ARMA 22\23

Question 1

What is stationarity in time series?

Answer 1

A process is stationary if its mean, variance and autocovariance do no not change over time

Question 2

How do you calculate the variance of a process et - iid(0,1)

Answer 2

Variance is the sum of the variances of all the terms

Question 3

What is the defining feature of an AR(1) process in terms of autocorrelation

Answer 3

The autocorrelation decays exponentially

Question 4

What is the purpose of an ACF?

Answer 4

It measures the correlation between a time series and its lagged values

Question 5

What does the PACF indicate?

Answer 5

It shows the direct effect of a lagged variable after accounting for shorter lags

Question 6

How does ACF differ for white noise vs AR(1)?

Answer 6

White noise has negligible auto correlation; AR(1) decays exponentially

Question 7

What is the formula for an h-step ahead forecast in an AR(1) model?

Answer 7

Ø^h yt

Question 8

What is the null hypothesis in the ADF test?

Answer 8

The process has a unit root (ø = 1)

Question 9

What does rejecting the ADF test null hypothesis mean?

Answer 9

The process is stationary

Question 10

What is the critical feature of an AR(1) process in PACF?

Answer 10

Sharp cutoff after lag 1

Question 11

How is the mean of a stationary process related to time?

Answer 11

The mean is constant over time

Question 12

What happens to autocovariance in a stationary process?

Answer 12

It depends only on the lag not on time t

Question 13

Why is stationarity important in time series analysis>

Answer 13

Stationarity allows consistent estimation of model parameters

Question 14

Why is PACF useful in empirical analysis?

Answer 14

It identifies the number of significant AR terms in a model

Question 15

What is the definition of white noise in a time series?

Answer 15

White noise is a sequence of random variables with zero mean, constant variance, no autocorrelation

Question 16

How does the ADF test differ from the KPSS test?

Answer 16

The ADF test checks for a unit root (non-stationarity), while the KPSS test checks for stationarity under the null hypothesis

Question 17

What is the role of lagged differences in the ADF test?

Answer 17

They account for serial correlation in the residuals

Question 18

What are the critical values in the ADF test based on?

Answer 18

They depend on the Samoyed size and the type of model (e.g. with a trend, intercept, or none)

Question 19

What is an AR(1) process?

Answer 19

A process where the current value depends on the immediately previous value and a stochastic error term

Question 20

What happens if |ø| >= 1 in a AR(1) process?

Answer 20

The process in non stationary (|ø|=1 implies a unit root)

Question 21

What is a unit root process?

Answer 21

A non stationary process where shocks have a permanent affect on the time series