M.Sc. (Semester IV) (CBCS) Examination Nov/Dec-2018
Statistics
TIME SERIES ANALYSIS
Time: 2½ Hours Max. Marks: 70
Instructions: Q. No. and Q. No. are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Choose the most correct alternative: 05
If T is the number of turning points of an iid sequence of length then
the expected value of T is
− 1 −
− −
If for a time series the joint distributions of … and
… are the same for all integers h and then the series
is called as
Weakly stationary Strictly stationary
Partial stationary Distributional stationary
The autocovariance function of a time series is always
non-negative positive
non-negative definite zero
The time series data, with the estimated trend component removed from
it is called
detrended deseasonalized
standard none of these
The autocovariance function of a time series
0 0 0 for all
for all All the above
Fill in the blanks: 05
A real valued function defined on integers is the autovariance function of
a stationary time series if and only if it is even and
A white noise sequence is stationary.
A process is called if can be expressed in term of the
future values of i.e. in terms of Zs, s t.
process is stationary.
Every process can be decomposed into stationary and deterministic
components using
State whether the following statement are True or False. 04
Every process needs to have seasonal component in it.
A process can be weak as well as strict stationary.
Every weakly stationary time series is strictly stationary also.
ARIMA is a stationary time series.
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SLR-VR-493
Q.2 Answer the following. 06
Describe the random walk model.
What is meant by strict stationarity of a time series?
Write short notes on the following: 08
MA models
Linear Process
Q.3 Explain white noise and IID noise. Also differentiate these two. 07
Discuss causality of process. 07
Q.4 Define an invertible process. State conditions under which an ARMA
process is invertible.
Examine whether the process − is
invertible.
07
Explain the method of estimating and eliminating trend using moving
average method as well as exponential smoothing method.
07
Q.5 Define ACVF, ACF. State their properties. Also find the ACVF and ACF of
IID Noise, White Noise and Random walk model.
07
Obtain the autocorrelation function of a stationary process. 07
Q.6 Explain in brief ARCH and GARCH process. 07
Explain Sample Autocorrelation function test and rank test for testing the
independence in estimated noise sequence.
07
Q.7 Explain the general approach to time series modeling. 07
Explain in brief the necessity of SARIMA model.