Fits an autoregressive model of order order to a one-dimensional signal
by the Yule-Walker method: the AR coefficients solve the Yule-Walker equations
formed from the signal's biased demeaned autocovariance (obtained via the
Durbin-Levinson recursion on autocorrelation), and the innovation
variance is the residual (one-step prediction) variance. This is the same
definition as statsmodels.regression.linear_model.yule_walker(method =
"mle"). AR modelling underlies forecasting, parametric (AR) spectra, and –
with the order chosen from the partialAutocorrelation cut-off –
compact descriptions of oscillatory dynamics.
Value
A list with ar (the length-order AR coefficient vector
\(\phi_1, \dots, \phi_p\)), var_pred (the innovation / one-step
prediction variance), and order.
References
Box, G.E.P., Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day.
Examples
set.seed(1)
arYuleWalker(as.numeric(arima.sim(list(ar = c(0.5, -0.3)), 500)), order = 2)
#> $ar
#> [1] 0.4890456 -0.3153433
#>
#> $var_pred
#> [1] 1.042764
#>
#> $order
#> [1] 2
#>