2. Time Series

Question 1

What is the AR(1) equation?

Answer 1

U(t) = ε(t) = Φε(t-1) + η(t)

Question 2

What is Φ?

Answer 2

Φ is the autoregressive parameter

Question 3

What is η(t)?

Answer 3

the error term

Question 4

What are the boundaries of Φ?

Answer 4

-1 < Φ < 1

Question 5

What does it mean when Φ is near 1?

Answer 5

There is strong positive autocorrelation

Question 6

What does it mean when Φ is near -1?

Answer 6

There is strong negative autocorrelation

Question 7

What does it mean when Φ is near 0?

Answer 7

There is weak autocorrelation

Question 8

When there is strong negative autocorrelation, what do we observe in the time series graph?

Answer 8

a yo-yo effect

Question 9

When there is positive autocorrelation, what do we observe in the time series graph?

Answer 9

more smooth fluctuations

Question 10

What is the equation for an AR(2)?

Answer 10

U(t) = ε(t) = Φ1ε(t-1) + Φ2ε(t-2) + η(t)

Question 11

What does SSAC stand for?

Answer 11

sample simple autocorrelation coefficient

Question 12

What does SPAC stand for?

Answer 12

sample partial autocorrelation coefficients

Question 13

How can you identify an AR(1) process from the SPAC?

Answer 13

Only the lag at time = 1 will be outside of the envelope

Question 14

How can you identify an AR(2) process from the SPAC?

Answer 14

Lags at time 1 and 2 will be outside of the envelope

Question 15

What does the SSAC of a positive AR(1) process look like?

Answer 15

They decrease exponentially with time

Question 16

What does the SSAC of a negative AR(1) process look like?

Answer 16

They decrease exponentially but in absolute value only: they alternate in sign, being negative at odd lags and positive at even lags.

Question 17

Looking at Aikake’s or Schwarz’s criteria, how do we know if the model is fitted?

Answer 17

The smaller the criterion the better

Question 18

When looking at parameter estimates, how do we know if the model is well fitted?

Answer 18

The more significant, i.e. the smaller the probability of significance, the better

Question 19

Looking at the sample simple autocorrelation coefficients calculated on the residuals, how do we know if the model is well fitted?

Answer 19

The lesser autocorrelation left in the residuals, i.e. the greater the probability of significance, the better

Question 20

When looking at a periodogram of negative autocorrelation, what do we see?

Answer 20

The highest values of the spectral density function [ f(ω) ] are in the highest frequencies (high ωs)

Question 21

When looking at a periodogram of positive autocorrelation, what do we see?

Answer 21

The highest values of the spectral density function [ f(ω) ] are in the lowest frequencies (low ωs)

Question 22

What is OLS?

Answer 22

Ordinary Least Squares

Question 23

What does OLS assume?

Answer 23

It assumes the absence of autocorrelation of the errors (since it assumes iid → iid = Corr = 0 because independent)

Question 24

What is EGLS?

Answer 24

Estimated generalized least squares

Question 25

Does EGLS assume iid?

Answer 25

no

Question 26

What does ARIMA mean

Answer 26

AutoRegressive Integrated Moving Average

Question 27

What does the RANNOR function do?

Answer 27

It is a SAS function that generates pseudo random numbers

Question 28

When using the RANNOR function, what is the seed?

Answer 28

The seed is the integer number that you put in parentheses

Question 29

Using the RANNOR function, what happens when the seed is positive?

Answer 29

When you run the code, it will always generate the same set of random numbers

Question 30

Using the RANNOR function, what happens when the seed is negative?

Answer 30

When you run the code, it will always generate a new set of random numbers

Question 31

Why would you run a code from -100 to 100 and then reject the first 100 results?

Answer 31

To develop a memory in the data to create better simulated data

Question 32

What is NLAG?

Answer 32

The number of time lags

Question 33

What is the recommended number of time lags?

Answer 33

1/4 of the number of time series (if you have 100, you will have 25 time lags)

Question 34

What is the first bar in the SSAC plot?

Answer 34

The lag of 0

Question 35

In the SSAC plot, what is the value of the lag of 0 (Bar #1)?

Answer 35

1

Question 36

Which lags (bars) are equal between the SSAC and the SPAC plots?

Answer 36

The lags at time 1. Bar #2 for SSAC and Bar #1 for SPAC

Question 37

Characteristic of an AR(p) process shown in the SPAC

Answer 37

The SPAC bars drop under the envelope after lag p

Question 38

What is SAS PROC AUTOREG

Answer 38

REGression analysis with temporally AUTOcorrelated errors PROC = procedure

Question 39

NLAG = 5 BACKSTEP SLSTAY = 0.05

Answer 39

* Assessing the presence of temporal autocorrelation of errors up to time lag of 5. * Backstep: starting with time lag 5 and removing what is unnecessary. * SLSTAY = 0.05 → with a significance level of 5%

Question 40

MSE (mean square error) is it better for it to be small or big?

Answer 40

small

Question 41

AIC (Aikake information criterion) is it better for it to be small or big?

Answer 41

small

Question 42

Total R-Square is it better for it to be small or big?

Answer 42

big

Question 43

In SAS Output, the Backward elimination of autoregressive terms table shows you what?

Answer 43

It shows you which lags are not statistically significant (can be eliminated)

Question 44

Model SS is directly proportional to the Amplitude (A) squared

Answer 44

true