Modeling Cycles

Question 1

How does the Moving Average (MA) model represent a time series?

Answer 1

Represents time series as a linear function of current and past error terms (shocks)

Question 2

What are some key characteristics about the Moving Average (MA) model?

Answer 2

1) Approximation to the Wold Representation
2) Distributed Lags of Shocks
3) Mathematical Representation

Question 3

What are key properties of Moving Average (MA) model?

Answer 3

1) short memory - it only depends on a finite number of past shocks, the effects of past disturbances
2) stationarity - meaning they do not exhibit trends or long-term dependencies
3) useful for forecasting - since it captures short-term dependencies, an MA model is often used in time series forecasting

Question 4

What is invertibility?

Answer 4

An MA process if invertible if it can be rewritten as a converging infinite-order AR process, expressing current shocks in terms of past observations, making estimation and forecasting more stable

Question 5

When can a MA model be invertible?

Answer 5

When the absolute value of theta is < 1, if greater or equal to it cannot be invertible

Question 6

What is the AutoRegressive (AR) model definition?

Answer 6

Time series model where past values predict the present

Question 7

What’s the autocorrelation of AR model?

Answer 7

gradual decay, smoother than MA models

Question 8

What is the difference from MA?

Answer 8

AR uses past values; MA uses past shocks

Question 9

What is an example of an AR model?

Answer 9

temperature today depends on the last two month’s temperatures

Question 10

What are Yule-Walker equations?

Answer 10

equations that estimate AR model coefficients using autocorrelations

Question 11

What are yule-walker equations used for?

Answer 11

AR parameter estimation, stationarity check, spectral analysis

Question 12

When changing the coefficients between an AR model and MA model, which one has a greater impact?

Answer 12

the AR model has a greater impact when there is a change in coefficients because it influences long-term behavior

Question 13

True or False. AR model are always covariance stationary?

Answer 13

False, it is only covariance stationary if the absolute value of p is < 1.

Question 14

Formula used to find covariance between X and Y

Answer 14

Var(X - Y) = Var(X) + Var(Y) - 2Cov(X,Y)

Question 15

Formula for calculating the lower bound with a 95% confidence interval

Answer 15

mean - (1.96)(standard deviation)