M.Sc. (Semester III) (CBCS) Examination Oct/Nov-2017
Statistics
TIME SERIES ANALYSIS
Day Date: Monday, 25-11-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
Instructions: Q.1 and Q.2 are compulsory.
Attempt five questions.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Select the correct alternative: 05
A sequence of independent and identical random variable is called
as
IID noise White noise
Random Walk MA
The process − where is WN, is
invertible, if
1 1
0 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 white noise 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 definite
Both and None of these
Q.1 Fill in the blanks: 05
In the classical decomposition model, the slowing changing function
of t is called as component.
If for a time series and are uncorrelated whenever
− then the process is called
The properties of time series which depends only on first and
second moment of are called properties.
The process − causal if
A real-valued function defined on the integers is the auto- covariance
function of a stationary time series if and only if it is even and
Q.1 State true and false 04
Random walk is a weakly stationary process.
Every white noise sequence is an IID noise.
If for every is expressible in terms of present and past values of
then the process is called as a causal process.
MA process is always causal.
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SLR-MS-663
Q.2 Explain turning point test to test estimated noise sequence. 06
Define white noise. Write down its mean and auto-covariance
function.
08
Write short notes on the following.
Write a short note on strict stationary of a time series. 08
Classical decomposition model of the time series. 06
Q.3 Explain the method of smoothing using moving averages, when
seasonality is present in the data.
08
Define an ARMA process and state condition for its
invertibility.
Examine whether the process is − 0.05
is invertible.
06
Q.4 Find ACVF of MA process and a stationary AR process. 07
Describe Yule-Walker method of estimating the parameters of an
process. Obtain the same for AR process.
07
Q.5 Obtain the condition under which AR process has the solution.
Explain the solution for uniqueness and stationarity.
06
Define linear process and Wold's decomposition theorem. Also obtain
mean and auto covariance function of a linear process.
08
Q.6 Describe run test and rank test to test the estimated noise sequence. 08
Write a short note on SARIMA models. 06
Q.7 Discuss the need of ARIMA model. Also discuss various terms in the
model.
07
Explain in brief GARCH models. 07