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Test for residual trading days effects

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 (sat) or on the irregular component (irrt). When the reasoning applies on both components, we will use yt. 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 irrt is not significant, we don’t compute the test on it, to avoid irrelevant results. We consider that irrt is significant if stdev(irrt)>0.01 (multiplicative case) or if stdev(irrt)/rms(sat)>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:

yt=μ+αyt1+βTDt+ϵt
Difference model

We compute by OLS:

Δyt¯Δyt=βTDt+ϵt

So, the latter model is a restriction of the first one (α=1,μ=μ=¯Δyt)

The tests are the usual joint F-tests on β(H0:β=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 et=βTDt+ϵt, where et are the one-step-ahead forecast errors.