I am trying to understand the difference between these three different specifications of an autoregressive model for variable
var in Stata:
reg L(0/3).var arima var L(1/3).var arima var, arima(3,0,0)
All thee provide similar (to an extent), answers. The first two have equal coefficients, but different standard errors. The last has similar coefficients.
However, when using them for forecasting. The last model provides wildly different results. For example, given this data:
v 31.75 32.31 38.25 42 45.7 45.3 45 45.24 46 45 44.38 44.21 44 43 43
gen t = _n tsset t
I would like to forecast the value of
var in future periods. I would like to find a predicted value as well as the lower and upper bounds: therefore I also solve for standard errors. In this example, I am looking forward 12 periods:
tsappend, add(12) reg L(0/3).var forecast create OLS, replace estimates store OLS forecast estimates OLS forecast solve, simulate(errors, statistic(stddev,prefix(olssd_)) reps(1000))
I have done this for all three models. The last model provides almost no variation in standard errors as the period increases.
So, what are the differences between these models? And which one should be used when it is believed that a series is autocorrelated?