Master of Science II (Statistics)Examination: Oct/Nov 2016
Semester III (New CBCS)
SLR No. Day
Date Time Subject Name Paper
No. Seat No.
SLR
SB 703
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
A sequence of independent and identical random variables is called
as
IID noise White noise
Random Walk MA
The process where is WN, is
MA
ARMA None of these
If mean and covariance functions are both independent of time then
the process is called as
Time Evolutionary Invertible process
Weakly stationary Strictly stationary
If γ is auto-covariance function of a WNO then
σ2 Tσ2
Zero None of the these
The auto-covariance function is
Symmetric function Non-negative definite
Both and Name of these
B. Fill in the blanks: 05
The data obtained after removal of seasonal component from the
original time series is called as
If γ is auto-covariance function of a process with usual
notations, then
The properties of time series which depends only on first and
second moments of Xt are called properties.
The process is casual, if
A real-valued function defined on the integers is the auto-covariance
function of a stationary time series iff it is and non-negative
definite.
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C. State whether following statements are true or false: 04
White noise is a strictly stationary process.
Randow walk is a white noise.
If for every Xt is expressible in terms of present and past values of Zt,
then the process is called as a causal process.
process is always invertible.
Q.2 A. Find auto-covariance and auto-correlation function of process 06
Explain sample mean, sample ACVF and sample ACF.
B. Write short note on the following 08
Second order properties of a time series.
Classical decomposition model of the time series.
Q.3 A. Explain the method of trend elimination by differencing in the absence of
seasonality.
08
B. Define an ARMA(p,q) process and state condition for its invertibility.
Examine whether the process Xt-0.45* Xt-1+0.05 Zt+0.4* Zt-1 is
invertible.
06
Q.4 A. Obtain weights for the ARMA(p,q) process with usual notations, by
expressing it as a linear process.
07
B. Describe Yule-Walker method of estimating the parameters of an
process. Obtain the same for process.
07
Q.5 A. Explain exponential smoothing in absence of seasonality. 06
B. Define linear process. Obtain its mean and auto covariance function. 08
Q.6 A. Describe turning point test and rank test to test the estimated noise sequence. 08
B. State and prove properties of auto-covariance function. 06
Q.7 A. Write a short note on ARIMA process. 07
B. Explain in brief ARCH models. 07
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