ABSTRACT
Yt = mt + ur, Ut = IJI(B)t:r. t E T = {1, 2, ... , e = (el-q• t:z-q, ... , eo, e1, ... , cr)' "'N(O, a 2fr+q) (6)
if It-sl :::: q
if It-sl > q (7) shows the key feature of model (6): observations distant more than q periods from each other are mutually independent. we are naturally led to consider model (6) for subsamples obtained as follows. Define subsets of ]; = {i, i + (q + 1), i + 2(q + 1), ... , i + ni(q + 1)}, where n; = I[(T-i)/(q + l)] (I[x] denotes the integer part of x), i = l, 2, ... , q + l, and consider the q + l equations
Equation (8) belongs to the class of model (1). In each equation, the error term satisfies the assumptions of the linear regression model, so that it is possible to apply usual inference procedures to test restriction on b, Ho : b E <1>. This null hypothesis can be seen as the intersection of q + 1 hypotheses Ho,i, each of which restricts the mean of the ith subsample to be in <I>, i = 1, 2, ... , q + 1. The methods presented in Sections II and III are perfectly suited to such situations. We build q + I critical regions with level aj(q + 1) to test each one of the hypotheses Ho,i, and reject the
In the next subsection we apply the procedure to a MA(l) process with a constant and provide comparisons with some alternative procedures such as asymptotic tests and bounds tests.
