ISYE 6402 Meta’s Prophet Model: Case Studies |
Latest 2025 Update with complete solutions.
A time series is an ARMA process if... - answer-it is stationary
AR or Auto Regressive - answer-models the relationship between Xt and past
or lagged observations.
MA or Moving Average - answer-we can model that the time series, the time t
is not only affected by the shock of time t, but also the shocks that have taken
place before time t.
The Moving Average (MA) is a .... - answer-linear combination of white noise
AR(?) MA(?) - answer-p,q
phi - answer-polynomial of order p with coefficients given by the AR portion of
the model
theta - answer-a polynomial of order q with coefficients given by the MA
portion of the model.
operator B - answer-a lag operator when applied to Xt we move the index back
one time unit giving Xt-1.
, Autocovariance function in terms of lag h - answer-the covariance function
decreases as we increase the lag h means that the dependence in a time series
becomes smaller and smaller as we increase the lag between two time points
of the time series
2 properties of ARMA process - answer-1. There exists an ARMA process for
any autocovariance function with this property.
2. the linear structure for ARMA models makes prediction easy to carry out.
How to check if ARMA process is stationary? - answer-The condition only
involves the AR polynomial phi. We need to get solutions to phi polynomial
and check whether on the unit circle or phi(z) is not equal to 1 in the unit
circle.
Causal process - answer-Being able to represent the process as a linear
combination of white noise (causal)
Invertible process - answer-Being able to represent the process as a linear
combination of lagged self (invertible).
AR processes are always... - answer-invertible
MA processes are always... - answer-causal
When is an ARMA process causal? - answer-1. We assume that the two
polynomials phi and theta do not have any common zeroes. That means the
solutions to the equation phi(z) are not equal to the solutions of the
polynomial theta is equal to 0.
Latest 2025 Update with complete solutions.
A time series is an ARMA process if... - answer-it is stationary
AR or Auto Regressive - answer-models the relationship between Xt and past
or lagged observations.
MA or Moving Average - answer-we can model that the time series, the time t
is not only affected by the shock of time t, but also the shocks that have taken
place before time t.
The Moving Average (MA) is a .... - answer-linear combination of white noise
AR(?) MA(?) - answer-p,q
phi - answer-polynomial of order p with coefficients given by the AR portion of
the model
theta - answer-a polynomial of order q with coefficients given by the MA
portion of the model.
operator B - answer-a lag operator when applied to Xt we move the index back
one time unit giving Xt-1.
, Autocovariance function in terms of lag h - answer-the covariance function
decreases as we increase the lag h means that the dependence in a time series
becomes smaller and smaller as we increase the lag between two time points
of the time series
2 properties of ARMA process - answer-1. There exists an ARMA process for
any autocovariance function with this property.
2. the linear structure for ARMA models makes prediction easy to carry out.
How to check if ARMA process is stationary? - answer-The condition only
involves the AR polynomial phi. We need to get solutions to phi polynomial
and check whether on the unit circle or phi(z) is not equal to 1 in the unit
circle.
Causal process - answer-Being able to represent the process as a linear
combination of white noise (causal)
Invertible process - answer-Being able to represent the process as a linear
combination of lagged self (invertible).
AR processes are always... - answer-invertible
MA processes are always... - answer-causal
When is an ARMA process causal? - answer-1. We assume that the two
polynomials phi and theta do not have any common zeroes. That means the
solutions to the equation phi(z) are not equal to the solutions of the
polynomial theta is equal to 0.
