ISYE 6501- MIDTERM 1 EXAM
COMBINED SET QUESTIONS
AND ANSWERS
What are second order differences? - Answer-difference between the observation at
time t and time t-1 minus the difference of t-1 and t-2.
[x(t)-x(t-1)] - [x(t-1)-x(t-2)]
Even if time-series data is not stationary, ______ may be stationary. - Answer-
differences
Stationary process - Answer-mean, variance, and other measures are expected to be
constant over time
Factors in exponential smoothing that would indicate non-stationary data - Answer-
trend, seasonality
What is autoregression? How does it differ from regression? - Answer-using earlier
values of the same thing you wish to predict to make the prediction
regression will use the values of other factors to make a prediction
Autoregression requires what kind of data? - Answer-time-series
What is p in an autoregressive model? - Answer-number of historical time periods to
use for prediction
What is the difference between an order-∞ and order-p autoregressive model? -
Answer-order-∞: uses all available historical data
order-p: uses only specified time periods (p)
What does ARIMA perform autoregression on? Why? - Answer-the d-th order
differences
observed data may be non-stationary, which does not work well in ARIMA, so the d-th
order differences provides a stationary measure.
What does the moving average in ARIMA use as predictors? - Answer-previous errors-
ɛ(t)
, How is ɛ(t) calculated for ARIMA? - Answer-predicted minus observed value
ɛ(t)= [^x(t) - x(t)]
what is q in ARIMA? - Answer-order-q moving average, where q specifies the number of
historical time periods to use in error calculation
What is ARIMA (0,0,q)? - Answer-Moving average model
What is ARIMA (p,0,0)? - Answer-Autoregressive model
What is ARIMA (0,1,1)? - Answer-basic exponential smoothing model
Fill in variable letters to ARIMA( , , ). - Answer-ARIMA(p,d,q)
Under what conditions does ARIMA work better than exponential smoothing? - Answer-
data is more stable with fewer peaks, valleys, and outliers
ARIMA and exponential smoothing can be used for ___________ forecasting. - Answer-
short-term
Approximately how big of a dataset do you need for ARIMA to work well? - Answer-~40
data points
What is forecasted for GARCH vs ARIMA? - Answer-GARCH: variance
ARIMA: differences
Define heteroscedasticity - Answer-refers to the circumstance in which the variability of
a variable is unequal across the range of values of a second variable that predicts it.
What does a variance forecast tell you? - Answer-How much higher or lower the
forecast might be compared to the true value (volatility)
What are two differences between the GARCH and ARIMA model? - Answer-1. GARCH
uses variances/squared error whereas ARIMA uses observations and linear error terms
2. GARCH uses the raw variances, whereas ARIMA uses differences
What are the parameters for the GARCH model? - Answer-GARCH (p, q)
What is maximum likelihood? What is it used for? - Answer-set of parameters that give
the highest probability density
used to optimize model fit
COMBINED SET QUESTIONS
AND ANSWERS
What are second order differences? - Answer-difference between the observation at
time t and time t-1 minus the difference of t-1 and t-2.
[x(t)-x(t-1)] - [x(t-1)-x(t-2)]
Even if time-series data is not stationary, ______ may be stationary. - Answer-
differences
Stationary process - Answer-mean, variance, and other measures are expected to be
constant over time
Factors in exponential smoothing that would indicate non-stationary data - Answer-
trend, seasonality
What is autoregression? How does it differ from regression? - Answer-using earlier
values of the same thing you wish to predict to make the prediction
regression will use the values of other factors to make a prediction
Autoregression requires what kind of data? - Answer-time-series
What is p in an autoregressive model? - Answer-number of historical time periods to
use for prediction
What is the difference between an order-∞ and order-p autoregressive model? -
Answer-order-∞: uses all available historical data
order-p: uses only specified time periods (p)
What does ARIMA perform autoregression on? Why? - Answer-the d-th order
differences
observed data may be non-stationary, which does not work well in ARIMA, so the d-th
order differences provides a stationary measure.
What does the moving average in ARIMA use as predictors? - Answer-previous errors-
ɛ(t)
, How is ɛ(t) calculated for ARIMA? - Answer-predicted minus observed value
ɛ(t)= [^x(t) - x(t)]
what is q in ARIMA? - Answer-order-q moving average, where q specifies the number of
historical time periods to use in error calculation
What is ARIMA (0,0,q)? - Answer-Moving average model
What is ARIMA (p,0,0)? - Answer-Autoregressive model
What is ARIMA (0,1,1)? - Answer-basic exponential smoothing model
Fill in variable letters to ARIMA( , , ). - Answer-ARIMA(p,d,q)
Under what conditions does ARIMA work better than exponential smoothing? - Answer-
data is more stable with fewer peaks, valleys, and outliers
ARIMA and exponential smoothing can be used for ___________ forecasting. - Answer-
short-term
Approximately how big of a dataset do you need for ARIMA to work well? - Answer-~40
data points
What is forecasted for GARCH vs ARIMA? - Answer-GARCH: variance
ARIMA: differences
Define heteroscedasticity - Answer-refers to the circumstance in which the variability of
a variable is unequal across the range of values of a second variable that predicts it.
What does a variance forecast tell you? - Answer-How much higher or lower the
forecast might be compared to the true value (volatility)
What are two differences between the GARCH and ARIMA model? - Answer-1. GARCH
uses variances/squared error whereas ARIMA uses observations and linear error terms
2. GARCH uses the raw variances, whereas ARIMA uses differences
What are the parameters for the GARCH model? - Answer-GARCH (p, q)
What is maximum likelihood? What is it used for? - Answer-set of parameters that give
the highest probability density
used to optimize model fit
