I
'[This
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question paper contains 4 printed pages.]
1156 4
Yoiur Roll No...............
define two processes of moving Summation. Show
that both have the same correlogram.
Sr. No. of Question Paper 11s6 c
(b) For the autoregressive series y,*, * ay,*, a by' = e,*r, Unique Paper Code 32377905
lbl < l, a'?- 4b < 0, show that the correlogram
of
Name of the Paper Time Series Analysis
,. sin(k0 + d)
p"-
order k is given by ,io* ;k=0.tI'+2'... Name of the Course B.Sc. (Hons.) Statistics
S e me ster
where p= J6. coso=-3, tanq=!1{tane
Duration : 3 Hours Maximum Marks : 75
(7,8)
(a) Explain clearly the steps involved in Box-Jenkins
lnstructions for Candidates
6
approach to forecasting. l. Write your Roll No. on the top immediately on receipt
of this question paPer.
(b) For the model (1 BXI 0 2B)y, = (1 - 0 5B)a,, 2. Attempt any five questions.
classify the model as an ARIMA(p,d,q) process'
3. All questions carry equal marks.
Determine whether the process is stationary and
I
invertible. Evaluate the first three y weights of
the model when expressed as an MA(oo) model' (a) Define a time series. Describe briefly the nature
of the various components of a time series.
(c) For the SARIMA (0,1,1) x (1,0,0)o model, obtain
the 4-step-ahead forecast at time n. (5,6,4) (b) Name the characteristic movement of the time
series with which you will mainly associate-
7 Write notes on any two of the following: (i) an increase in the sales of soft drinks
1a) Effect of detrending a time series during the summer months,
(b) Gompertz curve (ii) a bomb blast in Delhi,
(c) Exponential smoothing (7'/2,7 %) (iii) a fall in the death rate due to medical
advancement,
(1000)
I
P,T.O.
(
115 6 2 1156 3
(iv) Election, of the presideht in India (b) Use the'above result to show that
(c) The multiplicative model is more commonly used h2+k2+12-3
Yo+ 62yo
model as compared to the additive model in time frtnttult,lr.=l 24
series analysis. Give reasons. (7,4,4)
(c) In the above, if h = 5, k: 5, and I = 7, obtain the
2. (a) Derive the curve of the form weights of the iterated averages when the above
formula is approximated by a cubic polynomial.
(s,5,s)
u. -
'' ---0
1+6e '' "161
Show that this is a logistic curve. Explain the 4 (a) Describe the method for the estimation of the
method of three selected points for fitting this curve variance of the random component of a time
to the data regarding production in various years. series. How is this method used for finding the
degree of the trend polynomial to be fitted?
(b) What is meant by seasonal fluctuations of a time
(b) Distinguish between a strict stationary process and
series? How do they differ from cyclic fluctuations
a weak stationary process.
in a time series? Describe the method of link
relatives for measuring the seasonal variations, (c) If e, is a random series, show that the correlation
stating clearly the assumptions made. (7,8) between successive items of Ake,, for long series,
,k
3. (a) In the usual notations, prove that ls Examine the case when k is large.
k+l
(6,4,s)
h2 -l -,
[n]vo = Yo +_ b- Yo 5. (a) Let e, be purely random process. The relations
h 24
13333
._-er-t
Yt=
Uer
-gt,-z -Get-r i"r-o-"'
where [h] stands for the simple average of 'h'
h
terms
13333
=7et +-e,-t -!'€t-z +16e,-, +
Yt yert
P.T.O.
