Description

regarima/regarima_x13/regarima_tramoseats decomposes the time series in a linear deterministic component and in a stochastic component. The deterministic part of the series can contain outliers, calendar effects and regression effects. The stochastic part is defined by a seasonal multiplicative ARIMA model, as discussed by BOX, G.E.P., and JENKINS, G.M. (1970). jregarima/jregarima_x13/jregarima_tramoseats does the same computation but returns the Java objects without formatting the output

Usage

Arguments

Details

In the X13 and TRAMO-SEATS seasonal adjustment the first step consists of pre-adjusting the original series with a RegARIMA model, where the original series is corrected for any deterministic effects and missing observations. This step is also referred as linearization of the original series.

The RegARIMA model (model with ARIMA errors) is specified as below.

z_t=y_tβ+x_t

where:

• z_t - is the original series;

• β = (β_1,...,β_n) - a vector of regression coefficients;

• y_t = (y_{1t},...,y_{nt}) - n regression variables (outliers, calendar effects, user-defined variables);

• x_t - a disturbance that follows the general ARIMA process: φ(B)δ(B)x_t=θ(B)a_t; φ(B), δ(B) and θ(B) are the finite polynomials in B; a_t is a white-noise variable with zero mean and a constant variance.

The polynomial φ(B) is a stationary autoregressive (AR) polynomial in B, which is a product of the stationary regular AR polynomial in B and the stationary seasonal polynomial in B^s:

φ(B)=φ_p(B)Φ_{bp}(B^s)=(1+φ_1B+...+φ_pB^p)(1+Φ_1B^s+...+Φ_{bp}B^{bps})

where:

• p - number of regular AR terms (here and in 'JDemetra+' p ≤ 3);

• bp - number of seasonal AR terms (here and in 'JDemetra+' bp ≤ 1);

• s - number of observations per year (frequency of the time series).

The polynomial θ(B) is an invertible moving average (MA) polynomial in B, which is a product of the invertible regular MA polynomial in B and the invertible seasonal MA polynomial in B^s:

θ(B)=θ_q(B)Θ_{bq}(B^s)=(1+θ_1B+...+θ_qB^q)(1+Θ_1B^s+...+Θ_{bq}B^{bqs})

where:

• q - number of regular MA terms (here and in 'JDemetra+' q ≤ 3);

• bq - number of seasonal MA terms (here and in 'JDemetra+' bq ≤ 1);

The polynomial δ(B) is the non-stationary AR polynomial in B (unit roots):

δ(B)=(1-B)^d(1-B^s)^{d_s}

where:

• d - regular differencing order (here and in 'JDemetra+' d ≤ 1);

• d_s - seasonal differencing order (here and in 'JDemetra+' d_s ≤ 1);

Notations used for AR and MA processes, model denoted as ARIMA (P,D,Q)(BP,BD,BQ), are consistent with those in 'JDemetra+'.

As regards the available predefined 'JDemetra+' X13 and TRAMO-SEATS model specifications, they are described in the tables below.

X13:

TRAMO-SEATS:

Value

jregarima/jregarima_x13/jregarima_tramoseats return a jSA object. It contains the Java objects of the result of the preadjustment method without any formatting. Therefore the computation is faster than with regarima/regarima_x13/regarima_tramoseats. The results can the seasonal adjustment can be extract by get_indicators.

regarima/regarima_x13/regarima_tramoseats return an object of class "regarima" and sub-class "X13" or "TRAMO_SEATS". regarima_x13 returns an object of class c("regarima","X13") and regarima_tramoseats an object of class c("regarima","TRAMO_SEATS"). For the function regarima, the sub-class of the object depends on the used method that is defined by the class of the spec object.

An object of class "regarima" is a list containing the following components:

References

Info on 'JDemetra+', usage and functions: https://ec.europa.eu/eurostat/cros/content/documentation_en

BOX G.E.P. and JENKINS G.M. (1970), "Time Series Analysis: Forecasting and Control", Holden-Day, San Francisco.

BOX G.E.P., JENKINS G.M., REINSEL G.C. and LJUNG G.M. (2015), "Time Series Analysis: Forecasting and Control", John Wiley & Sons, Hoboken, N. J., 5th edition.

Examples