From cottrell@wfu.edu Wed Mar  2 09:18:17 2011
From: Allin Cottrell <cottrell@wfu.edu>
To: gretl-users@gretlml.univpm.it
Subject: Re: [Gretl-users] Q-statistic
Date: Wed, 02 Mar 2011 09:18:16 -0500
Message-ID: <Pine.A41.4.58.1103020912510.667908@f1n11.sp2net.wfu.edu>
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 32618_1299060857_p22AEGMR000750_snt141-w65026F7123383A3047421A8BC00@phx.gbl
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On Wed, 2 Mar 2011, Sam Sam wrote:

> I run ARIMA(1,0,1) by conditional maximum likelyhood.
> the residual is :
>
> table1:
> uhat2
> 1980:01
> 1980:02    -5.421687
> 1980:03    -0.506024
> 1980:04     1.867470
> 1980:05     1.698795
>
> I choose the options /Graphs/--/Risidual correlogram/
> output of Residual autocorrelation function shows:
>
> table2:
>  LAG      ACF          PACF          Q-stat. [p-value]
>
>     1       0.1567        0.1567          0.1964  [0.658]
>     2       -0.3373       -0.3710          1.5619  [0.458]
>     3      -0.3194       -0.2244          4.0097  [0.260]
>
> I caucualte Q-statistic by the formulation of Ljung-Box statistc from table1,
> but the values I cauculate by myself  seem not equal to the values of table2 (0.1964, 1.5619, and 4.0097)
> Maybe I mistake somewhere.

Here is a script that calculates ACF and Q just as gretl does,
using the residuals you got:

<script>
function scalar acf (int k, series y, scalar ybar)
    scalar num = 0
    scalar den = 0
    t1 = $t1
    t2 = $t2
    loop for (t=t1; t<=t2; t++) --quiet
	z = y[t] - ybar
	den += z * z
	if t - k >= t1
	    num += z * (y[t-k] - ybar)
	endif
    endloop
    return num / den
end function

function scalar LBQ (series y, int m)
    scalar ybar = mean(y)
    scalar T = $nobs
    scalar LB = 0
    # calculate acf up to lag m, cumulating LB
    loop for (k=1; k<=m; k++) --quiet
	a = acf(k, y, ybar)
	LB += a * a / (T - k)
    endloop
    LB *= T * (T + 2.0)
    return LB
end function

nulldata 5
setobs 12 1980:01 --time-series
series uhat2
smpl 1980:02 ;
uhat2 = {-5.421687, -0.506024, 1.867470, 1.698795}'

# do the calculation manually
lb = LBQ(uhat2, 1)
lb = LBQ(uhat2, 2)
lb = LBQ(uhat2, 3)

# compare gretl's built-in function
lb = ljungbox(uhat2, 1)
lb = ljungbox(uhat2, 2)
lb = ljungbox(uhat2, 3)
</script>

Allin Cottrell

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