# Expert Answers

In all the following questions, {Z

T E( Z

T k ≠ 0.

) = 0, Var ( Z

T ) = s

Z

2

} is a discrete-time, purely random process, such that and successive values of Z

T are independent so that Cov( Z

1. Show that the ac. f . of the second-order MA process

is given by t = Z

t

+ 0.7Z

ρ( k ) =

1 k = 0

t -1

- 0.2Z

0.37 k = ±1

-0.13 k = ±2

0 otherwise

2. Consider the infinite-order MA process {X

t

}, defined by

X

t

= Z

t

+ C( Z

t -1

+ Z

t -2

t -2

+ !)

where C is a constant. Show that the process is non-stationary. Also show that the series

of first differences {Yt Yt

} defined by

= X

t

- X

t -1

is a first-roder MA process and is stationary. Find the ac. f . of {Y

t

}.

t

, Z

t +k

) = 0,

T E( Z

T k ≠ 0.

) = 0, Var ( Z

T ) = s

Z

2

} is a discrete-time, purely random process, such that and successive values of Z

T are independent so that Cov( Z

1. Show that the ac. f . of the second-order MA process

is given by t = Z

t

+ 0.7Z

ρ( k ) =

1 k = 0

t -1

- 0.2Z

0.37 k = ±1

-0.13 k = ±2

0 otherwise

2. Consider the infinite-order MA process {X

t

}, defined by

X

t

= Z

t

+ C( Z

t -1

+ Z

t -2

t -2

+ !)

where C is a constant. Show that the process is non-stationary. Also show that the series

of first differences {Yt Yt

} defined by

= X

t

- X

t -1

is a first-roder MA process and is stationary. Find the ac. f . of {Y

t

}.

t

, Z

t +k

) = 0,

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