Data set for testing marima package (Copenhagen Stocks)

Description

Two years of prices for 18 shares from the Copenhagen Stock Exchange C20 index, covering the most valuable companies. Two shares have been removed (Maersk A = almost identical to Maersk B) and ISS which is incomplete for the period considered.

Usage

data(C20)

Format

A data frame (C20) with 1+18+18 columns and 517 rows (about two full years).

Dates

Format for date is 2016-04-01

CARL.fin

Closing price for stock 'Carlsberg' .

CHR..fin

Closing price for stock 'Christian Hansen' .

COLO.fin

Closing price for stock 'Coloplast' .

DANS.fin

Closing price for stock 'Danske Bank' .

DSV..fin

Closing price for stock 'DSV' .

GEN..fin

Closing price for stock 'Genmap' .

GN.2.fin

Closing price for stock 'GN St. Nord' .

FLS..fin

Closing price for stock 'FL Smidth' .

JYSK.fin

Closing price for stock 'Jyske Bank' .

MAER.fin

Closing price for stock 'Maersk B' .

NDA..fin

Closing price for stock 'Nordea Bank' .

NOVO.fin

Closing price for stock 'Novo' .

NZYM.fin

Closing price for stock 'Novozymes' .

PNDO.fin

Closing price for stock 'Pandora' .

TDC..fin

Closing price for stock 'TDC' .

TRYG.fin

Closing price for stock Pandora' .

VWS..fin

Closing price for stock 'Vestas Wind' .

WDH..fin

Closing price for stock 'Wiliam Demant' .

CARL.ave

Average price for stock 'Carlsberg' .

CHR..ave

Average price for stock 'Christian Hansen' .

COLO.ave

Average price for stock 'Coloplast' .

DANS.ave

Average price for stock 'Danske Bank' .

DSV..ave

Average price for stock 'DSV' .

GEN..ave

Average price for stock 'Genmap' .

GN.2.ave

Average price for stock 'GN St. Nord' .

FLS..ave

Average price for stock 'FL Smidth' .

JYSK.ave

Average price for stock 'Jyske Bank' .

MAER.ave

Average price for stock 'Maersk B' .

NDA..ave

Average price for stock 'Nordea Bank' .

NOVO.ave

Average price for stock 'Novo' .

NZYM.ave

Average price for stock 'Novozymes' .

PNDO.ave

Average price for stock Pandora' .

TDC..ave

Average price for stock 'TDC' .

TRYG.ave

Average price for stock 'Pandora' .

VWS..ave

Average price for stock 'Vestas Wind' .

WDH..ave

Average price for stock 'William Demant' .

Examples

# Example 1:

library(marima)
data(C20)

selects <- c(2,7,11)

cat("Multivariate model for ",colnames(C20)[selects]," \n")

Data <- data.frame(C20[,selects])
colnames(Data) <- colnames(C20)[selects]

log.Data <- log(Data)
kvar <- length(selects)
k    <- c(1:kvar)
difs <- rep(1,length(selects))

difference <- rbind(k , difs)

dlog.Data <- 100*t(define.dif(log.Data,difference)$y.dif)

cat("dlog.Data represents the percentage change from day
to day. \n")

mod <- define.model(kvar = kvar, ar=c(1:2),ma=c(1))

Model <- marima(dlog.Data,
   ar.pattern=mod$ar.pattern, ma.pattern=mod$ma.pattern,penalty=2)

short.form(Model$ar.estimates,leading=FALSE)
short.form(Model$ma.estimates,leading=FALSE)

# Example 2:
library(marima)
data(C20)

selects <- c(13)

cat("Univariate model for ",colnames(C20)[selects]," \n")

Data <- data.frame(C20[,selects])
colnames(Data) <- colnames(C20)[selects]

log.Data <- log(Data)
kvar <- length(selects)
k    <- c(1:kvar)
difs <- rep(1,length(selects))

difference <- rbind(k , difs)

dlog.Data <- 100*t(define.dif(log.Data,difference)$y.dif)

mod <- define.model(kvar = kvar, ar=c(1:2),ma=c(1))

Model <- marima(dlog.Data,
   ar.pattern=mod$ar.pattern, ma.pattern=mod$ma.pattern,penalty=2)

short.form(Model$ar.estimates,leading=FALSE)
short.form(Model$ma.estimates,leading=FALSE)

Results

Description

function which generates a matrix from summary(Model), where 'Model' is an 'lm' object. Is used by marima, in case there can be one or more non-identifiable (ar-)parameters when estimating the lm-object.

Usage

Results(Model = NULL)

Arguments

Value

Results = matrix with 4 columns containing the same information as summary(Model), but with "NA" rows replaced by rows = c(0, 0, 0, NaN).

arma.filter

Description

Filtering of (kvar-variate) time series with marima type model.

Calculation of residuals and filtered values of timeseries using a marima model.

Usage

arma.filter(series = NULL, ar.poly = array(diag(kvar), dim = c(kvar, kvar,
  1)), ma.poly = array(diag(kvar), dim = c(kvar, kvar, 1)), means = 1)

Arguments

Value

estimates = estimated values for input series

residuals = corresponding residuals. It is noted that the residuals computed by arma.filter may deviate slightly from the marima-residuals (which are taken from the last repeated regression step performed). The residuals computed by arma.filter are constructed by filtering (successive use of the arma model) and using a heuristic method for the first residuals.

averages = averages of variables in input series

mean.pattern = pattern of means as used in filtering

Examples

library(marima)
data(austr)
series<-t(austr)[,1:90]
# Define marima model
Model5 <- define.model(kvar=7,ar=1,ma=1,rem.var=1,reg.var=6:7)

# Estimate marima model
Marima5 <- marima(series,Model5$ar.pattern,Model5$ma.pattern,penalty=1)

# Calculate residuals by filtering
Resid <- arma.filter(series, Marima5$ar.estimates,
     Marima5$ma.estimates)

# Compare residuals

plot(Marima5$residuals[2, 5:90], Resid$residuals[2, 5:90],
xlab='marima residuals', ylab='arma.filter residuals')

arma.forecast

Description

Forecasting of (multivariate) time series of using marima type model.

Usage

arma.forecast(series = NULL, marima = NULL, nstart = NULL, nstep = 1,
  dif.poly = NULL, check = TRUE)

Arguments

Value

forecasts = forecasted values following the nstart first values of the input series (at time points 'nstart+1,...,nstart+nstep'). The forecasted values will be (over-) written in the input series at the proper future positions (if relevant).

residuals = corresponding residuals for input series followed by nstep future residuals (all=0).

prediction.variances = (kvar, kvar, nstep) array containing prediction covariance matrices corresponding to the nstep forecasts.

nstart = starting point for prediction (1st prediction at point nstart+1).

nstep = length of forecast

Examples

library(marima)
data(austr)
series<-austr
Model5 <- define.model(kvar=7, ar=1, ma=1, rem.var=1, reg.var=6:7)
Marima5 <- marima(ts(series[1:90, ]), Model5$ar.pattern, Model5$ma.pattern, 
penalty=1)

nstart  <- 90
nstep   <- 10
cat("Calling arma.forecast.\n")
cat("In the example the input series is dim(length,kvar).\n")
cat("and of type ts() (timeseries) for illustration. \n")
Forecasts <- arma.forecast(series=ts(series), marima=Marima5, 
               nstart=nstart, nstep=nstep )
Year<-series[91:100,1]
One.step <- Forecasts$forecasts[, (nstart+1)]
One.step
Predict  <- Forecasts$forecasts[ 2, 91:100]
Predict
stdv<-sqrt(Forecasts$pred.var[2, 2, ])
upper.lim=Predict+stdv*1.645
lower.lim=Predict-stdv*1.645
Out<-rbind(Year, Predict, upper.lim, lower.lim)
print(Out)
# plot results:
plot(series[1:100, 1], Forecasts$forecasts[2, ], type='l', xlab='Year', 
ylab='Rate of armed suicides', main='Prediction of suicides by firearms', 
ylim=c(0.0, 4.1))
lines(series[1:90, 1], series[1:90, 2], type='p')
grid(lty=2, lwd=1, col='black')
Years<-2005:2014
lines(Years, Predict, type='l')
lines(Years, upper.lim, type='l')
lines(Years, lower.lim, type='l')
lines(c(2004.5, 2004.5), c(0.0, 2.0), lty = 2)

Data set for testing marima package (australian killings)

Description

Data for marima examples.

Usage

data(austr)

Format

A data frame (austr) with 7 columns and 100 rows.

Year

Year for data

suic.fire

Rate of suicides by firearms

homi.fire

Rate of homicides by firearms

suic.other

Rate of suicides by non firearms

homi.other

Rate of homicides by non firearms

leg

Legislation against firearms in effect

acc.elg

Accumulated effect of legislation in years

check.one

Description

Function to check and insert leading unity matrix if NOT present.

Usage

check.one(polyn = NULL)

Arguments

Value

polyn (array) with a leading unity matrix being inserted if not present.

Examples

set.seed(4711)
X <- array(rnorm(32),dim=c(4, 4, 2))
X <- check.one(X)
short.form(X)

define.dif

Description

Function to generate and apply a differencing matrix polynomial (autoregressive form) defined by a pattern.

To be used before calling marima in order to difference the timeseries before the marima analysis. The averages of the variables in the time series are subtracted from the input series before differencing.

Usage

define.dif(series = series, difference = NULL)

Arguments

Value

y.dif = the differenced timeseries (the complete part)

y.lost = the first observations lost because of differencing

dif.poly = differencing polynomial array = c(kvar, kvar, ...) holding the autoregressive representation of the specified differencing

averages = the averages of the original series as they were subtracted before differencing

dif.series = the differenced series (y.lost followed by y.dif)

Examples

# Generate Y=series with 4 variables for illustration:
set.seed(4711)
Y<-matrix(round(100*rnorm(40)+10), nrow=4)

# Example 1: use of difference parameter: If
difference=c(2, 1, 2, 1, 3, 12)
difference
# the variable 2 is differenced
# twice, and variable 3 is differenced once with lag=12.

# Example 2:
poly <- define.dif(series=Y, difference=c(2, 1, 3, 1, 3, 1))
poly
# Generates a (4-variate) polynomial differencing array (with a leading
# unity matrix corresponding to lag=0, and (in the example) differencing
# of variable 2 for lag 1 and variable 3 for lag 1 but twice. Afterwards
# the series Y is differenced accordingly. Results in poly$series and
# poly$dif.poly .

# Example 3: Generation and application of multivariate differencing
# polynomial. Re-use the 4-variate time series and use the
# differencing polynomial (ar-form):
# var=1, dif=1, var=2, dif=6, and var=3 and 4, no differencing.
dif.y <-define.dif(Y, c(1, 1,  2, 6,  3, 0,  4, 0))
# Now dif.y contains the differenced series and the differencing
# polynomial. Print the generated polynomial in short form:
short.form(dif.y$dif.poly)
# Specifying no differencing (3, 0 and 4, 0) may be omitted:
dif.y <-define.dif(Y, c(1, 1,  2, 6))
dif.y

# Example 4:
y<-matrix(round(rnorm(1200)*100+50), nrow=6)
library(marima)
difference<-c(3, 2, 4, 0, 5, 0, 6, 7)
matrix(difference, nrow=2)
Y<-define.dif(y, difference=difference)
round(rowMeans(Y$dif.series), 2)
round(Y$averages, 2)

define.model

Description

Function to define multivariate arma model (indicator form) for marima.

Usage

define.model(kvar = 1, ar = 0, ma = 0, rem.var = 0, reg.var = 0,
  no.dep = NULL, print = 0, ar.fill = NULL, ar.rem = NULL,
  ma.fill = NULL, ma.rem = NULL, indep = NULL)

Arguments

Value

ar.pattern a matrix polynomium (an array) with 1's and 0's defining the autoregressive matrix polynomium to be fitted by marima (an array with dim=c(kvar, kvar, 1+ar_order) (with leading unity matrix)).

ma.pattern a matrix polynomium (an array) with 1's and 0's defining the moving average matrix polynomium to be fitted by marima (an array with dim=c(kvar, kvar, 1+ma_order) (including the leading unity matrix)).

Examples

#
# Example 1: 3-variate arma model with ar-lags at 1 and 2, and an
# ma-term at lag 1. And var=3 is a regression variable (X-variable).
#
 Model1 <- define.model(kvar=3, ar=c(1, 2), ma=c(1), reg.var=3)
 short.form(Model1$ar.pattern)
 short.form(Model1$ma.pattern, leading=FALSE)
#
# The object Model1 contains the ar- and ma-pattern arrays as defined.
#
# Model1$ar.pattern and Model1$ma.pattern are used as input to
# marima in order to define the model to be estimated.
#
# Example 2: arma model with ar-lags at 1, 2 and 6, and var=3
#  regression variable (X-variable).
#
 Model2 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3)
# Print the ar- and ma-polynomial patterns using
 short.form(Model2$ar.pattern, leading=FALSE)
 short.form(Model2$ma.pattern, leading=TRUE)
#
# Example 3: arma model with ar-lags at 1, 2 and 6, and reg.var=3
# (X-variable). ma-order=1. Finally (ar.fill=c(2, 3, 4) puts  a '1'
# for (dep-var=2, indep-var=3, ar-lag=4).
#
# If further modifications of the ar- or ma-patterns are needed, it
# can be accomplished before calling marima (Model3$ar.pattern and
# Model3$ma.pattern are arrays).
#
 Model3 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3,
    ar.fill=c(2, 3, 4))
 short.form(Model3$ar.pattern)
 short.form(Model3$ma.pattern)
#
 Model4 <- define.model(kvar=3, ar=c(1, 2, 6), ma=c(1), reg.var=3, 
 ar.fill=c(2, 3, 4), indep=c(1))
 short.form(Model4$ar.pattern)
 short.form(Model4$ma.pattern, leading=FALSE)

define.sum

Description

Function to aggregate multivariate time series. Reverse of function 'define.dif'.

Usage

define.sum(series = NULL, difference = NULL, averages = 0)

Arguments

Value

sum.series the summed series.

Examples

set.seed(4711)
y <- round(matrix(100*rnorm(48), nrow=4))
difference=matrix(c(1, 1,  1, 1,  2, 1,  3, 6), nrow=2)
dy <- define.dif(y, difference)$dif.series
averages <- define.dif(y, difference)$averages
sum.y <- define.sum(dy, difference, averages)$series.sum
y
dy
averages
sum.y

forec.var

Description

Function for calculation of variances of nstep forecasts using a marima type model.

Usage

forec.var(marima, nstep = 1, dif.poly = NULL)

Arguments

Value

pred.var = variance-covariances for nstep forecasts (an array with dimension (kvar, kvar, nstep).

rand.shock = corresponding random shock representation of the model used.

inverse.form

Description

Calculation of inverse form for arma model

Usage

inverse.form(ar.poly, ma.poly, L)

Arguments

Value

inverse form for arma model up to order L (array(k, k, L+1)).

Examples

set.seed(4711)
p1  <- check.one(matrix(rnorm(16), nrow=4))
p2  <- check.one(array(rnorm(32),dim=c(4, 4, 2)))
inverse <- inverse.form(ar.poly=p1, ma.poly=p2, L=6)
short.form(inverse)

lead.one

Description

Function to add (or remove) a leading unity matrix to (from) an array (being an array representation of ar- or ma-polynomial).

Usage

lead.one(polyn = NULL, add = 0)

Arguments

Value

changed array (with leading unity matrix inserted or removed).

marima

Description

Estimate multivariate arima and arima-x models. Setting up the proper model for (especially) arima-x estimation can be accomplished using the routine 'define.model' that can assist in setting up the necessary autoregressive and moving average patterns used as input to 'marima'.

A more elaborate description of 'marima' and how it is used can be downloaded from:

http://www.imm.dtu.dk/~hspl/marima.use.pdf

Usage

marima(DATA = NULL, ar.pattern = NULL, ma.pattern = NULL, means = 1,
  max.iter = 50, penalty = 0, weight = 0.33, Plot = "none",
  Check = FALSE)

Arguments

Value

Object of class marima containing:

N = N length of analysed series

kvar = dimension of time series (all random and non-random variables).

ar.estimates = ar-estimates

ma.estimates = ma-estimates

ar.fvalues = ar-fvalues (approximate)

ma.fvalues = ma-fvalues (approximate)

ar.stdv = standard devaitions of ar-estimates (approximate)

ma.stdv = standard deviations of ma-estimates (approximate)

ar.pvalues = ar.estimate p-values (approximate). If in the input data two series are identical or one (or more) series is (are) linearly dependent of the the other series the routine lm(...) generates "NA" for estimates t-values, p-values and and parameter standard deviations. In marima the corresponding estimates, F-values and parameter standard deviations are set to 0 (zero) while the p-value(s) are set to "NaN". Can happen only for ar-parameters.

ma.pvalues = ma.estimate p-values (approximate)

residuals = estimated residuals (for used.cases), leading values (not estimated values) are put equal to NA

fitted = estimated/fitted values for all data (including non random variables) (for used.cases), leading values (not estimated values) are put equal to NA

resid.cov = covariance matrix of residuals (including non random variables) (computed for used.cases)

data.cov = covariance matrix of (all) input data (for used.cases)

averages = averages of input variables

Constant = estimated model constant = (sum_i(ar[, , i])) x averages

call.ar.pattern = calling ar.pattern

call.ma.pattern = calling ma.pattern

out.ar.pattern = resulting ar.pattern (after possible model reduction)

out.ma.pattern = resulting ar.pattern (after possible model reduction)

max.iter = max no. of iterations in call

penalty = factor used in AIC model reduction, if penalty=0, no AIC model redukction is performed (default).

weight = weighting of successive residuals updating (default=0.33)

used.cases = cases in input which are analysed

trace = trace(random part of resid.cov)

log.det = log(det(random part of resid.cov))

randoms = which are random variables in problem?

one.step = one step ahead prediction (for time = N+1) based on whole series from obs. 1 to N. The computation is based on the marima residuals (as taken from the last regression step in the repeated pseudo-regression algorithm).

Source

The code is an R code which is based on the article (below) by Spliid (1983). A repeated (socalled) pseudo regression procedure is used in order to estimate the multivariate arma model.

References

Jenkins, G.M. & Alavi, A. (1981): Some aspects of modelling and forecasting multivariate time series, Journal of Time Series Analysis, Vol. 2, issue 1, Jan. 1981, pp. 1-47.

Madsen, H. (2008) Time Series Analysis, Chapmann \& Hall (in particular chapter 9: Multivariate time series).

Reinsel, G.C. (2003) Elements of Multivariate Time Series Analysis, Springer Verlag, 2$^nd$ ed. pp. 106-114.

Shumway, R.H. & Stoffer, D.S. (2000). Time Series Analysis and Its Applications, Springer Verlag, (4$^th$ ed. 2016).

Spliid, H.: A Fast Estimation Method for the Vector Autoregressive Moving Average Model With Exogenous Variables, Journal of the American Statistical Association, Vol. 78, No. 384, Dec. 1983, pp. 843-849.

Spliid, H.: Estimation of Multivariate Time Series with Regression Variables:

http://www.imm.dtu.dk/~hspl/marima.use.pdf

www.itl.nist.gov/div898/handbook/pmc/section4/pmc45.htm

Examples

# Example 1:
library(marima)
# Generate a 4-variate time series (in this example):
#
kvar<-4 ; set.seed(4711)
y4<-matrix(round(100*rnorm(4*1000, mean=2.0)), nrow=kvar)
# If wanted define differencing of variable 4 (lag=1)
# and variable 3 (lag=6), for example:
y4.dif<-define.dif(y4, difference=c(4, 1, 3, 6))
# The differenced series will be in y4.dif$y.dif, the observations
# lost by differencing being excluded.
#
y4.dif.analysis<-y4.dif$y.dif
# Give lags the be included in ar- and ma-parts of model:
#
ar<-c(1, 2, 4)
ma<-c(1)
# Define the multivariate arma model using 'define.model' procedure.
# Output from 'define.model' will be the patterns of the ar- and ma-
# parts of the model specified.
#
Mod <- define.model(kvar=4, ar=ar, ma=ma, reg.var=3)
arp<-Mod$ar.pattern
map<-Mod$ma.pattern
# Print out model in 'short form':
#
short.form(arp)
short.form(map)
# Now call marima:
Model <- marima(y4.dif.analysis, ar.pattern=arp, ma.pattern=map, 
                penalty=0.0)
# The estimated model is in the object 'Model':
#
ar.model<-Model$ar.estimates
ma.model<-Model$ma.estimates
dif.poly<-y4.dif$dif.poly  # = difference polynomial in ar-form.
# Multiply the estimated ar-polynomial with difference polynomial
# to compute the aggregated ar-part of the arma model:
#
ar.aggregated <- pol.mul(ar.model, dif.poly, L=12)
# and print everything out in 'short form':
#
short.form(ar.aggregated, leading=FALSE)
short.form(ma.model, leading=FALSE)

marima.sim

Description

Simulation of multivariate arma model of type 'marima'.

Usage

marima.sim(kvar = 1, ar.model = NULL, ar.dif = NULL, ma.model = NULL,
  averages = rep(0, kvar), resid.cov = diag(kvar), seed = NULL,
  nstart = 0, nsim = 0)

Arguments

Value

Simulated kvar variate time series of length = nsim.

Examples

library(marima)
data(austr)
old.data <- t(austr)[, 1:83]
Model2   <- define.model(kvar=7, ar=c(1), ma=c(1),
                    rem.var=c(1, 6, 7), indep=NULL)
Marima2  <- marima(old.data, means=1, ar.pattern=Model2$ar.pattern, 
 ma.pattern=Model2$ma.pattern, Check=FALSE, Plot="none", penalty=4)

resid.cov  <- Marima2$resid.cov
averages   <- Marima2$averages
        ar <- Marima2$ar.estimates
        ma <- Marima2$ma.estimates

N    <- 1000
kvar <- 7

y.sim <- marima.sim(kvar = kvar, ar.model = ar, ma.model = ma, 
  seed = 4711, averages = averages, resid.cov = resid.cov, nsim = N)

# Now simulate from model identified by marima (model=Marima2).
# The relevant ar and ma patterns are saved in 
# Marima2$out.ar.pattern and Marima2$out.ma.pattern, respectively: 

Marima.sim <- marima( t(y.sim), means=1, 
     ar.pattern=Marima2$out.ar.pattern, 
     ma.pattern=Marima2$out.ma.pattern, 
     Check=FALSE, Plot="none", penalty=0) 

cat("Comparison of simulation model and estimates", 
" from simulated data. \n")
   round(Marima2$ar.estimates[, , 2], 4)
round(Marima.sim$ar.estimates[, , 2], 4)

   round(Marima2$ma.estimates[, , 2], 4)
round(Marima.sim$ma.estimates[, , 2], 4)

pol.inv

Description

Calculation of left inverse of matrix polynomial. The leading term is expected to be the (k by k) identity matrix. This is checked and the proper leading unity term is taken into account when the inverse is calculated.

phi = matrix polynomial coefficients = I, phi1, phi2, ..., phi(p).

dim(phi) = c(k, k, p+1) where k = dimension of coefficient matrices (k by k), and L = order of polynomial (length = 1+L , including the leading unity matrix).

Usage

pol.inv(phi, L)

Arguments

Value

left inverse of phi of order L (L+1 terms including leading unity matrix)

Examples

set.seed(4711)
p2<-check.one(array(rnorm(32),dim=c(4,4,2)))
pi2<-pol.inv(p2,L=12)
short.form(pi2)

pol.mul

Description

Calculation of product of two matrix polynomials (arrays).

If one or both leading unity matrices (of eta and theta) are missing, they are (it is) generated (and taken into account).

Usage

pol.mul(eta, theta, L)

Arguments

Value

matrix polynomial product af eta and theta

Examples

set.seed(4711)
p1 <- check.one(matrix(rnorm(16), nrow=4))
p2 <- check.one(array(rnorm(32),dim=c(4, 4, 2)))
p12 <- pol.mul(p1, p2, L=(2+3))
short.form(p12)

pol.order

Description

Function to evaluate (significant) order of matrix polynomium.

Usage

pol.order(polyn = NULL, digits = 12)

Arguments

Value

pol.order order of polynomium polyn. (exclusive the leading unity matrix if present. pol.order=0 corresponds to the k by k unity matrix)

Examples

pol          <- array(1e-8*rnorm(96),dim=c(4,4,6))
pol[, , 1:3] <- array(rnorm(48), dim=c(4,4,3))
pol.order(polyn=pol, digits=12)
pol.order(polyn=pol, digits=4)

print.marima

Description

Print some (most relevant) content of a marima object.

Usage

## S3 method for class 'marima'
print(x, estimates = TRUE, pvalues = FALSE,
  pattern = TRUE, fvalues = TRUE, ...)

Arguments

rand.shock

Description

Calculation of random shock form for arma model

Usage

rand.shock(ar.poly, ma.poly, L)

Arguments

Value

random shock form of arma model up to order L (array(k,k,L+1))

Examples

set.seed(4711)
p1 <- check.one(matrix(rnorm(16),nrow=4))
p2 <- check.one(array(rnorm(32),dim=c(4, 4, 2)))
randshock <- rand.shock(ar.poly=p1, ma.poly=p2, L=6)
short.form(randshock)

season.lagging

Description

Generate new time series with (seasonally) lagged variables from lagging pattern.

Usage

season.lagging(y, lagging = NULL)

Arguments

Value

y.lagged = the part of the new series (including new lagged variables) that can be entered into marima

y.future = the part of the new series (including new lagged variables) that does not include future observation

y.lost = previous values of the time series that is incomplete with respect to the new variables generated by lagging

cbind(y.lost, y.lagged.y, y.future) is the complete series after creation and addition of the lagged variables.

Examples

set.seed(4711)
# generate bivariate time series
y<-round(matrix(10*rnorm(36), nrow=2))
y
# define new lagged variables (y3 and y4) with seasonalities 6 and 12
lagging <- c(1, 3, (6-1),  2, 4, (12-1)) 
season.lagging(y, lagging)

short.form

Description

Function to condensate (and/or) print out matrix polynomium leaving out empty lag matrices and, if specified, the leading (unity) matrix.

Usage

short.form(poly = NULL, name = "Lag=", leading = TRUE, tail = FALSE,
  digits = 6)

Arguments

Examples

Model<-define.model(kvar=4, ar=c(1, 2, 4), ma=c(1), reg.var=4)
short.form(Model$ar.pattern)
short.form(Model$ma.pattern)
short.form(Model$ar.pattern, leading=FALSE)
short.form(Model$ar.pattern, leading=FALSE)
#
M<-define.model(kvar=4, ma=c(1))
short.form(M$ar.pattern)
short.form(M$ar.pattern, tail=TRUE)
short.form(M$ar.pattern, leading=FALSE, tail=TRUE)