If MA(1) process is given as ${y_t} = {z_t} + 0.5{z_{t - 1}}$then mean will be equal to:

• A) 0
• B) 1
• C) 0.5
• D) 0.25

If ACVF for a MA process is given as ${\gamma _0} = 5\,\,and\,\,{\gamma _1} = 2$ then ACF ${\rho _0}$ will be equal to:

• A) 5
• B) 1
• C) 0
• D) 2

Random Walk process is:

• A) Stationary
• B) Not-Stationary
• C)
• D)

The rate of decay depends on:

• A) Time
• B) Lag
• C) Series
• D) Parameters of time MA and AR

The series of the first difference wt (wt= yt-yt-1) of an infinite order MA process have:

• A) MA process with infinite order
• B) MA process with order 1
• C)
• D)

Identification methods are called:

• A) rough procedures
• B) mathematical procedures
• C)
• D)

If ACVF for a MA process is given as ${\gamma _0} = 5\,\,and\,\,{\gamma _1} = 2$ then ACF ${\rho _1}$will be equal to:

• A) 2.5
• B) 0.4
• C)
• D)

The series of the first difference wt (wt= yt-yt-1) of an infinite order MA process will be:

• A) Not stationary
• B) Stationary
• C)
• D)

A stationary AR process is always:

• A) Reversible
• B) Invertible
• C)
• D)

For a MA process, if $\left| B \right| = 0.4$ then process will called:

• A) Invertible
• B) Not Invertible
• C)
• D)

PACF of ARMA (p, q) is a mixture of exponential and damped sine waves after:

• A) p+q Lag
• B) q Lag
• C) p Lag
• D) p-q Lag

In an ARMA model $\phi \left( B \right){y_t} = \theta \left( B \right){z_t}$, the term $\phi \left( B \right)$ represents:

• A) MA polynomial
• B) AR polynomial
• C)
• D)

In an ARMA model $\phi \left( B \right){y_t} = \theta \left( B \right){z_t}$, the term $\theta \left( B \right)$ represents:

• A) AR polynomial
• B) MA polynomial
• C)
• D)

Behavior of ACF of ARMA (p, q) is similar to:

• A) ACF OF MA (p)
• B) PACF of MA (p)
• C) PACF of AR (p)
• D) ACF of AR (p)

In computational efficiency of an algorithm, ---------------- played an important role.

• A) initial values
• B) parametric values
• C) all of these
• D) statistics values

Which of the following is for diagnostic checking?

• A) underfitting
• B) over fitting
• C)
• D)

In an AR(p) process, ${y_t} = {\phi _1}{y_t}_{ - 1} + {\phi _2}{y_{t - 2}} + ... + {\phi _p}{y_{t - p}} + {z_t}$, the term ${z_t}$ follows:

• A) normal distribution
• B) standardized normal distribution
• C)
• D)

For large sample size, the approximate LSE of ${\hat \phi _1}$ is given as:

• A) ${{\hat \phi }_1} = {r_1} + {r_2}$
• B) ${{\hat \phi }_1} = {r_1} - {r_2}$
• C) ${{\hat \phi }_1} = {r_1}\,$
• D) ${{\hat \phi }_1} = {r_1}^2$

Mostly, in AR process-MLE, white noise term Zt follow the distribution as:

• A) ${Z_t} \sim N(\mu ,{\sigma ^2})$
• B) ${Z_t} \sim N(0,{\sigma ^2})$
• C)
• D)

In Yule-Walker estimation, Replacing process auto-correlation with the sample aut-ocorrelation, we obtain an equation ------------- for solving Yule-Walker estimates:

• A) ${{\hat \phi }_1} = {r_1}{r_2}$
• B) ${\hat \phi _1} = {r_1}\,$
• C)
• D)