Time Series Analysis

Description

Contains R functions and datasets detailed in the book "Time Series Analysis with Applications in R (second edition)" by J.D. Cryer and K.S. Chan

Details

Author(s)

Kung-Sik Chan, Brian Ripley

Theoretical spectral density function of a stationary ARMA model

Description

Computes and plots the theoretical spectral density function of a stationary ARMA model

Usage

ARMAspec(model, freq = seq(0, 0.5, 0.001), plot = TRUE, ...)

Arguments

Value

a list:

Author(s)

Kung-Sik Chan

See Also

spec

Examples

theta=.9 # Reset theta for other MA(1) plots
ARMAspec(model=list(ma=-theta)) 

Determine the power transformation for serially correlated data

Description

Determine the appropriate power transformation for time-series data. The objective is to estimate the power transformation so that the transformed time series is approximately a Gaussian AR process.

Usage

BoxCox.ar(y, order, lambda = seq(-2, 2, 0.01), plotit = TRUE, 
method = c("mle", "yule-walker", "burg", "ols", "yw"), ...)

Arguments

Value

A list that contains the following:

Note

The procedure is very computer intensive. Be patient for the outcome

Author(s)

Kung-Sik Chan

Examples

data(hare)
# hare.transf=BoxCox.ar(y=hare)
# hare.transf$ci

Daily CREF Values

Description

Daily values of one unit of the CREF (College Retirement Equity Fund) Stock fund, 08/26/04 - 08/15/06.

Usage

data(CREF)

Format

The format is: Time-Series [1:501] from 1 to 501: 170 170 169 170 171 ...

Source

www.tiaa-cref.org/performance/retirement/data/index.html

Examples

data(CREF)
## maybe str(CREF) ; plot(CREF) ...

Quarterly earnings per share for the Johnson & Johnson Company

Description

Quarterly earnings per share for 1960Q1 to 1980Q4 of the U.S. company, Johnson & Johnson, Inc.

Usage

data(JJ)

Format

The format is: Time-Series [1:84] from 1960 to 1981: 0.71 0.63 0.85 0.44 0.61 0.69 0.92 0.55 0.72 0.77 ...

Source

http://www.stat.pitt.edu/stoffer/tsa2/

Examples

data(JJ)
## maybe str(JJ) ; plot(JJ) ...

Keenan's one-degree test for nonlinearity

Description

Carry out Keenan's 1-degree test for nonlinearity against the null hypothesis that the time series follows some AR process.

Usage

Keenan.test(x, order, ...)

Arguments

Details

The test is designed to have optimal local power against depature from the linear autoregressive function in the direction of the square of the linear autoregressive function.

Value

A list containing the following components

Author(s)

Kung-Sik Chan

References

Keenan, D. M. (1985), A Tukey nonadditivity-type test for time series Nonlinearity, Biometrika, 72, 39-44.

See Also

Tsay.test,tlrt

Examples

data(spots)
Keenan.test(sqrt(spots))

Portmanteau Tests for Fitted ARIMA models

Description

This function modifies the Box.test function in the stats package, and it computes the Ljung-Box or Box-Pierce tests checking whether or not the residuals appear to be white noise.

Usage

LB.test(model, lag = 12, type = c("Ljung-Box", "Box-Pierce"), no.error = FALSE,
 omit.initial = TRUE)

Arguments

Value

a list:

Author(s)

Kung-Sik Chan, based on A. Trapletti's work on the Box.test function in the stats package

References

Box, G. E. P. and Pierce, D. A. (1970), Distribution of residual correlations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65, 15091526.

Ljung, G. M. and Box, G. E. P. (1978), On a measure of lack of fit in time series models. Biometrika 65, 553564.

Examples

data(color)
m1.color=arima(color,order=c(1,0,0))
LB.test(m1.color)

McLeod-Li test

Description

Perform the McLeod-Li test for conditional heteroscedascity (ARCH).

Usage

McLeod.Li.test(object, y, gof.lag, col = "red", omit.initial = TRUE, 
plot = TRUE, ...)

Arguments

Details

The test checks for the presence of conditional heteroscedascity by computing the Ljung-Box (portmanteau) test with the squared data (if y is supplied and object suppressed) or with the squared residuals from an arima model (if an arima model is passed to the function via the object argument.)

Value

Author(s)

Kung-Sik Chan

References

McLeod, A. I. and W. K. Li (1983). Diagnostic checking ARMA time series models using squared residual autocorrelations. Journal of Time Series Analysis, 4, 269273.

Examples

data(CREF)
r.cref=diff(log(CREF))*100
McLeod.Li.test(y=r.cref)

Quarterly Standard & Poor's Composite Index of stock price values / time series

Description

Quarterly S&P Composite Index, 1936Q1 - 1977Q4.

Usage

data(SP)

Format

The format is: Time-Series [1:168] from 1936 to 1978: 149 148 160 172 179 ...

Source

Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.

Examples

data(SP)
## maybe str(SP) ; plot(SP) ...

Tsay's Test for nonlinearity

Description

Carry out Tsay's test for quadratic nonlinearity in a time series.

Usage

Tsay.test(x, order, ...)

Arguments

Details

The null hypothesis is that the true model is an AR process. The AR order, if missing, is estimated by minimizing AIC via the ar function, i.e. fitting autoregressive model to the data. The default fitting method of the ar function is "yule-walker."

Value

A list containing the following components

Author(s)

Kung-Sik Chan

References

Tsay, R. S. (1986), Nonlinearity test for time series, Biometrika, 73, 461-466.

See Also

Tsay.test,tlrt

Examples

data(spots)
Tsay.test(sqrt(spots))

Auto- and Cross- Covariance and -Correlation Function Estimation

Description

This function calls the acf function in the stats package and processes to drop lag-0 of the acf. It only works for univariate time series, so x below should be 1-dimensional.

Usage

acf(x, lag.max = NULL, type = c("correlation", "covariance", "partial")[1], 
plot = TRUE, na.action = na.fail, demean = TRUE, drop.lag.0 = TRUE, ...)

Arguments

Value

An object of class "acf", which is a list with the following elements:

Author(s)

Original authors of stats:::acf are: Paul Gilbert, Martyn Plummer, B.D. Ripley. This wrapper is written by Kung-Sik Chan

References

~put references to the literature/web site here ~

See Also

plot.acf, ARMAacf for the exact autocorrelations of a given ARMA process.

Examples

data(rwalk)
model1=lm(rwalk~time(rwalk))
summary(model1)
acf(rstudent(model1),main='')

Monthly Airline Passenger-Miles in the US

Description

Monthly U.S. airline passenger-miles: 01/1996 - 05/2005.

Usage

data(airmiles)

Format

The format is: 'ts' int [1:113, 1] 30983174 32147663 38342975 35969113 36474391 38772238 40395657 41738499 33580773 36389842 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "airmiles" - attr(*, "tsp")= num [1:3] 1996 2005 12

Source

www.bts.gov/xml/air_traffic/src/index.xml#MonthlySystem

Examples

data(airmiles)
## maybe str(airmiles) ; plot(airmiles) ...

Monthly total international airline passengers

Description

Monthly total international airline passengers from 01/1960- 12/1971.

Usage

data(airpass)

Format

The format is: Time-Series [1:144] from 1960 to 1972: 112 118 132 129 121 135 148 148 136 119 ...

Source

Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994) Time Series Analysis, Forecasting and Control. Second Edition. New York: Prentice-Hall.

Examples

data(airpass)
## maybe str(airpass) ; plot(airpass) ...

A simulated AR(1) series

Description

A simulated AR(1) series with the AR coefficient equal to 0.4.

Usage

data(ar1.2.s)

Format

The format is: Time-Series [1:60] from 1 to 60: -0.0678 1.4994 0.4888 0.3987 -0.5162 ...

Details

The model is Y(t)=0.4*Y(t-1)+e(t) where the e's are iid standard normal.

Examples

data(ar1.2.s)
## maybe str(ar1.2.s) ; plot(ar1.2.s) ...

A simulated AR(1) series

Description

A simulated AR(1) series with the AR coefficient equal to 0.9.

Usage

data(ar1.s)

Format

The format is: Time-Series [1:60] from 1 to 60: -1.889 -1.691 -1.962 -0.566 -0.627 ...

Details

The model is Y(t)=0.9*Y(t-1)+e(t) where the e's are iid standard normal.

Examples

data(ar1.s)
## maybe str(ar1.s) ; plot(ar1.s) ...

Asimulated AR(2) series / time series

Description

Asimulated AR(2) series with AR coefficients being equal to 1.5 and -0.75

Usage

data(ar2.s)

Format

The format is: Time-Series [1:120] from 1 to 120: -2.064 -1.937 0.406 2.039 2.953 ...

Details

The model is Y(t)=1.5*Y(t-1)-0.75*Y(t-2)+e(t) where the e's are iid standard normal random variables.

Examples

data(ar2.s)
## maybe str(ar2.s) ; plot(ar2.s) ...

Fitting an ARIMA model with Exogeneous Variables

Description

This function is identical to the arimax function which builds on and extends the capability of the arima function in R stats by allowing the incorporation of transfer functions, and innovative and additive outliers. For backward compatitibility, the function is also named arima. Note in the computation of AIC, the number of parameters excludes the noise variance. This function is heavily based on the arima function of the stats core of R, see the help page of this function for details on arguments x to kappa.

Usage

arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA),
 xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, 
init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(),
 kappa = 1e+06, io = NULL, xtransf, transfer = NULL)

Arguments

Value

An Arimax object contining the model fit.

Author(s)

Original author of the arima function in R stats: Brian Ripley. The arimax function is based on the stats:::arima function, with modifications by Kung-Sik Chan.

See Also

arima

Examples

data(hare)
arima(sqrt(hare),order=c(3,0,0))

Compute the Bootstrap Estimates of an ARIMA Model

Description

This function bootstraps time series according to the fitted ARMA(p,d,q) model supplied by the fitted object arima.fit, and estimate the same model using the arima function. Any bootstrap sample that has problem when fitted with the ARIMA model will be omitted from the final results and all error messages will be suppressed. You can check if there is any fitting problem by running the command geterrmessage().

Usage

arima.boot(arima.fit, cond.boot = FALSE, is.normal = TRUE, B = 1000, init, ntrans = 100)

Arguments

Value

a matrix each row of which consists of the coefficient estimates of a bootstrap time-series.

Author(s)

Kung-Sik Chan

Examples

data(hare)
arima.hare=arima(sqrt(hare),order=c(3,0,0))
boot.hare=arima.boot(arima.hare,B=50,init=sqrt(hare)[1:3],ntrans=100)
apply(boot.hare,2,quantile, c(.025,.975))
period.boot=apply(boot.hare,1,function(x){
roots=polyroot(c(1,-x[1:3]))
min1=1.e+9
rootc=NA
for (root in roots) {
if( abs(Im(root))<1e-10) next
if (Mod(root)< min1) {min1=Mod(root); rootc=root}
}
if(is.na(rootc)) period=NA else period=2*pi/abs(Arg(rootc))
period
})
hist(period.boot)
quantile(period.boot,c(0.025,.975))

Fitting an ARIMA model with Exogeneous Variables

Description

This function builds on and extends the capability of the arima function in R stats by allowing the incorporation of transfer functions, innovative and additive outliers. For backward compatitibility, the function is also named arima. Note in the computation of AIC, the number of parameters excludes the noise variance. See the help page of arima in stats for details on arguments x to kappa.

Usage

arimax(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA),
 xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, 
init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(),
 kappa = 1e+06, io = NULL, xtransf, transfer = NULL)

Arguments

Value

An Arimax object containing the model fit.

Author(s)

Original author of the arima function in R stats: Brian Ripley. The arimax function is based on the stats:::arima function, with modifications by Kung-Sik Chan.

See Also

arima

Examples

data(airmiles)
plot(log(airmiles),ylab='Log(airmiles)',xlab='Year', main='')
acf(diff(diff(window(log(airmiles),end=c(2001,8)),12)),lag.max=48,main='')
air.m1=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,1),
period=12),xtransf=data.frame(I911=1*(seq(airmiles)==69),
I911=1*(seq(airmiles)==69)),
transfer=list(c(0,0),c(1,0)),xreg=data.frame(Dec96=1*(seq(airmiles)==12),
Jan97=1*(seq(airmiles)==13),Dec02=1*(seq(airmiles)==84)),method='ML')

A Simulated ARMA(1,1) Series/ time series

Description

A simulated ARMA(1,1) series with the model given by: y_t=0.6*y_{t-1}+e_t+0.3*e_{t-1} where the e's are iid standard normal random variables.

Usage

data(arma11.s)

Format

The format is: Time-Series [1:100] from 1 to 100: -0.765 1.297 0.668 -1.607 -0.626 ...

Examples

data(arma11.s)
## maybe str(arma11.s) ; plot(arma11.s) ...

Selection of Subset ARMA Models

Description

This function finds a number of subset ARMA models. A "long" AR model is fitted to the data y to compute the residuals which are taken as a proxy of the error process. Then, an ARMA model is approximated by a regression model with the the covariates being the lags of the time series and the lags of the error process. Subset ARMA models may then be selected using the subset regression technique by leaps and bounds, via the regsubsets function of the leaps package in R.

Usage

armasubsets(y, nar, nma, y.name = "Y", ar.method = "ols", ...)

Arguments

Value

An object of the armasubsets class to be processed by the plot.armasubsets function.

Author(s)

Kung-Sik Chan

Examples

set.seed(92397)
test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120)
res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols')
plot(res)

Monthly beer sales / time series

Description

Monthly beer sales in millions of barrels, 01/1975 - 12/1990.

Usage

data(beersales)

Format

The format is: Time-Series [1:192] from 1975 to 1991: 11.12 9.84 11.57 13.01 13.42 ...

Source

Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.

Examples

data(beersales)
## maybe str(beersales) ; plot(beersales) ...

Blue Bird Potato Chip Data

Description

Weekly unit sales (log-transformed) of Bluebird standard potato chips (New Zealand) and their price for 104 weeks.

Usage

data(bluebird)

Format

The format is: mts [1:104, 1:2] 11.5 11.5 11.8 11.9 11.3 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:2] "log.sales" "price" - attr(*, "tsp")= num [1:3] 1 104 1 - attr(*, "class")= chr [1:2] "mts" "ts"

Source

www.stat.auckland.ac.nz/~balemi/Assn3.xls

Examples

data(bluebird)
## maybe str(bluebird) ; plot(bluebird) ...

Bluebird Lite potato chip data

Description

Weekly unit sales (log-transformed) of Bluebird Lite potato chips (New Zealand) and their price for 104 weeks.

Usage

data(bluebirdlite)

Format

A data frame with 104 observations on the following 2 variables.

log.sales

a numeric vector

price

a numeric vector

Source

www.stat.auckland.ac.nz/~balemi/Assn3.xls

Examples

data(bluebirdlite)
## maybe str(bluebirdlite) ; plot(bluebirdlite) ...

Monthly public transit boardings and gasoline price in Denver

Description

Monthly public transit boardings (mostly buses and light rail) and gasoline price (both log-transformed), Denver, Colorado region, 08/2000 - 03/2006.

Source

Personal communication from Lee Cryer, Project Manager, Regional Transportation District, Denver, Colorado. Denver gasoline prices were obtained from the Energy Information Administration, U.S. Department of Energy, Washington, D.C.at www.eia.doe.gov

Examples

data(boardings)
plot(boardings)
## maybe str(boardings) ; plot(boardings) ...

Levels of Carbon Dioxide at Alert, Canada / Time series

Description

Monthly CO2 level at Alert, Northwest Territories, Canada, near the Artic Circle, 01/1994 - 12/2004.

Usage

data(co2)

Format

The format is: Time-Series [1:132] from 1994 to 2005: 363 364 365 364 364 ...

Source

http://cdiac.ornl.gov/trends/co2/sio-alt.htm

Examples

data(co2)
## maybe str(co2) ; plot(co2) ...

Color property/time series

Description

Color property from 35 consecutive batches in an industrial process.

Usage

data(color)

Format

The format is: Time-Series [1:35] from 1 to 35: 67 63 76 66 69 71 72 71 72 72 ...

Source

“The Estimation of Sigma for an X Chart”, Journal of Quality Technology, Vol. 22, No. 3 (July 1990), by Jonathan D. Cryer and Thomas P. Ryan.

Examples

data(color)
## maybe str(color) ; plot(color) ...

Daily CREF Bond Values

Description

Daily values of one unit of the CREF (College Retirement Equity Fund) Bond fund, 08/26/04 - 08/15/06.

Usage

data(CREF)

Source

www.tiaa-cref.org/performance/retirement/data/index.html

Examples

data(CREF)
## maybe str(CREF) ; plot(CREF) ...

Number of days between payment to Winegard Corp. / time series

Description

Accounts receivable data. Number of days until a distributor of Winegard Company products pays their account.

Usage

data(days)

Format

The format is: Time-Series [1:130] from 1 to 130: 39 39 41 26 28 28 25 26 24 38 ...

Source

Personal communication from Mark Selergren, Vice President, Winegard, Inc., Burlington, Iowa.

Examples

data(days)
## maybe str(days) ; plot(days) ...

Deviations of an industrial process at Deere & Co. – Series 1

Description

82 consecutive values for the amount of deviation (in 0.000025 inch units) from a specified target value in an industrial machining process at Deere & Co.

Usage

data(deere1)

Format

The format is: Time-Series [1:82] from 1 to 82: 3 0 -1 -4 7 3 7 3 3 -1 ...

Source

Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.

Examples

data(deere1)
## maybe str(deere1) ; plot(deere1) ...

Deviations of an industrial process at Deere & Co. – Series 2

Description

102 consecutive values for the deviation (in 0.0000025 inch units) from a specified target value.

Usage

data(deere2)

Format

The format is: Time-Series [1:102] from 1 to 102: -18 -24 -17 -27 -37 -34 -8 14 18 7 ...

Source

Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.

Examples

data(deere2)
## maybe str(deere2) ; plot(deere2) ...

Deviations of an industrial process at Deere & Co. – Series 3

Description

Fifty seven consecutive values for the deviation (in 0.0000025 inch units) from a specified target value.

Usage

data(deere3)

Format

The format is: Time-Series [1:57] from 1 to 57: -500 -1250 -500 -3000 -2375 ...

Source

Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.

Examples

data(deere3)
## maybe str(deere3) ; plot(deere3) ...

Additive Outlier Detection

Description

This function serves to detect whether there are any additive outliers (AO). It implements the test statistic lambda_{2,t} proposed by Chang, Chen and Tiao (1988).

Usage

detectAO(object, alpha = 0.05, robust = TRUE)

Arguments

Value

A list containing the following components:

Author(s)

Kung-Sik Chan

References

Chang, I.H., Tiao, G.C. and C. Chen (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.

See Also

detectIO

Examples

set.seed(12345)
y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100)
y[10]
y[10]=10
y=ts(y,freq=1,start=1)
plot(y,type='o')
acf(y)
pacf(y)
eacf(y)
m1=arima(y,order=c(1,0,0))
m1
detectAO(m1)
detectAO(m1, robust=FALSE)
detectIO(m1)

Innovative Outlier Detection

Description

This function serves to detect whether there are any innovative outliers (IO). It implements the test statistic lambda_{2,t} proposed by Chang, Chen and Tiao (1988).

Usage

detectIO(object, alpha = 0.05, robust = TRUE)

Arguments

Value

A list containing the following components:

Author(s)

Kung-Sik Chan

References

Chang, I.H., Tiao, G.C. and C. Chen (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.

See Also

detectIO

Examples

set.seed(12345)
y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100)
y[10]
y[10]=10
y=ts(y,freq=1,start=1)
plot(y,type='o')
acf(y)
pacf(y)
eacf(y)
m1=arima(y,order=c(1,0,0))
m1
detectAO(m1)
detectAO(m1, robust=FALSE)
detectIO(m1)

Compute the sample extended acf (ESACF)

Description

Computes the sample extended acf (ESACF) for the time series stored in z. The matrix of ESACF with the AR order up to ar.max and the MA order up to ma.max is stored in the matrix EACFM.

Usage

eacf(z, ar.max = 7, ma.max = 13)

Arguments

Value

A list containing the following two components:

Side effect of the eacf function: The function prints a coded ESACF table with significant values denoted by * and nosignificant values by 0.

Author(s)

Kung-Sik Chan

References

Tsay, R. and Tiao, G. (1984). "Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models." Journal of the American Statistical Association, 79 (385), pp. 84-96.

Examples

data(arma11.s)
eacf(arma11.s)

EEG Data

Description

An electroencephalogram (EEG) is a noninvasive test used to detect and record the electrical activity generated in the brain. These data were measured at a frequency of 256 per second and came from a patient suffering a seizure. This a portion of a series on the website of Professor Richard Smith, University of North Carolina. His source: Professors Mike West and Andrew Krystal, Duke University.

Usage

data(eeg)

Format

The format is: ts [1:13000, 1] -3.08 -20.15 -45.05 -69.95 -94.57 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "eeg" - attr(*, "tsp")= num [1:3] 2001 15000 1

Source

http://www.stat.unc.edu/faculty/rs/s133/Data/datadoc.html

Examples

data(eeg)
## maybe str(eeg) ; plot(eeg) ...

Monthly US electricity production / time series

Description

Monthly U.S. electricity generation (in millions of kilowatt hours) of all types: coal, natural gas, nuclear, petroleum, and wind, 01/1973 - 12/2005.

Usage

data(electricity)

Format

The format is: 'ts' int [1:396, 1] 160218 143539 148158 139589 147395 161244 173733 177365 156875 154197 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "electricity" - attr(*, "tsp")= num [1:3] 1973 2006 12

Source

Source: www.eia.doe.gov/emeu/mer/elect.html

Examples

data(electricity)
## maybe str(electricity) ; plot(electricity) ...

A digitized sound file of a B flat played on a euphonium

Description

A digitized sound file of about 0.4 seconds of a B flat just below middle C played on a euphonium by one of the authors (JDC), a member of the group Tempered Brass.

Usage

data(euph)

Format

The format is: Time-Series [1:1105] from 1 to 1105: 0.244 0.635 0.712 0.608 0.317 ...

Examples

data(euph)
## maybe str(euph) ; plot(euph) ...

A simulated explosive AR(1) series

Description

A simulated AR(1) series with the AR(1) coefficient being 3.

Usage

data(explode.s)

Format

The format is: Time-Series [1:8] from 1 to 8: 0.63 0.64 3.72 12.67 39.57 ...

Examples

data(explode.s)
## maybe str(explode.s) ; plot(explode.s) ...

Fitted values of an arima model.

Description

Computes the fitted values of an arima model.

Usage

## S3 method for class 'Arima'
fitted(object,...)

Arguments

Value

fitted values

Author(s)

Kung-Sik Chan

See Also

arima

Examples

data(hare)
hare.m1=arima(sqrt(hare),order=c(3,0,0))
fitted(hare.m1)

Monthly River Flow for the Iowa River

Description

Flow data (in cubic feet per second) for the Iowa river measured at Wapello, Iowa for the period 09/1958 - 08/2006.

Usage

data(flow)

Source

http://waterdata.usgs.gov/ia/nwis/sw

Examples

data(flow)
## maybe str(flow) ; plot(flow) ...

Generalized Portmanteau Tests for GARCH Models

Description

Perform a goodness-of-fit test for the GARCH model by checking whether the standardized residuals are iid based on the ACF of the absolute residuals or squared residuals.

Usage

gBox(model, lags = 1:20, x, method = c("squared", "absolute")[1], plot = TRUE)

Arguments

Value

Author(s)

Kung-Sik Chan

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

Examples

require(tseries) # need to uncomment this line when running the example
data(CREF)
r.cref=diff(log(CREF))*100
m1=tseries::garch(x=r.cref,order=c(1,1))
summary(m1)
gBox(m1,x=r.cref,method='squared')

Simulate a GARCH process

Description

Simulate a GARCH process.

Usage

garch.sim(alpha, beta, n = 100, rnd = rnorm, ntrans = 100,...)

Arguments

Details

Simulate data from the GARCH(p,q) model: x_t=\sigma_{t|t-1} e_t where \{e_t\} is iid, e_t independent of past x_{t-s}, s=1,2,\ldots, and

\sigma_{t|t-1}=\sum_{j=1}^p \beta_j \sigma_{t-j|t-j-1}+ \alpha_0+\sum_{j=1}^q \alpha_j x_{t-i}^2

Value

simulated GARCH time series of size n.

Author(s)

Kung-Sik Chan

Examples

set.seed(1235678)
garch01.sim=garch.sim(alpha=c(.01,.9),n=500)
plot(garch01.sim,type='l', main='',ylab=expression(r[t]),xlab='t')

Gold Price / time series

Description

Daily price of gold (in $ per troy ounce) for the 252 trading days of 2005

Usage

data(gold)

Format

The format is: Time-Series [1:252] from 1 to 252: 427 426 426 423 421 ...

Source

www.lbma.org.uk/2005dailygold.htm

Examples

data(gold)
## maybe str(gold) ; plot(gold) ...

Daily returns of the google stock

Description

Daily returns of the google stock from 08/20/04 - 09/13/06.

Usage

data(google)

Format

The format is: Time-Series [1:521] from 1 to 521: 0.0764 0.0100 -0.0423 0.0107 0.0179 ...

Source

http://finance.yahoo.com/q/hp?s=GOOG

Examples

data(google)
## maybe str(google) ; plot(google) ...

Canadian hare data/ time series

Description

Annual number of hare data.

Usage

data(hare)

Format

The format is: Time-Series [1:31] from 1905 to 1935: 50 20 20 22 27 50 55 78 70 59 ...

Details

These are yearly hare abundances for the main drainage of the Hudson Bay, based on trapper questionnaires.

Source

MacLulich, D. A. (1937) Fluctuations in the Number of the Varying Hare (Lepus americanus) (Univ. of Toronto Press, Toronto)

References

Stenseth, N. C., Falck, W., Bjornstad, O. N. and Krebs. C. J. (1997) Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx. Proc. Natl. Acad. Sci., 94, 5147-5152.

Examples

data(hare)

Construct harmonic functions for fitting harmonic trend model

Description

The function creates a matrix of the first m pairs of harmonic functions for fitting a harmonic trend (cosine-sine trend, Fourier regresssion) models with the response being x, a time series.

Usage

harmonic(x, m = 1)

Arguments

Value

a matrix consisting of \cos(2k \pi t), \sin(2k \pi t), k=1,2,...,m, excluding any zero functions.

Author(s)

Kung-Sik Chan

See Also

season

Examples

data(tempdub)
# first creates the first pair of harmonic functions and then fit the model
har.=harmonic(tempdub,1)
model4=lm(tempdub~har.)
summary(model4)

Average hours worked in US manufacturing sector / time series

Description

Average hours worked (times 10) in U.S. manufacturing sector, from 07/1982 - 06/1987

Usage

data(hours)

Format

The format is: Time-Series [1:60] from 1983 to 1987: 389 390 389 390 393 397 392 388 396 398 ...

Source

Cryer, J. D. Time Series Analysis, Duxbury Press, 1986.

Examples

data(hours)
## maybe str(hours) ; plot(hours) ...

Simulated IMA(2,2) series / time series

Description

A simulated IMA(2,2) series with theta1=1 and theta2=-0.6

Usage

data(ima22.s)

Format

The format is: Time-Series [1:62] from 1 to 62: 0.00000 0.00000 -0.00569 2.12404 2.15337 ...

Examples

data(ima22.s)
## maybe str(ima22.s) ; plot(ima22.s) ...

Kurtosis

Description

Computes the Kurtosis.

Usage

kurtosis(x, na.rm = FALSE)

Arguments

Details

Given data x_1,x_2,\ldots, x_n, the sample kurtosis is defined by the formula:

\frac{\sum_{i=1}^n (x_i-\bar{x})^4/n}{(\sum_{i=1}^n (x_i-\bar{x})^2/n)^2}-3.

Value

The function returns the kurtosis of the data.

Author(s)

Kung-Sik Chan

Examples

data(CREF)
r.cref=diff(log(CREF))*100
kurtosis(r.cref)

Lagged Regression Plot

Description

Computes and plots the nonparametric regression function of a time series against its various lags.

Usage

lagplot(x, lag.max = 6, deg = 1, nn = 0.7, method = c("locfit", "gam", "both")[1])

Arguments

Value

Side effects: The nonparametric lagged regression functions are plotted lag by lag, with the raw data superimposed on the plots.

Author(s)

Kung-Sik Chan

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

Examples

set.seed(2534567)
par(mfrow=c(3,2))
y=arima.sim(n=61,model=list(ar=c(1.6,-0.94),ma=-0.64))
# lagplot(y)

Annual rainfall in Los Angeles / time series

Description

Annual precipitation (in inches) in Los Angeles, 1878-1992.

Usage

data(larain)

Format

The format is: Time-Series [1:115] from 1778 to 1892: 20.86 17.41 18.65 5.53 10.74 ...

Source

Personal communication from Professor Donald Bentley, Pomona College, Claremont, California. For more data see http://www.wrh.noaa.gov/lox/climate/cvc.php

Examples

data(larain)
## maybe str(larain) ; plot(larain) ...

A simulated MA(1) series / time series

Description

A simulated MA(1) series with the MA(1) coefficient equal to 0.9.

Usage

data(ma1.1.s)

Format

The format is: Time-Series [1:120] from 1 to 120: 0.182 -0.748 -0.355 1.014 -2.363 ...

Details

The model is Y(t)=e(t)-0.9e(t-1) where the e's are iid standard normal.

Examples

data(ma1.1.s)
## maybe str(ma1.1.s) ; plot(ma1.1.s) ...

A simulated MA(1) series / time series

Description

A simulated MA(1) series with the MA(1) coefficient equal to -0.9.

Usage

data(ma1.2.s)

Format

The format is: Time-Series [1:120] from 1 to 120: 1.511 1.821 0.957 -1.538 -2.888 ...

Details

The model is Y(t)=e(t)+0.9e(t-1) where the e's are iid standard normal.

Examples

data(ma1.2.s)
## maybe str(ma1.2.s) ; plot(ma1.2.s) ...

A simulated MA(2) series

Description

A simulated MA(2) series with MA coefficients being 1 and -0.6.

Usage

data(ma2.s)

Format

The format is: Time-Series [1:120] from 1 to 120: -0.4675 0.0815 0.9938 -2.6959 2.8116 ...

Details

The model is Y(t)=e(t)-e(t-1)+0.6*e(t-2) where the e's are iid standard normal random variables.

Examples

data(ma2.s)
## maybe str(ma2.s) ; plot(ma2) ...

Monthly Milk Production

Description

Average monthly milk production per cow in the US, 01/1994 - 12/2005

Usage

data(milk)

Format

The format is: 'ts' int [1:144, 1] 1343 1236 1401 1396 1457 1388 1389 1369 1318 1354 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "milk" - attr(*, "tsp")= num [1:3] 1994 2006 12

Examples

data(milk)
str(milk) 
plot(milk) 

Monthly Oil Price / time series

Description

Monthly spot price for crude oil, Cushing, OK (in U.S. dollars per barrel), 01/1986 - 01/2006.

Usage

data(oil.price)

Format

The format is: Time-Series [1:241] from 1986 to 2006: 22.9 15.4 12.6 12.8 15.4 ...

Source

tonto.eia.doe.gov/dnav/pet/hist/rwtcM.htm

Examples

data(oil.price)
## maybe str(oil.price) ; plot(oil.price) ...

Monthly sales to dealers of a specialty oil filter/time series

Description

Monthly wholesale specialty oil filters sales, Deere & Co, 07/1983 - 06/1987.

Usage

data(oilfilters)

Format

The format is: Time-Series [1:48] from 1984 to 1987: 2385 3302 3958 3302 2441 3107 5862 4536 4625 4492 ... - attr(*, "freq")= num 12 - attr(*, "start")= num [1:2] 1987 7

Source

Data courtesy of William F. Fulkerson, Deere & Company, Technical Center, Moline, Illinois.

Examples

data(oilfilters)
## maybe str(oilfilters) ; plot(oilfilters) ...

Computing the periodogram

Description

This is a wrapper that computes the periodogram

Usage

periodogram(y,log='no',plot=TRUE,ylab="Periodogram", xlab="Frequency",lwd=2,...) 

Arguments

Value

A list that contains the following elements:

References

Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.

Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. Second edition. Springer.

Examples

data(star)
plot(star,xlab='Day',ylab='Brightness')
periodogram(star,ylab='Variable Star Periodogram');  abline(h=0)

Compute and Plot the Forecasts Based on a Fitted Time Series Model

Description

Plots the time series data and its predictions with 95% prediction bounds.

Usage

## S3 method for class 'Arima'
plot(x, n.ahead = 12, col = "black", ylab = object$series, 
lty = 2, n1, newxreg, transform, Plot=TRUE, ...)

Arguments

Value

Side effects of the function: plot the forecasts and their 95% prediction bounds, unless Plot is set to be FALSE. The part of the observed series is plotted with all data plotted as open circles and linked by a smooth line. By default the predicted values are plotted as open circles joined up by a dashed line. The plotting style of the predicted values can be altered by supplying relevant plotting options, e.g specifying the options type='o', pch=19 and lty=1 will plot the predicted values as solid circles that are overlaid on the connecting smooth solid line. The prediction limits are plotted as dotted lines, with default color being black. However, the prediction limits can be drawn in other colors. For example, setting col='red' paints the prediction limits in red. An interesting use of the col argument is setting col=NULL which has the effect of not drawing the prediction limits.

The function returns an invisible list containing the following components.

Author(s)

Kung-Sik Chan

Examples

data(oil.price)
oil.IMA11alt=arima(log(oil.price),order=c(0,1,1),
# create the design matrix of the covariate for prediction
xreg=data.frame (constant=seq(oil.price)))
n=length(oil.price)
n.ahead=24
newxreg=data.frame(constant=(n+1):(n+n.ahead))
# do the prediction and plot the results
plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg,
ylab='Log(Oil Price)',xlab='Year',n1=c(2000,1))
# do the same thing but on the orginal scale
plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg,
ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19, lty=1,type='o')
# Setting pch=19 plots the predicted values as solid circles.
res=plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg,
ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19,col=NULL)
# Setting col=NULL will make the prediction bands invisible. Try col='red'. 
res
# prints the predicted values and their 95% prediction limits.

Plot the Best Subset ARMA models

Description

This function is adapted from the plot.regsubsets function of the leaps package, and its main use is to plot the output from the armasubsets function.

Usage

## S3 method for class 'armasubsets'
plot(x, labels = obj$xnames, main = NULL, 
scale = c("BIC", "AICc", "AIC", "Cp", "adjR2", "R2"), 
col = gray(c(seq(0.4, 0.7, length = 10), 0.9)), draw.grid = TRUE, 
axis.at.3 = TRUE, ...)

Arguments

Value

Plot the few best subset ARMA models.

Author(s)

Kung-Sik Chan, based on previoud work by Thomas Lumley and Merlise Clyde

See Also

armasubsets

Examples

set.seed(53331)
test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120)
res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols')
plot(res)

Plot1

Description

A workhorse function for the acf function in the TSA pacakage.

Author(s)

Kung-Sik Chan

Prediction based on a fitted TAR model

Description

Predictions based on a fitted TAR model. The errors are assumed to be normally distributed. The predictive distributions are approximated by simulation.

Usage

## S3 method for class 'TAR'
predict(object, n.ahead = 1, n.sim = 1000,...)

Arguments

Value

Author(s)

Kung-Sik Chan

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

tar

Examples

data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
set.seed(2357125)
pred.prey=predict(prey.tar.1,n.ahead=60,n.sim=1000)
yy=ts(c(log(prey.eq),pred.prey$fit),frequency=1,start=1)
plot(yy,type='n',ylim=range(c(yy,pred.prey$pred.interval)),ylab='Log Prey',
xlab=expression(t))
lines(log(prey.eq))
lines(window(yy, start=end(prey.eq)[1]+1),lty=2)
lines(ts(pred.prey$pred.interval[2,],start=end(prey.eq)[1]+1),lty=2)
lines(ts(pred.prey$pred.interval[1,],start=end(prey.eq)[1]+1),lty=2)

Cost per prescription / time series

Description

Monthly U.S. average prescription costs for the months 08/1986 - 03/1992.

Usage

data(prescrip)

Format

The format is: Time-Series [1:68] from 1987 to 1992: 14.5 14.7 14.8 14.6 14.3 ...

Source

Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.

Examples

data(prescrip)
## maybe str(prescrip) ; plot(prescrip) ...

Prewhiten a Bivariate Time Series, and Compute and Plot Their Sample Cross-Correlation Function

Description

The bivariate time series are prewhitened according to an AR model fitted to the x-component of the bivariate series. Alternatively, if an ARIMA model is provided, it will be used to prewhiten both series. The CCF of the prewhitened bivariate series is then computed and plotted.

Usage

prewhiten(x, y, x.model = ar.res,ylab="CCF", ...)

Arguments

Value

A list containing the following components:

Author(s)

Kung-Sik Chan

Examples

data(milk)
data(electricity)
milk.electricity=ts.intersect(milk,log(electricity))
plot(milk.electricity,yax.flip=TRUE,main='') 
ccf(as.numeric(milk.electricity[,1]),as.numeric(milk.electricity[,2]),
main='milk & electricity',ylab='CCF')
me.dif=ts.intersect(diff(diff(milk,12)),diff(diff(log(electricity),12)))
prewhiten(as.numeric(me.dif[,1]),as.numeric(me.dif[,2]),
,ylab='CCF' )

Prey series / time series

Description

The stationary part of the Didinium series in the veilleux data frame.

Usage

data(prey.eq)

Format

The format is: Time-Series [1:57] from 7 to 35: 26.9 53.2 65.6 81.2 143.9 ...

See Also

veilleux

Examples

data(prey.eq)
## maybe str(prey.eq) ; plot(prey.eq) ...

Simulate a first-order quadratic AR model

Description

Simulates a first-order quadratic AR model with normally distributed noise.

Usage

qar.sim(const = 0, phi0 = 0, phi1 = 0.5, sigma = 1, n = 20, init = 0)

Arguments

Details

The quadratic AR(1) model specifies that

Y_t = \mathrm{const}+\phi_0 Y_{t-1}+\phi_1 Y^2_{t-1}+e_t

where e_t are iid normally distributed with zero mean and standard deviation \sigma. If \sigma=0, the model is deterministic.

Value

A simulated series from the quadratic AR(1) model, as a vector

Author(s)

Kung-Sik Chan

See Also

tar.sim

Examples

set.seed(1234567)
plot(y=qar.sim(n=15,phi1=.5,sigma=1),x=1:15,type='l',ylab=expression(Y[t]),xlab='t')
y=qar.sim(n=100,const=0.0,phi0=3.97, phi1=-3.97,sigma=0,init=.377)
plot(y,x=1:100,type='l',ylab=expression(Y[t]),xlab='t')
acf(y,main='')

U.K. retail sales / time series

Description

Monthly total UK (United Kingdom) retail sales (non-food stores in billions of pounds), 01/1983 - 12/1987.

Usage

data(retail)

Format

The format is: Time-Series [1:60] from 1983 to 1988: 81.3 78.9 93.8 94 97.8 1.6 99.6 1.2 98 1.7 ...

Source

www.statistics.gov.uk/statbase/TSDdownload1.asp

Examples

data(retail)
## maybe str(retail) ; plot(retail) ...

The distance of a robot from a desired position / time series

Description

Final position in the x direction of an industrial robot put through a series of planned exercises many times.

Usage

data(robot)

Format

The format is: Time-Series [1:324] from 1 to 324: 0.0011 0.0011 0.0024 0 -0.0018 0.0055 0.0055 -0.0015 0.0047 -1e-04 ...

Source

Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.

Examples

data(robot)
## maybe str(robot) ; plot(robot) ...

Compute the Standardized Residuals from a Fitted ARIMA Model

Description

Computes the internally standardized residuals from a fitted ARIMA model.

Usage

## S3 method for class 'Arima'
rstandard(model,...)

Arguments

Details

residuals/(error std. dev.)

Value

time series of standarized residuals

Examples

data(oil.price)
m1.oil=arima(log(oil.price),order=c(0,1,1))
plot(rstandard(m1.oil),ylab='Standardized residuals',type='l')
abline(h=0)

Runs test

Description

Test the independence of a sequence of random variables by checking whether there are too many or too few runs above (or below) the median.

Usage

runs(x,k=0)

Arguments

Details

The runs test examines the data in sequence to look for patterns that would give evidence against independence. Runs above or below k are counted. A small number of runs would indicate that neighboring values are positively dependent and tend to hang together over time. On the other hand, too many runs would indicate that the data oscillate back and forth across their median of zero. Then neighboring residuals are negatively dependent. So either too few or too many runs lead us to reject independence. When applied to residuals, the runs test is useful for model diagnostics.

Value

Author(s)

Kung-Sik Chan

Examples

data(tempdub)
month.=season(tempdub) # the period sign is included to make the printout from
# the following command clearer.
model3=lm(tempdub~month.) # intercept is automatically included so one month (Jan) is dropped
summary(model3)
runs(rstudent(model3))

A simulated random walk / Time series

Description

A simulated random walk with standard normal increments

Usage

data(rwalk)

Examples

data(rwalk)
## maybe str(rwalk) ; plot(rwalk) ...

Extract the season info from a time series

Description

Extract the season info from a equally spaced time series and create a vector of the season info. For example for monthly data, the function outputs a vector containing the months of the data.

Usage

season(x, labels)

Arguments

Details

The time series must have frequency greater than 1, otherwise the function will stop and issue an error message. If labels is missing, labels will be set as follows: It is set to be c("1Q","2Q","3Q","4Q) if the frequency of x equals 4, c("January",...,"December") if the frequency equals 12, and c("Monday",...,"Sunday") if frequency equals 7. Otherwise, it is set to be c("S1",...)

Value

An invisible vector containing the seasons of the data

Author(s)

Kung-Sik Chan

See Also

harmonic

Examples

data(tempdub)
month.=season(tempdub) # the period sign is included to make the printout from
# the commands two line below clearer; ditto below.
model2=lm(tempdub~month.-1) # -1 removes the intercept term 
summary(model2)

Skewness

Description

Computes the skewness of the data

Usage

skewness(x, na.rm = FALSE)

Arguments

Details

Given data x_1,x_2,\ldots, x_n, the sample skewness is defined by the formula:

\frac{\sum_{i=1}^n (x_i-\bar{x})^3/n}{(\sum_{i=1}^n (x_i-\bar{x})^2/n)^{3/2}}.

Value

The function returns the skewness of the data.

Author(s)

Kung-Sik Chan

Examples

data(CREF)
r.cref=diff(log(CREF))*100
skewness(r.cref)

Computing the spectrum

Description

This is a wrapper that allows the user to invoke either the spec.pgram function or the spec.ar function in the stats pacakge. Note that the seasonal attribute of the data, if it exists, will be removed, for our preferred way of presenting the output.

Usage

 spec(x, taper = 0, detrend = FALSE, demean = TRUE, method = c("pgram", 
    "ar")[1], ci.plot = FALSE, ylim = range(c(lower.conf.band, upper.conf.band)), 
    ...) 

Arguments

A list that contains the following:

Value

The output is from the spec.pgram function or spec.ar function, and the following description of the output is taken from the help manual of the spec function in the stats package. An object of class "spec", which is a list containing at least the following components:

The result is returned invisibly if plot is true.

References

Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.

Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. Second edition. Springer.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth edition. Springer. (Especially pages 3927.)

Examples

set.seed(271435); n=200; phi=-0.6
y=arima.sim(model=list(ar=phi),n=n)
k=kernel('daniell',m=15)
sp=spec(y,kernel=k,main='',sub='',xlab='Frequency',
ylab='Log(Smoothed Sample Spectrum)',ci.plot=TRUE,ci.col='black')
lines(sp$freq,ARMAspec(model=list(ar=phi),sp$freq,plot=FALSE)$spec,lty=4)
abline(h=0)

Relative annual sunspot number / time series

Description

Annual American (relative) sunspot numbers collected from 1945 to 2007. The annual (relative) sunspot number is a weighted average of solar activities measured from a network of observatories.

Usage

data(spots)

Format

The format is: Time-Series [1:61] from 1945 to 2005: 32.3 99.9 170.9 166.6 174.1 ...

Source

http://www.ngdc.noaa.gov/stp/SOLAR/ftpsunspotnumber.html#american

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

Examples

data(spots)
## maybe str(spots) ; plot(spots) ...

Annual international sunspot numbers

Description

Annual international sunspot numbers, NOAA National Geophysical Data Center, 1700 - 2005.

Usage

data(spots1)

Format

The format is: ts [1:306, 1] 5 11 16 23 36 58 29 20 10 8 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "spots" - attr(*, "tsp")= num [1:3] 1700 2005 1

Source

ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/YEARLY.PLT

Examples

data(spots1)
## maybe str(spots1) ; plot(spots1) ...

Star Brightness

Description

Brightness (magnitude) of a particular star at midnight on 600 consecutive nights.

Usage

data(star)

Source

Whittaker, E. T. and Robinson, G., (1924). The Calculus of Observations. London: Blackie and Son.

Examples

data(star)
## maybe str(star) ; plot(star) ...
data(star)
plot(star,xlab='Day',ylab='Brightness')

Summary of output from the armasubsets function

Description

Add the calculation of AIC and AICc. See the help manual of regsubsets function of the leaps package

Usage

## S3 method for class 'armasubsets'
summary(object, all.best = TRUE, matrix = TRUE, matrix.logical = FALSE,
 df = NULL, ...)

Arguments

Author(s)

Kung-Sik Chan, based on previous work of Thomas Lumley

Estimation of a TAR model

Description

Estimation of a two-regime TAR model.

Usage

tar(y, p1, p2, d, is.constant1 = TRUE, is.constant2 = TRUE, transform = "no",
 center = FALSE, standard = FALSE, estimate.thd = TRUE, threshold, 
method = c("MAIC", "CLS")[1], a = 0.05, b = 0.95, order.select = TRUE, print = FALSE)

Arguments

Details

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

Y_t = \phi_{1,0}+\phi_{1,1} Y_{t-1} +\ldots+ \phi_{1,p} Y_{t-p_1} +\sigma_1 e_t, \mbox{ if } Y_{t-d}\le r

Y_t = \phi_{2,0}+\phi_{2,1} Y_{t-1} +\ldots+\phi_{2,p_2} Y_{t-p}+\sigma_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A list of class "TAR" which can be further processed by the by the predict and tsdiag functions.

Author(s)

Kung-Sik Chan

References

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

predict.TAR, tsdiag.TAR, tar.sim, tar.skeleton

Examples

data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)

Simulate a two-regime TAR model

Description

Simulate a two-regime TAR model.

Usage

tar.sim(object, ntransient = 500, n = 500, Phi1, Phi2, thd, d, p, sigma1, 
sigma2, xstart = rep(0, max(p,d)), e)

Arguments

Details

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

Y_t = \phi_{1,0}+\phi_{1,1} Y_{t-1} +\ldots+ \phi_{1,p} Y_{t-p_1} +\sigma_1 e_t, \mbox{ if } Y_{t-d}\le r

Y_t = \phi_{2,0}+\phi_{2,1} Y_{t-1} +\ldots+\phi_{2,p_2} Y_{t-p}+\sigma_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A list containing the following components:

...

Author(s)

Kung-Sik Chan

References

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford "Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

tar

Examples

set.seed(1234579)
y=tar.sim(n=100,Phi1=c(0,0.5),
Phi2=c(0,-1.8),p=1,d=1,sigma1=1,thd=-1,
sigma2=2)$y
plot(y=y,x=1:100,type='b',xlab="t",ylab=expression(Y[t]))

Find the asympotitc behavior of the skeleton of a TAR model

Description

The skeleton of a TAR model is obtained by suppressing the noise term from the TAR model.

Usage

tar.skeleton(object, Phi1, Phi2, thd, d, p, ntransient = 500, n = 500, 
xstart, plot = TRUE,n.skeleton = 50)

Arguments

Details

The two-regime Threshold Autoregressive (TAR) model is given by the following formula:

Y_t = \phi_{1,0}+\phi_{1,1} Y_{t-1} +\ldots+ \phi_{1,p} Y_{t-p_1} +\sigma_1 e_t, \mbox{ if } Y_{t-d}\le r

Y_t = \phi_{2,0}+\phi_{2,1} Y_{t-1} +\ldots+\phi_{2,p_2} Y_{t-p}+\sigma_2 e_t, \mbox{ if } Y_{t-d} > r.

where r is the threshold and d the delay.

Value

A vector that contains the trajectory of the skeleton, with the burn-in discarded.

Author(s)

Kung-Sik Chan

References

Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford. "Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

tar

Examples

data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
tar.skeleton(prey.tar.1)

A digitized sound file of a B flat played on a tenor trombone

Description

A digitized sound file of about 0.4 seconds of a B flat just below middle C played on a tenor trombone by Chuck Kreeb, a member of Tempered Brass and a friend of one of the authors.

Usage

data(tbone)

Format

The format is: Time-Series [1:17689] from 1 to 17689: 0.0769 0.0862 0.0961 0.1050 0.1129 ...

Examples

data(tbone)
## maybe str(tbone) ; plot(tbone) ...

Monthly average temperature in Dubuque/time series

Description

Monthly average temperature (in degrees Fahrenheit) recorded in Dubuque 1/1964 - 12/1975.

Usage

data(tempdub)

Format

The format is: Time-Series [1:144] from 1964 to 1976: 24.7 25.7 30.6 47.5 62.9 68.5 73.7 67.9 61.1 48.5 ...

Source

http://mesonet.agron.iastate.edu/climodat/index.phtml?station=ia2364&report=16

Examples

data(tempdub)
## maybe str(tempdub) ; plot(tempdub) ...

Likelihood ratio test for threshold nonlinearity

Description

Carry out the likelihood ratio test for threshold nonlinearity, with the null hypothesis being a normal AR process and the alternative hypothesis being a TAR model with homogeneous, normally distributed errors.

Usage

tlrt(y, p, d = 1, transform = "no", a = 0.25, b = 0.75,...)

Arguments

Details

The search for the threshold parameter may be narrower than that defined by the user as the function attempts to ensure adequate sample size in each regime of the TAR model. The p-value of the test is based on large-sample approximation and also is more reliable for small p-values.

Value

Author(s)

Kung-Sik Chan

References

Chan, K.S. (1990). Percentage points of likelihood ratio tests for threshold autoregression. Journal of Royal Statistical Society, B 53, 3, 691-696.

See Also

Keenan.test, Tsay.test

Examples

data(spots)
pvaluem=NULL
for (d in 1:5){
res=tlrt(sqrt(spots),p=5,d=d,a=0.25,b=0.75)
pvaluem= cbind( pvaluem, round(c(d,signif(c(res$test.statistic, 
res$p.value))),3))
}
rownames(pvaluem)=c('d','test statistic','p-value')
pvaluem

Model Diagnostics for a Fitted ARIMAX Model

Description

This function is modified from the tsdiag function of the stats package.

Usage

## S3 method for class 'Arimax'
tsdiag(object, gof.lag, tol = 0.1, col = "red", omit.initial = TRUE,...)

Arguments

Value

Side effects: Plot the time plot of the standardized residuals. Red dashed line at +/-qnorm(0.025/no of data) are added to the plot. Data beyond these lines are deemed outliers, based on the Bonferronni rule. The ACF of the standardized residuals is plotted. The p-values of the Ljung-Box test are plotted using a variety of the first K residuals. K starts at the lag on and beyond which the moving-average weights (in the MA(infinity) representation) are less than tol.

Author(s)

Kung-Sik Chan, based on the tsdiag function of the stats pacakage

Examples

data(color)
m1.color=arima(color,order=c(1,0,0))
tsdiag(m1.color,gof=15,omit.initial=FALSE)

Model diagnostics for a fitted TAR model

Description

The time series plot and the sample ACF of the standardized residuals are plotted. Also, a portmanteau test for detecting residual correlations in the standardized residuals are carried out.

Usage

## S3 method for class 'TAR'
tsdiag(object, gof.lag, col = "red",xlab = "t", ...)

Arguments

Value

Side effects: plot the time-series plot of the standardized residuals, their sample ACF and portmanteau test for residual autocorrelations in the standardized errors.

Author(s)

Kung-Sik Chan

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

See Also

tar

Examples

data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
tsdiag(prey.tar.1)

A digitized sound file of a B flat played on a BB flat tuba

Description

A digitized sound file of about 0.4 seconds of a B flat an octave and one whole step below middle C played on a BB flat tuba by Linda Fisher, a member of Tempered Brass and a friend one of the authors.

Usage

data(tuba)

Format

The format is: Time-Series [1:4402] from 1 to 4402: 0.217 0.209 0.200 0.195 0.196 ...

Examples

data(tuba)
## maybe str(tuba) ; plot(tuba) ...

Annual sales of certain large equipment

Description

Annual sales of certain large equipment, 1983 - 2005.

Usage

data(units)

Format

The format is: ts [1:24, 1] 71.7 78.6 111.1 125.6 133.0 ... - attr(*, "tsp")= num [1:3] 1982 2005 1 - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "Units"

Source

Proprietary sales data from a large international company

Examples

data(units)
## maybe str(units) ; plot(units) ...

Daily US Dollar to Hong Kong Dollar Exchange Rates

Description

Daily USD/HKD (US dollar to Hong Kong dollar) exchange rate from January 1, 2005 to March 7, 2006

Usage

data(usd.hkd)

Format

A data frame with 431 observations on the following 6 variables.

r

daily returns of USD/HKD exchange rates

v

estimated conditional variances based on an AR(1)+GARCH(3,1) model

hkrate

daily USD/HKD exchange rates

outlier1

dummy variable of day 203, corresponding to July 22, 2005

outlier2

dummy variable of day 290, another possible outlier

day

calendar day

Source

http://www.oanda.com/convert/fxhistory

References

"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan

Examples

data(usd.hkd)
## maybe str(usd.hkd) ; plot(usd.hkd) ...

An experimental prey-predator time series

Description

A data frame consisting of bivariate time series from an experiment for studying prey-predator dynamics. The first time series consists of the numbers of prey individuals (Didinium natsutum) per ml measured every twelve hours over a period of 35 days; the second time series consists of the corresponding number of predators (Paramecium aurelia) per ml.

Usage

data(veilleux)

Format

The format is: mts [1:71, 1:2] 15.7 53.6 73.3 93.9 115.4 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:2] "Didinium" "Paramecium" - attr(*, "tsp")= num [1:3] 0 35 2 - attr(*, "class")= chr [1:2] "mts" "ts"

Source

http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/

References

Veilleux (1976) "The analysis of a predatory interaction between Didinium and Paramecium", Masters thesis, University of Alberta.

Jost & Ellner (2000) "Testing for predator dependence in predator-prey dynamics: a non-parametric approach", Proceedings of the Royal Society of London B, 267, 1611-1620.

Examples

data(veilleux)
## maybe str(veilleux) ; plot(veilleux) ...

Average hourly wages in the apparel industry / time series

Description

Average hourly wages in the apparel industry, from 07/1981 - 06/1987.

Usage

data(wages)

Format

The format is: Time-Series [1:72] from 1982 to 1987: 4.92 4.96 5.04 5.05 5.04 5.04 5.18 5.13 5.15 5.18 ...

Source

Cryer, J. D. Time Series Analysis, Duxbury Press, 1986.

Examples

data(wages)
## maybe str(wages) ; plot(wages) ...

Monthly unit sales of recreational vehicles / time series

Description

Monthly unit sales of recreational vehicles from Winnebago, Inc., Forrest City, Iowa, from 11/1966 - 02/1972.

Usage

data(winnebago)

Format

The format is: Time-Series [1:64] from 1967 to 1972: 61 48 53 78 75 58 146 193 124 120 ...

Source

Roberts, H. V., Data Analysis for Managers with Minitab, second edition, The Scientific Press, 1991.

Examples

data(winnebago)
## maybe str(winnebago) ; plot(winnebago) ...

Compute the lag of a vector.

Description

Computes the lag of a vector, with missing elements replaced by NA

Usage

zlag(x, d= 1)

Arguments

Value

A vector whose k-th element equals x[k-d] with x[t]=NA for t<=0

Author(s)

Kung-Sik Chan

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.
x=1:5
zlag(x,2)