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Type:

Package

Title:

Multiple Unobserved Sources of Error State Space Models

Version:

0.1.0

Date:

2026-06-26

URL:

https://github.com/config-i1/muse

BugReports:

https://github.com/config-i1/muse/issues

Language:

en-GB

Description:

Implements the Power / Trend / Seasonal (PTS) model, a unified state-space framework based on the Multiple Source of Error (MSOE) model. It brings the trend, seasonal and irregular component models of Harvey (1989) <doi:10.1017/CBO9781107049994>, Durbin and Koopman (2012) <doi:10.1093/acprof:oso/9780199641178.001.0001>, Proietti (2000) <doi:10.1016/S0169-2070(00)00037-6>, Sbrana and Silvestrini (2023) <doi:10.1016/j.ijforecast.2022.03.003> and others together under a single estimation, selection and forecasting interface, with an optional Box-Cox power transformation. Models are estimated by maximum likelihood through the Kalman filter and smoother, with automatic component selection by information criteria.

License:

LGPL-2.1

Depends:

R (≥ 3.0.2), greybox, smooth

Imports:

Rcpp (≥ 0.12.3), generics (≥ 0.1.2), zoo

LinkingTo:

Rcpp, RcppArmadillo (≥ 0.8.100.0.0)

Suggests:

testthat (≥ 3.0.0), knitr, rmarkdown

VignetteBuilder:

knitr

Config/testthat/edition:

Encoding:

UTF-8

ByteCompile:

true

Config/roxygen2/version:

8.0.0

RoxygenNote:

8.0.0

NeedsCompilation:

yes

Packaged:

2026-06-25 16:48:33 UTC; config

Author:

Diego J. Pedregal

[aut, ctb], Ivan Svetunkov

[aut, cre] (Senior Lecturer at Centre for Marketing Analytics and Forecasting, Lancaster University, UK)

Maintainer:

Ivan Svetunkov <ivan@svetunkov.com>

Repository:

CRAN

Date/Publication:

2026-06-30 20:30:17 UTC

muse package

Description

Package contains functions implementing Multiple Source of Error state space models for purposes of time series analysis and forecasting.

Details

Package:	muse
Type:	Package
Date:	2024-10-18 - Inf
License:	LGPL-2.1

The following functions are included in the package:

Author(s)

Diego J. Pedregal, Diego.Pedregal@uclm.es

Ivan Svetunkov, ivan@svetunkov.com

Examples


x <- rnorm(100,100,10)

Initial state values for a fitted `pts` object.

Description

Returns the smoothed structural states at the first observation, with the "Error" and "Fit" columns dropped. For deterministic components – e.g. the slope under the global (G) trend, where the slope is fixed throughout the horizon – this equals the t = 0 initial value; for stochastic components it is the smoother's estimate at t = 1, a close proxy to the t = 0 initial.

Usage

initials(object, ...)

Arguments

object

A fitted object of class "pts".

...

Unused.

Value

Named numeric vector of initial structural-state values.

pts: Power / Trend / Seasonal state-space model

Description

Estimates a PTS (Power / Trend / Seasonal) state-space model for a univariate time series. This is the user-facing entry point of the muse package and mirrors the calling convention used elsewhere in the smooth family: pts() estimates the model, and forecast.pts produces forecasts from the fitted object without re-estimating.

Usage

pts(data, model = "ZZZ", lags = stats::frequency(data), orders = list(ar
  = 0, ma = 0, select = FALSE), formula = NULL, regressors = c("use"),
  outliers = c("ignore", "use", "select"), level = 0.99, ic = c("AICc",
  "BICc", "BIC", "AIC"), lambda_estim = c("likelihood", "guerrero",
  "decomp-guerrero"), biasadj = FALSE, h = 0, holdout = FALSE,
  verbose = FALSE, ...)

Arguments

data

response series. Either a univariate ts / zoo / numeric vector, OR a matrix / data.frame whose first column is the response and whose remaining columns are external regressors (xregs).

model

3-letter PTS specification string. The three positions encode Power / Trend / Seasonal:

Power: Z to estimate Box-Cox \lambda, or a numeric value (e.g. "0", "0.5", "1").
Trend: Z (auto), N (none / random walk), L (local linear), D (damped / smooth random walk), G (global / deterministic).
Seasonal: Z (auto), N (none), D (discrete / linear), T (trigonometric / equal).

lags

seasonal period (default frequency(data)). Scalar for the structural seasonal; may also be a vector c(1, s) mirroring smooth::adam's convention – the last entry is the structural period, the full vector becomes the default lag set for the irregular's ARMA blocks (overridable per-fit via orders$lags).

orders

ARMA / SARMA spec for the irregular component. Three forms:

Full list list(ar, ma, select) for a non-seasonal ARMA(p, q) – ar, ma non-negative scalars (default 0); select = TRUE asks the engine to search ARMA orders up to that cap.
Numeric shortcut c(p, q) – equivalent to list(ar = p, ma = q, select = FALSE); c(p) is treated as c(p, 0).
Seasonal list(ar = c(p, P), ma = c(q, Q), lags = c(1, s)) for SARMA(p, q)(P, Q)_s – ar / ma are length-L vectors paired position-wise with lags, with lags[1] = 1 (non-seasonal block) and lags[2] = s (seasonal block). If orders$lags is omitted the default falls back to the top-level lags argument (or c(1, frequency(data))). The seasonal SARMA polynomial is multiplied internally, so the BFGS only optimises the free \phi_i, \Phi_j, \theta_i, \Theta_j coefficients. select = TRUE runs a grid search over every (p', q', P', Q') tuple with 0 \le p' \le ar[1] and so on, and picks the candidate with the lowest ic.

PTS has no differencing – any orders$i supplied is silently ignored.

formula

optional formula response ~ x1 + x2 + ...; only meaningful when data is a matrix or data.frame. Used to pick the response column + xreg columns explicitly.

regressors

handling of xregs. Currently only "use" (apply all supplied xregs as fixed-coefficient covariates). Adam's "select" and "adapt" modes are not yet implemented.

outliers

what to do about outliers, mirroring adam()'s interface: "ignore" (default – fit ignores the possibility of outliers) or "use" (run the engine's outlier detector once after the structural fit, classify each event as AO / LS / SC, and refit with the detected events as fixed regressor dummies). Adam's "select" mode (IC-pruning of detected dummies) is not yet supported – passing it errors with a clear message. When outliers = "use" the detected events are returned on the fitted object as $outliersDetected (a data frame with time and type columns) and the corresponding dummy coefficients appear in coef(m) as Beta(...) entries.

level

confidence level driving the outlier z-score threshold (default 0.99). Translated to a two-sided z via qnorm((1 + level) / 2): 0.99 -> ~= 2.576, 0.95 -> ~= 1.960. The z drives the AO threshold; LS / SC scale proportionally to preserve the engine's relative stiffness (LS ~= 1.087*z, SC ~= 1.304*z). Ignored when outliers = "ignore".

ic

information criterion for automatic model selection; one of "AICc" (default), "BICc", "BIC", "AIC". Matches the adam option set; AICc is the default, as in adam.

lambda_estim

how the Box-Cox power \lambda is chosen when the power slot of model is "Z"; one of:

"likelihood" (default) – estimate \lambda jointly with the structural parameters by maximum likelihood in the engine.
"guerrero" – the classical Guerrero (1993) variance- stabilisation screen on raw season-length blocks.
"decomp-guerrero" – Guerrero on an msdecompose-smoothed trend (the former default).

Ignored when a numeric power is supplied (e.g. "0.5ZZ").

biasadj

logical (default FALSE). Point forecasts are the back-transformed conditional median g^{-1}(\mu). When TRUE, a second-order bias correction is applied so the point forecast approximates the conditional mean (as in forecast::InvBoxCox(biasadj = TRUE)). Prediction-interval quantiles are unaffected. Has no effect at \lambda = 1.

h

forecast horizon. If h > 0 a forecast is computed at fit time and cached on the object; forecast(object, h) can later recompute for a different horizon cheaply.

holdout

logical. If TRUE and h > 0, the last h observations of data are withheld from estimation and returned in $holdout for later accuracy assessment.

verbose

logical: print intermediate optimisation output.

...

advanced / undocumented passthroughs. Supported keys:

B - numeric vector of starting values for the optimiser (natural-scale variances, in the order returned in $B by a default fit). Mirrors the same hatch in smooth::adam(). The optimised vector is returned in the $B slot of the output regardless of whether the user supplied one.

Value

An object of class c("pts", "smooth"). Slot names mirror smooth::adam()'s return list where the concept is shared; pts-only extensions are flagged below.

Inputs / spec: y, model, modelUC*, lags, lambda*
Parameters: B (estimated parameter vector), covp* (parameter covariance), nParam – an adam-style 2 x 5 matrix (rows Estimated / Provided; columns nParamInternal, nParamXreg, nParamOccurrence, nParamScale, nParamAll). nparam() returns the [Estimated, nParamAll] cell. Estimated structural initials (level/slope, cycle, seasonal states) are folded into nParamInternal, exactly as smooth::adam does
In-sample fit: fitted, residuals, states plus pts-specific comp* (additive BC-scale decomposition with Error/Fit columns)
Cached forecast: forecast (original scale, if h > 0) and forecast_args* for cheap re-forecasting
Likelihood + diagnostics: logLik, table* (C++ validation text)
Scalars read by plot.smooth / diagnostics: distribution = "dnorm", loss = "likelihood", occurrence = NULL, holdout
Bookkeeping: call, timeElapsed

AIC / AICc / BIC / BICc are derived on demand via the methods, not stored on the object. (* = pts-specific extension.)

Author(s)

Diego J. Pedregal, Diego.Pedregal@uclm.es

Ivan Svetunkov, ivan@svetunkov.com

Examples

# Automatic model selection (Power / Trend / Seasonal) on monthly data
model <- pts(AirPassengers, model = "ZZZ", h = 12, holdout = TRUE)
model

# A fixed specification: no transform, local-linear trend, trigonometric
# seasonality, with a 12-step forecast
fixedModel <- pts(AirPassengers, model = "1LT", h = 12)
forecast(fixedModel, h = 12)

S3 methods for objects of class `pts`

Description

Standard accessors and printing for fitted pts objects. forecast(object, h) generates forecasts from the fitted parameters without re-running the optimiser; predict(object) returns the in-sample fitted values.

print.pts mirrors smooth::print.adam (smooth/R/adam.R:5862) section by section, substituting the PTS-specific MSOE concepts where ETS-specific ones do not apply: the "initialisation" line becomes the Box-Cox \lambda block, and the "Persistence vector g" block becomes the MSOE innovation variances (the same variances are otherwise the structural pieces of the B parameter vector). The C++ validation diagnostics live on $cppOutput should the user want them.

forecast.pts uses the C++ forecastOnly entry point: it skips re-estimation and just propagates the Kalman filter h steps forward from the fitted state, so changing h is cheap. interval selects the variance source:

"prediction" (default): state propagation + future shocks (the engine's yForV). Bands the next observation.
"confidence": conditional-mean variance. In a state-space model var(E[y_{t+h}\,|\,obs]) = var(y_{t+h}\,|\,obs) - \sigma^2, where \sigma^2 is the BC-scale residual variance: we read it straight off the fitted scale, no reforecast needed.
"simulated": empirical quantiles of nsim forward paths from simulate.pts(). Returns the path matrix in $scenarios when scenarios = TRUE.
"none": no bands; lower = upper = mean.

level accepts a vector; lower / upper are then h \times nLevels matrices (or 1 \times nLevels when cumulative = TRUE). side produces two-sided / upper-only / lower-only intervals – the absent side is set to \mp\infty on the BC scale and back-transformed to the original-scale support boundary (0 for \lambda > 0, -\infty for the identity transform). cumulative = TRUE collapses the horizon into one total – exact for interval = "simulated" (sum within each path); the engine does not expose cross-step state covariance, so the other intervals fall back to simulation totals.

Usage

## S3 method for class 'pts'
print(x, digits = 4, ...)

## S3 method for class 'pts'
plot(x, which = c(1, 2, 4, 6), ...)

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

## S3 method for class 'pts'
residuals(object, ...)

## S3 method for class 'pts'
coef(object, ...)

## S3 method for class 'pts'
vcov(object, ...)

## S3 method for class 'pts'
nobs(object, all = FALSE, ...)

## S3 method for class 'pts'
logLik(object, ...)

## S3 method for class 'pts'
predict(object, newdata = NULL, ...)

## S3 method for class 'pts'
forecast(object, h = 10, newdata = NULL,
  interval = c("prediction", "confidence", "simulated", "none"),
  level = 0.95, side = c("both", "upper", "lower"), cumulative = FALSE,
  nsim = NULL, scenarios = FALSE, biasadj = NULL, ...)

## S3 method for class 'pts'
initials(object, ...)

Arguments

x, object

A fitted object of class "pts".

digits

number of significant digits used in printed output.

...

further arguments passed to underlying generics.

which

integer vector of plot panels to draw; passed through to plot.smooth (see ?smooth::plot.adam). Defaults to c(1, 2, 4, 6).

all

logical; if TRUE the holdout sample is included in the observation count. Default FALSE.

newdata

unused (reserved for forecast paths with new regressors).

h

forecast horizon (steps ahead).

interval

interval type; one of "prediction", "confidence", "simulated", or "none".

level

confidence level for prediction intervals (default 0.95).

side

one of "both", "upper", "lower" – selects two-sided vs one-sided intervals.

cumulative

if TRUE, return the cumulative h-step total.

nsim

number of simulated paths when interval = "simulated" or under the cumulative fallback (default 10000).

scenarios

if TRUE and interval = "simulated", return the simulated path matrix as $scenarios.

biasadj

point-forecast back-transform: FALSE (median, the default) or TRUE (bias-corrected mean). Defaults to the value the model was fitted with (object$biasadj).

Value

The methods return the following:

fitted, predict – the in-sample fitted values as a ts / numeric vector on the original (back-transformed) scale.
residuals – the model residuals as a ts / numeric vector on the Box-Cox scale.
coef – a named numeric vector of the estimated parameters (structural variances plus any ARMA / damping coefficients).
vcov – the parameter variance-covariance matrix.
nobs – an integer, the number of in-sample observations (plus the holdout when all = TRUE).
nparam – an integer, the number of estimated parameters (the degrees of freedom used by the information criteria).
logLik – an object of class "logLik": the maximised log-likelihood, with df and nobs attributes.
sigma, extractSigma – a numeric scalar, the residual standard deviation; extractScale – the maximum-likelihood scale of the assumed distribution.
actuals – the original response series.
modelType – a character string with the PTS model code (e.g. "PTS(0,N,T)"); modelName – a human-readable description; errorType – the character error type ("A", additive on the Box-Cox scale).
lags – the integer seasonal period; orders – a list of the irregular ARMA orders (ar, ma, lags); initials – a named numeric vector of the estimated initial structural-state values.
forecast – an object of class "pts.forecast": a list with the point forecast $mean and the interval bounds $lower / $upper (original scale), together with the forecast variance, level, and interval metadata.
print and plot are called for their side effects (console output and a diagnostic plot, respectively) and invisibly return their first argument.

Author(s)

Diego J. Pedregal, Diego.Pedregal@uclm.es

Ivan Svetunkov, ivan@svetunkov.com

References

Granger, C. W. J., & Newbold, P. (1976). Forecasting transformed series. Journal of the Royal Statistical Society: Series B (Methodological), 38(2), 189-203. doi:10.1111/j.2517-6161.1976.tb01585.x
Pankratz, A., & Dudley, U. (1987). Forecasts of power-transformed series. Journal of Forecasting, 6(4), 239-248. doi:10.1002/for.3980060403
Guerrero, V. M. (1993). Time-series analysis supported by power transformations. Journal of Forecasting, 12(1), 37-48. doi:10.1002/for.3980120104

Examples

model <- pts(AirPassengers, model = "1LT", h = 12, holdout = TRUE)
print(model)
fitted(model)
residuals(model)
# forecast 12 steps ahead with 95% prediction intervals
forecast(model, h = 12, interval = "prediction", level = 0.95)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

generics: forecast()

Package {muse}

muse package

Description

Details

Author(s)

See Also

Examples

Initial state values for a fitted `pts` object.

Description

Usage

Arguments

Value

pts: Power / Trend / Seasonal state-space model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

S3 methods for objects of class `pts`

Description

Usage

Arguments

Value

Author(s)

References

Examples

Objects exported from other packages

Description

Package {muse}

muse package

Description

Details

Author(s)

See Also

Examples

Initial state values for a fitted pts object.

Description

Usage

Arguments

Value

pts: Power / Trend / Seasonal state-space model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

S3 methods for objects of class pts

Description

Usage

Arguments

Value

Author(s)

References

Examples

Objects exported from other packages

Description

Initial state values for a fitted `pts` object.

S3 methods for objects of class `pts`