
389Dependent Stochastic Processes and Time Series
a time series. It is often of interest to separate the signal from the noise. Several options are moving
average lter, running median lter, and exponential smoothing lter with forecast.
11.5 EXERCISES
Exercise 11.1
What is the stationary probability distribution when p
21
= 0.6 and p
12
= 0.4?
Exercise 11.2
Calculate the steady state for the matrix
P =
..
..
..
54
0095
56
00
Demonstrate that it is equal to X* = [0.27, 0.33, 0.33, 0.07]
T
. Conrm by examining the steady state
in Figure 11.8.
Exercise 11.3
Evaluate the stationary states according to Equation 11.23 and demonstrate that we g ...