y******g
发帖数: 41 | 1 My judgement would be no.
What do you think?
thanks |
z****g
发帖数: 1978 | 2 what do you mean?
GARCH model deals with volatility, not the noise itself.
Do you mean the dynamic of volatility? If so, clearly not, since volatility
is always positive. |
y******g
发帖数: 41 | 3 thanks for the reply.
my understanding is that garch talks aboutthe conditional variance of the
prediction error, which means that the conditional variance is a linear
funtion of past random shocks and past volatility.
My question is: if a time series shows a white noise feature in its ACF, is
it possible that its volatility having a GARCH model?
because even though the ACF shows a white noise feature (close to 0 at all
lags), but the time series plot still shows somewhat clustered volatility. |
t********a
发帖数: 810 | 4 I cant remember the basic concepts, but I think it could. basically Garch
talks about the clustering of variance, which means non-linear correlation,
while white noise is mostly about linear correlation.
in other words, garch says the second moment of w_t and w_{t-1} are not
orthogonal, while white noise says the first moment of w_t and w_{t-1} are
orthogonal. these might not be contradictory. that's why you see flat acf
for garch at non-zero lags. |
z****g
发帖数: 1978 | 5 Poor basic knowledge
Let's start from the very beginning of basic time series.
AR type models, they deal with the conditional mean.
ARCH type model, they deal with the conditional variance.
So they describe structure of the different momentum of the unit innovation
.(if
you don't know what is a unit innovation, you should do a serious review)
ACF and PACF only give information of the mean part. Then after you figure
out the
structure of conditional mean, if you still find the innovation not the
【在 y******g 的大作中提到】
: thanks for the reply.
: my understanding is that garch talks aboutthe conditional variance of the
: prediction error, which means that the conditional variance is a linear
: funtion of past random shocks and past volatility.
: My question is: if a time series shows a white noise feature in its ACF, is
: it possible that its volatility having a GARCH model?
: because even though the ACF shows a white noise feature (close to 0 at all
: lags), but the time series plot still shows somewhat clustered volatility.
|
y******g
发帖数: 41 | 6 thanks for the responses.I would clarify my understandings here then:
AR model
= linear combination of lagged data (can be seen as the conditional mean) +
white noise
ARCH assumes:
yt = conditional mean (which is seen as the prediction at the time) +
prediction error
and prediction error follows an ARCH if it is a linear combination of
prediction errors of past and their variances
I figure ACF talks about the autocorrelation among lagged data, which can
form the base of assuming the conditional |
z****g
发帖数: 1978 | 7 The calculation of ACF an PACF assumes the variance of the innovation is
constant.
when there is dynamics in variance, ACF/PACF itself is wrong. If you still
STICK to
PACF/ACF, we call it overfitting
+
【在 y******g 的大作中提到】
: thanks for the responses.I would clarify my understandings here then:
: AR model
: = linear combination of lagged data (can be seen as the conditional mean) +
: white noise
: ARCH assumes:
: yt = conditional mean (which is seen as the prediction at the time) +
: prediction error
: and prediction error follows an ARCH if it is a linear combination of
: prediction errors of past and their variances
: I figure ACF talks about the autocorrelation among lagged data, which can
|
y******g
发帖数: 41 | 8 i see.
why would you say that calculating ACF has to have an assumption on the
variance?
btw, even if the conditional variance themselves are time-variant, the
unconditional variance in the long time are still constants by ARCH's
properties. |
y******g
发帖数: 41 | 9 actually how would you interpret "uncorrelated"?
means tat the two is not a funtion of the other? |
z****g
发帖数: 1978 | 10 In real life, you just don't know.
In math, then you know the formula. |
z****g
发帖数: 1978 | 11 that's depends the time framework you are using.
【在 y******g 的大作中提到】
: i see.
: why would you say that calculating ACF has to have an assumption on the
: variance?
: btw, even if the conditional variance themselves are time-variant, the
: unconditional variance in the long time are still constants by ARCH's
: properties.
|
y******g
发帖数: 41 | 12 hmmmmm, okie, let me think think
thanks for the input though! |
t********a
发帖数: 810 | 13
not really. it means their first moments are orthogonal. In general,
uncorrelated is not the same as independent.
【在 y******g 的大作中提到】
: actually how would you interpret "uncorrelated"?
: means tat the two is not a funtion of the other?
|
y******g
发帖数: 41 | 14 Thanks for your input. Covariance = 0 means that E(XY) = E(X)E(Y), is this
what you mean by orthogonal first moments?
yup, they are independent only when they are normals, I get that part.
Thanks :)
【在 t********a 的大作中提到】
:
: not really. it means their first moments are orthogonal. In general,
: uncorrelated is not the same as independent.
|
