UC function

UC

Runs all relevant functions for UC modelling

UC(
  y,
  u = NULL,
  model = "?/none/?/?",
  h = 9999,
  lambda = 1,
  outlier = 9999,
  tTest = FALSE,
  criterion = "aic",
  periods = NA,
  verbose = FALSE,
  stepwise = FALSE,
  p0 = -9999.9,
  arma = TRUE,
  TVP = NULL,
  trendOptions = "none/rw/llt/dt",
  seasonalOptions = "none/equal/different",
  irregularOptions = "none/arma(0,0)"
)

Arguments

• y: a time series to forecast (it may be either a numerical vector or a time series object). This is the only input required. If a vector, the additional input periods should be supplied compulsorily (see below).

• u: a matrix of external regressors included only in the observation equation. (it may be either a numerical vector or a time series object). If the output wanted to be forecast, matrix u should contain future values for inputs.

• model: the model to estimate. It is a single string indicating the type of model for each component. It allows two formats "trend/seasonal/irregular" or "trend/cycle/seasonal/irregular". The possibilities available for each component are:

  • Trend: ? / none / rw / irw / llt / dt / td;
  • Seasonal: ? / none / equal / different;
  • Irregular: ? / none / arma(0, 0) / arma(p, q) - with p and q integer positive orders;
  • Cycles: ? / none / combination of positive or negative numbers. Positive numbers fix the period of the cycle while negative values estimate the period taking as initial condition the absolute value of the period supplied. Several cycles with positive or negative values are possible and if a question mark is included, the model test for the existence of the cycles specified. The following are valid examples with different meanings: 48, 48?, -48, -48?, 48+60, -48+60, -48-60, 48-60, 48+60?, -48+60?, -48-60?, 48-60?.

• h: forecast horizon. If the model includes inputs h is not used, the lenght of u is used instead.

• lambda: Box-Cox transformation lambda, NULL for automatic estimation

• outlier: critical level of outlier tests. If NA it does not carry out any outlier detection (default). A positive value indicates the critical minimum t test for outlier detection in any model during identification. Three types of outliers are identified, namely Additive Outliers (AO), Level Shifts (LS) and Slope Change (SC).

• tTest: augmented Dickey Fuller test for unit roots used in stepwise algorithm (TRUE / FALSE). The number of models to search for is reduced, depending on the result of this test.

• criterion: information criterion for identification ("aic", "bic" or "aicc").

• periods: vector of fundamental period and harmonics required.

• verbose: intermediate results shown about progress of estimation (TRUE / FALSE).

• stepwise: stepwise identification procedure (TRUE / FALSE).

• p0: initial parameter vector for optimisation search.

• arma: check for arma models for irregular components (TRUE / FALSE).

• TVP: vector of zeros and ones to indicate TVP parameters.

• trendOptions: trend models to select amongst (e.g., "rw/llt").

• seasonalOptions: seasonal models to select amongst (e.g., "none/differentt").

• irregularOptions: irregular models to select amongst (e.g., "none/arma(0,1)").

Returns

An object of class UComp. It is a list with fields including all the inputs and the fields listed below as outputs. All the functions in this package fill in part of the fields of any UComp object as specified in what follows (function UC fills in all of them at once):

After running UCforecast or UCestim:

• p: Estimated parameters
• v: Estimated innovations (white noise in correctly specified models)
• yFor: Forecasted values of output
• yForV: Forecasted values +- one standard error
• criteria: Value of criteria for estimated model
• iter: Number of iterations in estimation
• grad: Gradient at estimated parameters
• covp: Covariance matrix of parameters

After running UCvalidate:

• table: Estimation and validation table

After running UCcomponents:

• comp: Estimated components in matrix form
• compV: Estimated components variance in matrix form

After running UCfilter, UCsmooth or UCdisturb:

• yFit: Fitted values of output
• yFitV: Variance of fitted values of output
• a: State estimates
• P: Variance of state estimates
• aFor: Forecasts of states
• PFor: Forecasts of states variances

After running UCdisturb:

• eta: State perturbations estimates
• eps: Observed perturbations estimates

Details

UC is a function for modelling and forecasting univariate time series according to Unobserved Components models (UC). It sets up the model with a number of control variables that govern the way the rest of functions in the package work. It also estimates the model parameters by Maximum Likelihood, forecasts the data, performs smoothing, estimates model disturbances, estimates components and shows statistical diagnostics. Standard methods applicable to UComp objects are print, summary, plot, fitted, residuals, logLik, AIC, BIC, coef, predict, tsdiag.

Examples

## Not run:

y <- log(AirPassengers)
m1 <- UC(y)
m1 <- UC(y, model = "llt/different/arma(0,0)")
## End(Not run)

See Also

UC, UCvalidate, UCfilter, UCsmooth, UCdisturb, UCcomponents, UChp

Author(s)

Diego J. Pedregal