Master of Science II (Statistics)Examination: Oct/Nov 2016
Semester III (Old CGPA)
SLR No. Day
Date Time Subject Name Paper
No. Seat No.
SLR SB
698
Wednesday
23/11/2016
02.30 PM
to
05.00 PM
Time Series Analysis
C
XIV
Instructions: Answer any five questions.
Q. No. and Q. No. are compulsory.
Attempt any three from Q. No. to Q. No.
Figures to the right indicate full marks.
Total Marks:70
Q.1 A. Select the correct alternative: 05
The ARMA process is nonintvertible if
1 1
3/2 None of these
A sequence of uncorrelated random variable, each with zero mean and
variance σ2 is called
IID noise White noise
MA AR
If mean and covariance function are both independent of time then the
process is
Weak stationary Strict stationary
Evolutionary process None of these
The autocovariance function satisfies
γ 0 for all h
γ for all h All of these
The ARMA process is casual if
1 1
3/2 Name of these
B. Fill in the blanks: 05
A White noise sequence is stationery.
A real-valued function defined on the integers is the autocovariance
function of a stationary time series if and only if it is even and
The Spencer 15-point moving average is a filter that passes polynomials
upto degree without distortion.
A stationary time series is if whenever
The process is stationary.
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C. State whether following statements are true or false: 04
Weak stationarity implies strict stationarity.
Mean function of weak stationary time series depends on t.
The process{Xt} is casual, if Xt has the representation in terms of
s t}.
ARCH model is used to describe a changing, possibly volatile variance.
Q.2 A. Write a short note on:
Autocorrelation function 04
iid noise and white noise 04
B. Define:
Strictly stationary time series 02
process 02
process 02
Q.3 A. Define a casual process. State conditions under which an ARMA process is
casual. Examine whether the process Xt 1.6* Xt-1 Zt 0.4 Zt-1 is casual.
06
B. Define an ARMA process and state conditions for its invertibility.
Examine the process Xt 0.5Xt-1 0.3 Xt-2 Zt 0.2Zt-1 for invertibility.
08
Q.4 A. What do you mean by smoothing of a time series? Also explain Holt-Winter
exponential smoothing.
08
B. What are the different methods of diagnostic checking in time series?
Explain the role of residual analysis in model checking.
06
Q.5 A. Describe Yule-Walker method of estimating the parameters of an
process. Obtain the same for process.
06
B. Obtain the autocorrelation function of a stationary process. 08
Q.6 A. Discuss maximum likelihood estimation of process. 08
B. Obtain an expression for one step ahead forecast of ARMA(1,1) process. 06
Q.7 A. Discuss recursive prediction of an ARMA process. 07
B. Discuss the innovation algorithm in brief. 07
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