Order of integration, denoted I(d), is a summary statistic for a time series. It reports the minimum number of differences required to obtain a covariance stationary series.
A time series is integrated of order 0 if it admits a moving average representation with
where is the possibly infinite vector of moving average weights (coefficients or parameters). This implies that the autocovariance is decaying to 0 sufficiently quickly. This is a necessary, but not sufficient condition for a stationary process. Therefore, all stationary processes are I(0), but not all I(0) processes are stationary.
A time series is integrated of order d if
is integrated of order 0, where is the lag operator and
is the first difference, i.e.
In other words, a process is integrated to order d if taking repeated differences d times yields a stationary process.
An I(d) process can be constructed by summing an I(d − 1) process:
I1, i1, or I-1 may refer to :
[I15:]
Uh check this out ma,
Look I didn't mean to hurt you,
But I thought we had an understanding about how it's gonna be,
You know, (Yeaah Mann!)
You roll through or I roll through, (F to the A-B)
And we just do what we do,
You know what I'm saying, (I-15)
I ain't looking for no relationship,
But I'm goin ahead let my boy Fab holla at you...
[Fabolous:]
Yeah, this is real talk,
I told you there was others,
Now we go to war like soldiers with each other,
I'm trying to let it go not hold you like a lover,
See I'm simply P-I-M-P,
So I gotta stable-a chicks,
Unable to pick,
A babe I can lick out,
And I be labelled a trick,
If you down you can roll and if you not you can stroll,
It's just that easy,
When F-A-B's here...
[I15:]
Girl you got it twisted,
You already know how I get down,
Now you out here trippin',
On some sh*t that we already talked about,
I just want to hit it,
And you said that was cool with you,
Now you here crying to me,
Saying you want to be with a player like me,
That ain't cool...
[Chorus: I15]
My bad, didn't mean you to make you want it like that,
And I hang up, and you call me right back,
It's like you don't even know how to act, (What's going on...)
My bad, baby girl we barely even friends,
I just like to smash it now and then,
Now you got me scared to hit it again,
[I15:]
Now I don't mean to hurt you,
But it's not like you didn't know,
From the beginning,
Now you saying that you can't stand to be without me,
Now girl you talking crazy,
I'm not trying to deal with you,
Gonna keep it real with you,
Shorty I don't want to be with you...
[Chorus: I15]
My bad, didn't mean you to make you want it like that,
And I hang up, and you call me right back, (Back...)
It's like you don't even know how to act, (What's going on...)
My bad, baby girl we barely even friends, (Friends...)
I just like to smash it now and then,
Now you got me scared to hit it again, (Yeah...)
[Fabolous:]
Now you know I come through every now and then,
To see how you been couple of thou' to spend,
But you knows how it goes,
Girls act like you suppose to propose... After a month,
But I choose to refuse,
I'm the kind of the man that do's what I choose,
Whenever I want,
And it's never to front,
It's just to let you know,
It's cheaper to keep her,
I'll still will let you go, girl...
[I15:]
I've lost my patience,
With these ultimatums,
Tryin' to lock me down like incarceration,
I don't cuff 'em when I grab 'em,
I thug them with the passion,
Still running from the last one,
They tugging on my ass clip,
I don't what it is, I'm cool on that "Might Be" tip,
I ain't Damon, I'm too young for a wife and kids,
I kick it "if we", like Vivica and 50,
Like Fab said simply, we P-I-M-P...
[Chorus x2: I15]
My bad, didn't mean you to make you want it like that,
And I hang up, and you call me right back,
It's like you don't even know how to act,
My bad, baby girl we barely even friends,
I just like to smash it now and then,