Residual trading days

The new tests are largely based on the diagnostics developed in the last versions of the software Tramo-Seats (A. Maravall).

Notations

We consider below tests on the seasonally adjusted series ($sa_t$) or on the irregular component ($irr_t$). When the reasoning applies on both components, we will use $y_t$. The functions $stdev$ stands for “standard deviation” and $rms$ for “root mean squares”

The tests are computed on the log-transformed components in the case of multiplicative decomposition.

TD are the usual contrasts of trading days, 6 variables (no specific calendar).

Non significant irregular

When $irr_t$ is not significant, we don’t compute the test on it, to avoid irrelevant results. We consider that $irr_t$ is significant if $stdev( irr_t)>0.01$ (multiplicative case) or if $stdev(irr_t)/rms(sa_t) >0.01$ (additive case).

F test

The test is the usual joint F-test on the TD coefficients, computed on the following models:

Autoregressive model (AR modelling option)

We compute by OLS:

Difference model

We compute by OLS:

So, the latter model is a restriction of the first one ($\alpha =1, \mu =μ=\overline{\Delta y_t}$)

The tests are the usual joint F-tests on $\beta \quad (H_0:\beta=0)$.

By default, we compute the tests on the 8 last years of the components, so that they might highlight moving calendar effects.

Remark:

In Tramo, a similar test is computed on the residuals of the Arima model. More exactly, the F-test is computed on $e_t=\beta TD_t + \epsilon_t$, where $e_t$ are the one-step-ahead forecast errors.