2. Time Series Flashcards
What is the AR(1) equation?
U(t) = ε(t) = Φε(t-1) + η(t)
What is Φ?
Φ is the autoregressive parameter
What is η(t)?
the error term
What are the boundaries of Φ?
-1 < Φ < 1
What does it mean when Φ is near 1?
There is strong positive autocorrelation
What does it mean when Φ is near -1?
There is strong negative autocorrelation
What does it mean when Φ is near 0?
There is weak autocorrelation
When there is strong negative autocorrelation, what do we observe in the time series graph?
a yo-yo effect
When there is positive autocorrelation, what do we observe in the time series graph?
more smooth fluctuations
What is the equation for an AR(2)?
U(t) = ε(t) = Φ1ε(t-1) + Φ2ε(t-2) + η(t)
What does SSAC stand for?
sample simple autocorrelation coefficient
What does SPAC stand for?
sample partial autocorrelation coefficients
How can you identify an AR(1) process from the SPAC?
Only the lag at time = 1 will be outside of the envelope
How can you identify an AR(2) process from the SPAC?
Lags at time 1 and 2 will be outside of the envelope
What does the SSAC of a positive AR(1) process look like?
They decrease exponentially with time
What does the SSAC of a negative AR(1) process look like?
They decrease exponentially but in absolute value only: they alternate in sign, being negative at odd lags and positive at even lags.
Looking at Aikake’s or Schwarz’s criteria, how do we know if the model is fitted?
The smaller the criterion the better
When looking at parameter estimates, how do we know if the model is well fitted?
The more significant, i.e. the smaller the probability of significance, the better
Looking at the sample simple autocorrelation coefficients calculated on the residuals, how do we know if the model is well fitted?
The lesser autocorrelation left in the residuals, i.e. the greater the probability of significance, the better
When looking at a periodogram of negative autocorrelation, what do we see?
The highest values of the spectral density function [ f(ω) ] are in the highest frequencies (high ωs)
When looking at a periodogram of positive autocorrelation, what do we see?
The highest values of the spectral density function [ f(ω) ] are in the lowest frequencies (low ωs)
What is OLS?
Ordinary Least Squares
What does OLS assume?
It assumes the absence of autocorrelation of the errors (since it assumes iid → iid = Corr = 0 because independent)
What is EGLS?
Estimated generalized least squares
Does EGLS assume iid?
no
What does ARIMA mean
AutoRegressive Integrated Moving Average
What does the RANNOR function do?
It is a SAS function that generates pseudo random numbers
When using the RANNOR function, what is the seed?
The seed is the integer number that you put in parentheses
Using the RANNOR function, what happens when the seed is positive?
When you run the code, it will always generate the same set of random numbers
Using the RANNOR function, what happens when the seed is negative?
When you run the code, it will always generate a new set of random numbers
Why would you run a code from -100 to 100 and then reject the first 100 results?
To develop a memory in the data to create better simulated data
What is NLAG?
The number of time lags
What is the recommended number of time lags?
1/4 of the number of time series (if you have 100, you will have 25 time lags)
What is the first bar in the SSAC plot?
The lag of 0
In the SSAC plot, what is the value of the lag of 0 (Bar #1)?
1
Which lags (bars) are equal between the SSAC and the SPAC plots?
The lags at time 1.
Bar #2 for SSAC and Bar #1 for SPAC
Characteristic of an AR(p) process shown in the SPAC
The SPAC bars drop under the envelope after lag p
What is SAS PROC AUTOREG
REGression analysis with temporally AUTOcorrelated errors
PROC = procedure
NLAG = 5 BACKSTEP SLSTAY = 0.05
- 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%
MSE (mean square error) is it better for it to be small or big?
small
AIC (Aikake information criterion) is it better for it to be small or big?
small
Total R-Square is it better for it to be small or big?
big
In SAS Output, the Backward elimination of autoregressive terms table shows you what?
It shows you which lags are not statistically significant (can be eliminated)
Model SS is directly proportional to the Amplitude (A) squared
true
