.ca> |
| Description: | Data sets, and functions for simulating and fitting nonlinear time series with minification and nonparametric models. |
| Depends: | KernSmooth, locpol |
| LazyLoad: | true |
| LazyData: | true |
| ZipData: | no |
| License: | Unlimited |
| NeedsCompilation: | no |
| Packaged: | 2023-01-17 02:13:54 UTC; johbraun |
| Repository: | CRAN |
| Date/Publication: | 2023-01-17 10:10:02 UTC |
Fit a nonlinear AR1 model using local polynomial regression
Description
This function uses local polynomial regression to nonparametrically estimate the autoregression function in a nonlinear AR1 model.
Usage
ARlocpoly(z, deg = 1, h, ...)
Arguments
z |
numeric vector of time series observations. |
deg |
numeric, degree of local polynomial fit. |
h |
numeric, bandwidth for local polynomial estimate. |
... |
any other arguments taken by |
Value
A list containing
x |
numeric vector of evaluation points. |
y |
numeric vector of nonparametric estimates at the values in |
h |
numeric, bandwidth |
Author(s)
L. Han and S. Snyman
References
Fan, J. and Yao, Q. (2008) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer.
Examples
x <- nonlinearAR1.sim(100, g = function(x) x*sin(x), sd = 1.5) # simulated data
ARlocpoly(x, deg = 0, h = 0.5)
BC Fire Area
Description
The BCfireArea time series object consists of 13 observations on annual area burnt in the province of BC.
Usage
data(BCfireArea)Format
A time series object
Examples
ts.plot(BCfireArea)
Beer Volume Time Series
Description
Weekly volumes (in litres) of produced at a large brewery for 137 weeks.
Usage
data(FWI)Format
A time series object
Examples
acf(BeerVolume)
Fit a nonlinear AR1 model using local polynomial regression via the method of Cheng et al.
Description
This function uses local polynomial regression to nonparametrically estimate the autoregression function in a nonlinear AR1 model using Cheng's bias reduction method.
Usage
ChengTS(z, degree = 1, hopt, ...)
Arguments
z |
numeric vector of time series observations. |
degree |
numeric, degree of local polynomial fit. |
hopt |
numeric, base bandwidth for local polynomial estimate. |
... |
any other arguments taken by |
Value
A list containing
x |
numeric vector of evaluation points. |
y |
numeric vector of nonparametric estimates at the values in |
Author(s)
L. Han and S. Snyman
References
Cheng, M., Huang, R., Liu, P. and Liu, H. (2018) Bias reduction for nonparametric and semiparametric regression models. Statistica Sinica 28(4):2749-2770.
Examples
x <- nonlinearAR1.sim(100, g = function(x) x*sin(x), sd = 1.5) # simulated data
ChengTS(x, degree = 1, hopt = 0.5)
x <- nonlinearAR1.sim(100, g = function(x) x*sin(x), sd = 0.5) # simulated data
degree <- 1; xrange <- c(-.5, .5); n <- length(x)
h <- thumbBw(x[-n], x[-1], deg = degree, kernel=gaussK)
x.lp <- ARlocpoly(x, deg = degree, h = h, range.x = xrange)
x.shp <- sharpARlocpoly(x, deg = degree, range.x = xrange, h = x.lp$h*n^(4/45))
x.cheng <- ChengTS(x, degree = degree, hopt = h, range.x = xrange)
lag.plot(x, do.lines=FALSE)
lines(x.lp)
lines(x.shp, col=2)
lines(x.cheng, col=4)
Fire Weather Index Series
Description
The FWI list consists of 4 vectors containing daily
Fire Weather Index observations.
Usage
data(FWI)Format
This list contains the following vectors:
- PG2008
FWI observations from Prince George, BC for 2008
- PG2009
FWI observations from Prince George, BC for 2009
- ED2013
FWI observations from Edmonton, AB for 2013
- ED2014
FWI observations from Edmonton, AB for 2014
Examples
RCMTmle(FWI$PG2009[c(100:300)])
Global Average Temperature Changes
Description
Global average temperatures are recorded in terms of number of Celsius degrees above a baseline temperature from 1880 to 2016. The baseline temperature is the average temperature for the year 1990.
Usage
data(Globaltemps)Format
A numeric vector
Examples
temps <- ts(Globaltemps, start = 1880, end = 2016)
ts.plot(temps, ylab = "Change in Temperature")
Tailed Exponential and Weibull Random Coefficient Minification Maximum Likelihood Estimation
Description
This function estimates parameters for tailed exponential and Weibull random coefficient minification process models from a nonnegative time series.
Usage
RCMTmle(y)
Arguments
y |
numeric vector of nonnegative observations. |
Value
A list containing
n |
the number of time series observations. |
p |
estimated power for transformation from exponential to Weibull. |
p.eps |
estimated tailed exponential probability parameter when preceding observation is nonzero. |
p.delta |
estimated tailed exponential probability parameter when preceding observation is 0 |
mu |
estimated mu parameter for lognormal distribution used to simulated random coefficients. |
sigma |
estimated sigma parameter for lognormal distribution used to simulate random coefficients. |
lambda |
estimated tailed exponential rate parameter when preceding observation is nonzero. |
gamma |
estimated tailed exponential rate parameter when preceding observation is 0. |
like |
maximum value of likelihood. |
y |
original observations |
Author(s)
L. Han
References
Han, L., Braun, W.J. and Loeppky (2018) Random Coefficient Minification Processes. Statistical Papers, pp 1-22.
Longitudinal Acceleration Measurements on an Air Tanker
Description
Longitudinal acceleration measurements of an air tanker fighting a forest wildfire taken at 1 second intervals.
Usage
data(longitudinalAcceleration)Format
A time series object
Examples
acf(longitudinalAcceleration)
Electroless nickel concentrations
Description
Electroless nickel concentrations in a chrome plating process were measured at the beginning of each eight hour work shift for a period of 25 days. A concentration of 4.5 ounces per gallon is considered optimal in this application.
Usage
data(nickel)Format
A time series object
Source
Farnum, N. (1994) Statistical Quality Control and Improvement. Belmont, Duxbury Press.
Examples
ts.plot(nickel)
Nonlinear AR1 Simulator
Description
This function simulates sequences of variates follow a nonlinear autoregressive order 1 process of the form z_n = g(z_n-1) + epsilon. A normal distribution is assumed for the innovations.
Usage
nonlinearAR1.sim(n, g, ...)
Arguments
n |
number of observations. |
g |
autoregression function. |
... |
any parameters that are taken by |
Author(s)
L. Han and S. Snyman
Examples
x <- nonlinearAR1.sim(50, g = function(x) x*sin(x), sd = 2.5)
ts.plot(x)
Tailed Exponential Random Number Generator
Description
This function simulates sequences of tailed exponential variates which have survivor function P(X > x) = (1-p)exp(-lambda x), for x > 0 and P(X = 0) = p.
Usage
rET(n, prob, rate)
Arguments
n |
number of observations. |
prob |
vector of probabilities. |
rate |
vector of exponential rate parameters. |
Author(s)
L. Han
References
Littlejohn, R.P. (1994) A Reversibility Relationship for Two Markovian Time Series Models with Stationary Exponential Tailed Distribution. Journal of Applied Probability. 31 pp 575-581.
Tailed Exponential and Weibull Random Coefficient Minification Process Simulator
Description
This function simulates sequences of tailed exponential and Weibull random coefficient minification process variates. Random coefficients are lognormal distributed with parameters mu and sigma.
Usage
rRCMT(n, p, p.delta, p.eps, lambda, gamma, mu, sigma, RCMTobj)
Arguments
n |
number of observations. |
p |
power for transformation from exponential to Weibull. |
p.delta |
tailed exponential probability parameter when preceding observation is 0 |
p.eps |
tailed exponential probability parameter when preceding observation is nonzero. |
lambda |
tailed exponential rate parameter when preceding observation is nonzero. |
gamma |
tailed exponential rate parameter when preceding observation is 0. |
mu |
mu parameter for lognormal distribution used to simulated random coefficients. |
sigma |
sigma parameter for lognormal distribution used to simulate random coefficients. |
RCMTobj |
list containing elements n, p, p.delta, p.eps, lambda and gamma |
Author(s)
L. Han
References
Han, L., Braun, W.J. and Loeppky (2018) Random Coefficient Minification Processes. Statistical Papers, pp 1-22.
Tatum's Robust Estimate of the Standard Deviation
Description
Standard deviation estimate which is insensitive to outliers and random trends.
Usage
robustSD(x)
Arguments
x |
A numeric vector. |
Author(s)
L. Han
References
Tatum, L.G. (1997) Robust Estimation of the Process Standard Deviation for Control Charts. Journal of the American Statistical Association 39, pp 127-141.
Examples
robustSD(EuStockMarkets[,1])
Fit a nonlinear AR1 model using local polynomial regression and data sharpening
Description
This function uses local polynomial regression to nonparametrically estimate the autoregression function in a nonlinear AR1 model, after employing data sharpening on the responses.
Usage
sharpARlocpoly(z, deg = 1, h, ...)
Arguments
z |
numeric vector of time series observations. |
deg |
numeric, degree of local polynomial fit. |
h |
numeric, bandwidth for local polynomial estimate. |
... |
any other arguments taken by |
Value
A list containing
x |
numeric vector of evaluation points. |
y |
numeric vector of nonparametric estimates at the values in |
Author(s)
L. Han and S. Snyman
References
Choi, E., Hall, P. and Rousson, V. (2000) Data Sharpening Methods for Bias Reduction in Nonparametric Regression. Annals of Statistics 28(5):1339-1355.
Examples
x <- nonlinearAR1.sim(100, g = function(x) x*sin(x), sd = 1.5) # simulated data
sharpARlocpoly(x, deg = 0, h = 0.5)