Q1: Assume our AR(1) model has significant autocorrelation on lag 1 and lag 2, lag 3 & lag 4 are insignificant, can we use MA(1) model on the same data series?
Q2: Also, for MA(2): X(t) = e(t) + (theta1).e(t-1) + (theta2).e(t-2); is the relation (1>theta1>theta2) valid or am I understanding this wrong?
1 Yes you can fit MA 1 series if after fitting the AR model, the error exhibits autocorrelation at lag 1. Ideally we use ACF and PACF plots to decide order of ARMA
2 For MA2 model, correlation will decay till lag 2 and cuts off after lag 3