[R] Ljung-Box test (Box.test)

Rui Barradas
Tue, 26 Jun 2012 19:13:28 -0000

Hello,

That's a statistics question, but it's also about using an R function.

The Ljung-Box test isn't supposed to be used in such a context, to test
the residuals of an ols y = bX + e. It is used to test time independence
of the original series or of the residuals of an ARMA(p, q) fit.

In both cases you are right, 'x' is a series.
'lag' can be explained as follows: you have a time series and want to
know if the value observed today depends on what was observed in the
past. Then, a linear regression of "today" on "yesterday"
could be

X[t] = b[1]*X[t-1] + e[t], e ~ Normal(0, sigma^2)

A linear regression on two time units in the past would be

X[t] = b[1]*X[t-1] + b[2]*X[t-2] + e[t], e ~ Normal(0, sigma^2)

etc. This is a regression of the series on itself lagged by a certain
number of time units, the present is regressed on the past. Function
ar() fits this kind of model to a time series. In the first case, the
order is p=1, in the second, p=2.

Now, in the first case, is there second order serial correlation? Test
the residuals with lag=2, fitdf=1, the value of p. Third order? lag=3,
fitdf=p=1, etc.

You are NOT fitting this type of model, so the Ljung-Box test is
misused. Test the original series with default parameters, lag=1. If
there is serial correlation, fit an AR (Auto-Regressive) model with
ar(). See the help page ?ar. And see a statiscian with experience in
time series. It's a world on its own, I haven't even mentioned
seasonality. And almost everything else about time series.

Do ask someone near you.

Hope this helps,

Rui Barradas
Em 26-06-2012 19:01, Steven Winter escreveu:
> I fit a simple linear model y = bX to a data set today, and that produced
24 residuals (I have 24 data points, one for each year from 1984-2007). I would
like to test the time-independence of the residuals of my model, and I was
recommended by my supervisor to use the Ljung-Box test. The Box.test function in
R takes 4 arguments:
>
> x a numeric vector or univariate time series.
> lag the statistic will be based on lag autocorrelation
> coefficients.
> type test to be performed: partial matching is used.
> fitdf number of degrees of freedom to be subtracted if x is a series of
residuals.
>
> Unfortunately, I never took a statistics class where I learned the
Ljung-Box test, and information about it online is hard to find. What does
"lag" mean, and what value would you guys recommend I use for the
test? Also, what does "fitdf" represent, and what would the value for
that parameter be in my case? Finally, the value of x is a vector of my 24
residuals, correct?
>
> Thank you all so much. I apologize for the basic nature of the question.
>
> Steven
> 	[[alternative HTML version deleted]]
>
>
>
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