c********l
发帖数: 8138 | 1 【 以下文字转载自 Statistics 讨论区 】
发信人: coupondeal (coupon and deal), 信区: Statistics
标 题: 问一个Time Series的概念问题
发信站: BBS 未名空间站 (Sun Feb 26 19:39:12 2012, 美东)
一条是说：
“For a specific autoregressive(AR) model, a good fit to the data, the
autocorrelations of the error term should be 0 at all lags.”
另一条是说：
“The autocorrelations of most autoregressive time series start large and
decline gradually, whereas the autocorrelations of an MA(q) time series
suddenly drop to 0 after the first q autocorrelations. This helps in
distinguishing between autoregressive and moving-average time series.”
前者说AR的autocorrelation都应该是0，不然就是mis-specified model
后者说AR对于(t, t+h)的autocorrelation在的时候,在h比较小的时候可以明显不为0，
但在h比较大的时候就应该逐渐趋近于0
这难道不是自相矛盾了？ | C***m
发帖数: 120 | 2 第一条说的是 after model built, e_t and {e_s} s
然model不好。
第二条说的是observation y_t之间的关系。具体怎么回事我就不懂了。
【在 c********l 的大作中提到】
: 【 以下文字转载自 Statistics 讨论区 】
: 发信人: coupondeal (coupon and deal), 信区: Statistics
: 标 题: 问一个Time Series的概念问题
: 发信站: BBS 未名空间站 (Sun Feb 26 19:39:12 2012, 美东)
: 一条是说：
: “For a specific autoregressive(AR) model, a good fit to the data, the
: autocorrelations of the error term should be 0 at all lags.”
: 另一条是说：
: “The autocorrelations of most autoregressive time series start large and
: decline gradually, whereas the autocorrelations of an MA(q) time series
| R********n
发帖数: 519 | 3 我理解第二条是针对input time series，分析什么时候适合用AR或MA。对于适合用AR
的series，应该是autocorrelations function呈现出一种渐进下降的趋势（从r=0起）
【在 c********l 的大作中提到】
: 【 以下文字转载自 Statistics 讨论区 】
: 发信人: coupondeal (coupon and deal), 信区: Statistics
: 标 题: 问一个Time Series的概念问题
: 发信站: BBS 未名空间站 (Sun Feb 26 19:39:12 2012, 美东)
: 一条是说：
: “For a specific autoregressive(AR) model, a good fit to the data, the
: autocorrelations of the error term should be 0 at all lags.”
: 另一条是说：
: “The autocorrelations of most autoregressive time series start large and
: decline gradually, whereas the autocorrelations of an MA(q) time series
| k*****y
发帖数: 744 | 4 1)
For example, an AR(1) model is like
Y_t = E_t + A*Y_{t-1}, where {E_t} is white noise.
If the {y_t} is really a sample of this model, using linear regression we can find an 'a' and {e_t} such that:
y_t = e_t + a*y_{t-1}, and 'a' will be the maximum likelihood estimate of A given the sample {y_t}.
So the error term 'e_t' should be like a sample of white noise, hence has 0 autocorrelation at all lags.
2)
For MA(1) model: X_t = E_t + B*E_{t-1},
cor(X_t, X_{t-1}) = B/(1+B^2)
cor(X_t, X_{t-k}) = 0, when k>1.
For AR(1) model: Y_t = E_t + A*Y_{t-1}
cor(Y_t, Y_{t-k}) = A^k, hence declines gradually when |A|<1.
So the samples of these models should exhibit similar behaviors respectively.
【在 c********l 的大作中提到】
: 【 以下文字转载自 Statistics 讨论区 】
: 发信人: coupondeal (coupon and deal), 信区: Statistics
: 标 题: 问一个Time Series的概念问题
: 发信站: BBS 未名空间站 (Sun Feb 26 19:39:12 2012, 美东)
: 一条是说：
: “For a specific autoregressive(AR) model, a good fit to the data, the
: autocorrelations of the error term should be 0 at all lags.”
: 另一条是说：
: “The autocorrelations of most autoregressive time series start large and
: decline gradually, whereas the autocorrelations of an MA(q) time series
| A**u
发帖数: 2458 | 5 你们的Time series都怎么学的
诚心请教, | k*****y
发帖数: 744 | 6 同问，除了翻翻Time Series Applications to Finance by Ngai Hang Chan和Time
Series Analysis by James Hamilton这两本?
还有实际工作中会用到些什么?用来fit ARMA和GARCH?还是要generalize这些models?
Thanks.
【在 A**u 的大作中提到】
: 你们的Time series都怎么学的
: 诚心请教,
| c********l
发帖数: 8138 | |
|
