M.Sc. Statistics (SEM-III) (CBCS) EXAMINATION 2017
TIME SERIES ANALYSIS (Elective
Day Date: Tuesday, 25-04-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
Instructions: Attempt five questions.
Question No. 1 and 2 are compulsory
Attempt any 3 questions from Q.No.3 to Q.No.7
Figures to the right indicate full marks.
Q.1 Choose the correct alternatives 05
A sequence of uncorrelated random variables each with zero
mean and variance 2 is called
IID noise White noise
Random Walk MA
The process Xt- Zt, where is WN, is a causal
function of if
I I<1
If mean and covariance functions are both independent of
time then the process is called as
Time Evolutionary Invertible process
Weakly stationary Strictly stationary
The random walk process is
Weakly stationary process
Strictly stationary process
Not a stationary process
None of the these
The auto-covariance function is
Symmetric function Non-negative
Both and None of these
Fill in the blanks. 05
IID noise is stationary process.
If for a time series Xs and Xk are independent whenever
then the process is called
White noise process is stationary.
The process Xt- is invertible, if
A real-valued function defined on the integers is the autocovariance
function of a stationary time series if and only if it
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is even and
State whether following statements are true or false: 04
Every causal AR process is invertible.
Every IID noise sequence is a white noise sequence.
If for every Zt is expressible in terms of present and past
values of Xt, then the process is called as a causal process.
process is always stationary.
Q.2 Write a short note on weak stationary of a time series.
ii) Differentiate between white noise and IID noise.
Write short notes on the following:
Properties of strict stationary time series.
ii) Classical decomposition model of the time series. 6+8
Q.3 Explain moving average smoothing in the absence of
seasonality.
Define an ARMA process and state conditions for its
causality.
Examine whether the process Xt 0.45*Xt-1 +0.05 Xt-2 =Zt
0.4*Zt-1 is causal.
8+6
Q.4 Define AR process. Also, find its ACF and ACVF of a
stationary AR process.
Describe Yule-Walker method of estimating the parameters of an
AR process. Obtain the same for AR process.
7+7
Q.5 Describe the method of exponential smoothing in detail.
Define linear process. Obtain its mean and auto covariance
function.
7+7
Q.6 Describe any two methods to test the estimated noise sequence.
State and prove properties of auto-covariance function. 8+6
Q.7 Write a short note on ARIMA process.
Explain in brief ARCH and GARCH models. 7+7