1.6
Seasonal variation
The time plot should be examined to see which model, whether additive or
multiplicative is likely to give a better description. The seasonal indices
cfw_st
are
usually assumed
3.2
Autoregressive Processes
Autoregressive processes as their name suggests regressions on themselves.
A pth order autoregressive process cfw_Yt is given by
Yt = 1Yt 1 + 2Yt 2 + . pYt p + Zt
(3.2.1)
2.
STATIONARY PROCESSES
We shall describe the fundamental concepts in theory of time series models.
Introduce the concepts of stochastic processes, mean and covariance functions,
stationary processes
3.3
ARMA
An ARMA model, of order ( p, q ) is defined by
Yt = 1Yt 1 + . + pYt p + Z t + 1Z t 1 + . + q Z t q
(3.3.1)
ie
p
q
i =1
i =0
Yt = iYt i + i Z t i
which is an autoregressive moving average proc
3.
MODELS FOR STATIONARY TIME SERIES
The process cfw_Yt is called a linear process if it has a representation of the form
Yt = +
i Z t i
i =
where:
is a common mean
cfw_ i
cfw_Z t
is a sequence of
1.
INTRODUCTION
Data obtained from observations collected sequentially over time are extremely
common. For example:
In business, we observe weekly interest rates, daily closing stock prices,
monthly
3.4
Partial Autocorrelation Function (PACF)
Consider the general statement:- the partial correlation coefficient between X and Y
with dependence on a third variable Z removed is given by
Corr ( X , Y
1.5
Serial Dependence
Recall that the y ' s are not independent but are serially dependent. We can describe
the nature of the dependence using a set of autocorrelations.
1.5.1 Autocorrelation
( y1,.,
1.
INTRODUCTION
Data obtained from observations collected sequentially over time are extremely
common. For example:
In business, we observe weekly interest rates, daily closing stock prices,
monthly