Compare AR and MA models

Time Series Analysis in R

David S. Matteson

Associate Professor at Cornell University

MA and AR processes

MA model: $Today = Mean + Noise + Slope * (Yesterday's Noise)$ $$Y_t = \mu + \epsilon_t + \theta\epsilon_{t-1}$$
AR model:

$(Today - Mean) = Slope*(Yesterday - Mean)$ $$+ Noise$$ $$Y_t - \mu = \phi(Y_{t-1} - \mu) +\epsilon_t$$

$$\epsilon_t \sim WhiteNoise(0, \sigma^2_t)$$

MA_inflation_changes <-
arima(inflation_changes, 
order = c(0,0,1))

         ma1 intercept
     -0.7932    0.0010
s.e.  0.0355    0.0281
sigma^2 estimated as 8.882: 
log likelihood = -1230.85, 
aic = 2467.7

AIC(MA_inflation_changes)
BIC(MA_inflation_changes)

2467.703
2480.286

AR_inflation_changes <- 
arima(inflation_changes, 
order = c(1,0,0))

         ar1 intercept
     -0.3849    0.0038
s.e.  0.0420    0.1051
sigma^2 estimated as 10.37: 
log likelihood = -1268.34, 
aic = 2542.68

AIC(AR_inflation_changes)
BIC(AR_inflation_changes)

2542.679
2555.262

Time Series Analysis in R