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I want to analyze the unemployment rate in Austria from 1999 to 2017, quaterly data.

Here's the code for the time series:

data<-ts(c(4.7,3.5,3.2,3.5,4.7,3.1,3.1,3.2,4.0,3.4,3.3,3.7,4.9, 
      3.6,3.6,3.8,4.8,4.2,3.9,4.3,5.8,5.4,5.3,5.4,5.7,5.7,5.6,5.6,6.0, 
      5.2,4.9,4.9,5.2,5.0,4.9,4.4,4.5,3.7,4.0,4.3,5.0,5.3,5.7,5.3, 
      5.2,4.9,4.8,4.4,5.1,4.4,4.0,4.8,4.7,4.8,5.1,4.9,5.7,5.0,5.3, 
      5.4,6.0,5.4,5.6,5.6,5.8,5.8,5.6,5.7,6.3,6.1,6.1,5.6,6.0,5.4), start=c(1999,1), end=c(2017,2), frequency=4)

What I did first was a graph to catch some features of the data generating process:Austria unemployment

What I'm wondering is: this time series comes from an I(1) is a I(0). Basically Do I need to differentiate?

I would expect not to differentiate, cause I suppose that the unemployment rate should be around the natural rate of unemployment. Maybe that's not the case and there's a structural change in the economy which shift the NA.r.u. up.

The identify if it's need a differention I performed an ADF- Augmented with constant. The result is: it inclued no delay and p-value is slightly above 5% (0.05415). So I can't reject the null hypothesis of unit root. So this indicates me to differentiate.

But first I want to see the original correlogram:

enter image description here According to this graph and my knowledge and I'm not worried for unit roots. Maybe it's only higly persistent.

So I would implement an ARMA(1,0)(2,0) which provides a good residual correlogram but not so good forecasting: enter image description here

Maybe Should I drop the first observation (till 2004) cause it seems to be more seasonl effected than the other part of time series.

Should I differentiate? And, overall, my reasonings are right?

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I am not familiar with the Austrian economy so I cannot assess the claim about the unemployment rate being close to the natural level; I understand that, should that be the case, that claim would be equivalent to asserting that there is a cointegrating relationship between the actual and the natural rates of unemployment. With that in mind, such a relationship would not disqualify the possibility that both series are explosive, in a 'similar' way.

Additionally, the recent financial crisis and its aftermath would probably justify some considerations about breaks in structural parameters of the european economy in general and Austria in particular; of course that is a tentative assumption; more testing is needed.

Taking a look at the formal tests you provide, I personally would not be comfortable treating the unemployment rate as stationary series; there seems to be indications for AR(1) components from the correlograms and the ADF does not reject the Null.

Depending on what you intend to do, I think that you'd be better off exploring some other specifications of the ADF tests and/or consider the output of stationarity tests like KPSS.

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  • $\begingroup$ According to ADF with constant I accept the null (pvalue 0.05415). If I perform and ADF with constant and trend I reject the null (pvalue 0.005531). This latter case does make no sense, unemployment rate can't be stationary on line (does that mean it's going to increase no matter what I do in the long run). Same thing with constant, lineare and quadratic trend (but this is not significant). KPSS rejects null hypothesis of level stationarity. I'm will be okay with that, but as I saw in the correlogram it's like there's no need to differentiate, the first lag is not close to1 $\endgroup$ – Mario Migliaccio Jan 21 '18 at 20:10
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    $\begingroup$ Accept Null in ADF w. const.->unempl. has unit root; Reject Null in ADF w. const+lin. trend->unempl. is trend stationary: it might seem unusual, but if you consider the case of increasing natural rate perhaps it's less counterintuitive; KPSS rejects Null->non-stationary series; ACF and PACF seem typical of AR(1); talking about the magnitude of the AR(1) coef. should be within a context of an AR(1) regression; in any case, it is really up to you how to interpret your findings and how to assess the research question; $\endgroup$ – yosimitsu kodanuri Jan 22 '18 at 8:35

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