Parameter and Order Estimation Flashcards
What derivation is the asusmption of normally distirbuted white noise important for?
Derivation of the logmlikelihood
Name two r functions for finding the MLEs of parameters
Arima and sarmina
Describe the arima function
arima(x, order = c(p, d, q), include.mean = TRUE)
x: time series
order: (p, d, q) are the AR order, degree of differencing, and the MA order.
▸ include.mean: Should the ARMA model include a mean/intercept term? The default is TRUE for undifferenced
series, and it is ignored for models with differencing.
What happens to a mean or intercept with differencing
It disappears
What r function allows us to simulate a trajectory
arima.sim(n=…,list(ar=c(…),ma=c(…)),sd=…)
What funciton allows resutls to stay the same and not vary
Set.seed()
Explain difference in decay of an acf for s tstaionary vs non stationary series
Stationary series - decays exponentially to zero very quickly
Non stationary series will have a slow decay
What is the log transformation typically used for
To stabilise the variance - variance is different at one set of times time than an other
What is the r function for the quantile used for a 95% confidence interval
qnorm(1-0.05/2)
How do we get the standard error for the parameter estimates?
Find the diagonal elements of a covariance matrix and square root them
How do we get information on the order of a MA(q) process
The ACF of a MA(q) process can give us information on the order since it is zero for lags greater than q and non-zero for the lag q.
How do we get information on the order of an AR(p) process
Similarly, the partial ACF (PACF) of an AR(p) process can give
us information on the order since it is zero for lags greater than p
and non-zero for the lag p.
How do we identify the order of an ARMA model
Both ACF and PACF can be used to give us an idea about the
possible maximum orders to be considered for an ARMA model. We can then decide which p and q to use out of all possible combinations by assessing some criteria
How do you test the significance of lags int he model?
Find the estimates for the parameter coefficients of each lag then find a 95% confidence interval for these estimates. If it includes zero those lags are non significant
In the AIC what is 2K term
Penalty function to select a parsimonious model
