Time Series #2

Question 1

What are time-series models?

Answer 1

Models that describe the behavior of variables using their past (lagged) values as explanatory variables.

Question 2

Why are time-series models useful?

Answer 2

1. Forecasting future values
2. Analyzing impacts of shocks on variables over time

Question 3

What is stationarity in a time-series?

Answer 3

A property where the mean, variance and autocorrelation structure remain constant over time.

Question 4

What is a white noise process?

Answer 4

A time-series with no discernible structure, zero autocorrelation, and normally distributed values.

Question 5

What is the autocorrelation function (ACF)?

Answer 5

A function that plots the correlation of a time-series with its lagged values.

Question 6

What is an autoregressive (AR) model?

Answer 6

A model where a variable is regressed on its lagged values.

Question 7

What is an AR (p) model?

Answer 7

A generalization of the AR model where Yt depends on p lagged values.

Question 8

What are ARMA models?

Answer 8

Models that combine autoregressive (AR) and moving average (MA) terms for better modeling short-term patterns.

Question 9

Why is stationarity important?

Answer 9

1. Ensures validity of OLS assumptions
2. Avoids spurious results in regressions

Question 10

What are indicators of stationarity?

Answer 10

Stable mean, variance, and autocorrelation structure without trends or seasonality.

Question 11

What happens if a variable is non-stationary?

Answer 11

Forecasting and regression analysis may give misleading results.

Question 12

What mathematical condition defines stationarity in AR models?

Answer 12

For AR (1), stationarity holds if -1 < AR < 1.

Question 13

How can stationarity be tested?

Answer 13

By examining whether autocorrelations decay as lag increases.

Question 14

What does a flat line in the ACF plot indicate?

Answer 14

No autocorrelation (white noise)

Question 15

What does a slowly decaying ACF suggest?

Answer 15

Potential non-stationarity in the data.

Question 16

What corrective actions are taken for non-stationarity data?

Answer 16

Differencing or detrending the data to achieve stationarity.

Question 17

What are the conditions for AR (1) model stationarity?

Answer 17

-1 < AR < 1

Question 18

How is the optimal lag length in AR (p) chosen?

Answer 18

By using:
1. Statistical significance of lags
2. Information criteria like AIC or SBIC

Question 19

What is the difference between AIC and SBIC?

Answer 19

AIC prefers larger models, less penalty for complexity.
SBIC penalizes larger models more, consistent in lag selection.

Question 20

What does the persistence of shocks in AR models imply?

Answer 20

Shocks have a decaying but long-lasting impact.

Question 21

How does the ACF behave for AR models?

Answer 21

For AR > 0, the ACF decays positively.
For AR < 0, the decay alternates in signs and decays.

Question 22

What does adding additional lags do in an AR model?

Answer 22

Improves fit but risks overfitting if not carefully chosen.

Question 23

What is the difference between AR and ARMA models?

Answer 23

ARMA includes both lagged dependent variables and lagged error terms.

Question 24

What are in-sample forecasts?

Answer 24

Predictions for the same data used to estimate the model.

Question 25

What are out-of-sample forecasts?

Answer 25

Predictions for data not used during model estimation, a better test of predictive power.

Question 26

What are single-step and multi-step forecasts?

Answer 26

1. Single-step: predicts one future value.
2. Multi-step: predicts multiple future values sequentially.

Question 27

How is forecast accuracy assessed?

Answer 27

Using metrics like:
Mean Squared Error (MSE)
Mean Absolute Error (MAE)
Mean Absolute Percentage Error (MAPE)

Question 28

What is the role of economic loss functions in forecasting?

Answer 28

They assess forecasts based on their financial impact rather than statistical accuracy.

Question 29

What does an accurate forecast require?

Answer 29

1. Stationarity of data
2. Robust model selection

Question 30

Why do forecasts degrade over longer horizons?

Answer 30

Errors propagate, and structural breaks or regime changes may occur.

Question 31

How do AR models make forecasts?

Answer 31

By using the conditional expectation.

Question 32

How do expanding and rolling windows differ for forecasting?

Answer 32

Expanding: adds all previous data to each new forecast.
Rolling: uses a fixed-size window, moving as new data arrive.

Question 33

What can cause poor forecast performance?

Answer 33

1. Non-stationarity
2. Structural breaks
3. Poor model fit

Question 34

What is an impulse response function?

Answer 34

A tool that shows how a shock to one variable propagates through a system over time.

Question 35

What is a VAR model?

Answer 35

A Vector Autoregressive model that extends AR models to multiple interdependent variables.

Question 36

How does VAR differ from AR models?

Answer 36

VAR models include multiple dependent variables with lagged values of all variables in the system.

Question 37

What are the assumptions for VAR model estimation?

Answer 37

Stationarity of all variables
No contemporaneous feedback unless explicitly modeled.

Question 38

What are the steps to estimate a VAR?

Answer 38

1. Specify lag order
2. Estimate coefficients using OLS
3. Check residuals for serial correlation

Question 39

How are impulse responses calculated?

Answer 39

By simulating the VAR system’s response to a one-time shock while holding other shocks at zero.

Question 40

What does a decaying impulse response indicate?

Answer 40

A stationary system where shocks dissipate over time.

Question 41

What does Lochstoer-Muir’s VAR model analyze?

Answer 41

How investors react to volatility shocks in equity markets.

Question 42

Why standardize variables in VAR models?

Answer 42

To make coefficients comparable as one-standard deviation effects.

Question 43

What does the Ljung-Box test evaluate?

Answer 43

The joint null hypothesis that all autocorrelations up to lag m are zero.

Question 44

How do you interpret a significant Ljung-Box test?

Answer 44

Rejects the null, indicating that autocorrelations are present in the residuals.

Question 45

What does a high p-value in the Box-Pierce test suggest?

Answer 45

No significant autocorrelations, indicating a good model fit.

Question 46

How do you interpret an AIC-selected lag structure?

Answer 46

The model likely balances fit and complexity well for short-term forecasts.

Question 47

What does a significant AR (1) coefficient close to 1 imply?

Answer 47

High persistence, where shocks have prolonged effects.

Question 48

How do you interpret poor forecast accuracy?

Answer 48

The model may lack important predictors or be misspecified.

Question 49

What does the decay rate in the ACF reveal?

Answer 49

Faster decay indicates less persistent shocks; slower decay suggests higher persistence.

Question 50

How do impulse response functions assist analysis?

Answer 50

By quantifying the temporal impact of shocks on dependent variables.