N = 50   N=200   N=1000   λ LRT  Score LRT  Score LRT  Score 0 0.058 0.053 0.53 0.50 0.048 0.047 0.1 0.062 0.056 0.061 0.062 0.093 0.091 0.2 0.067 0.061 0.090 0.086 0.260 0.258 0.3 0.079 0.074 0.140 0.137 0.560 0.557 0.4 0.095 0.089 0.220 0.214 0.839 0.839 0.5 0.118 0.112 0.333 0.329 0.969 0.968 0.6 0.149 0.141 0.470 0.464 0.997 0.998 0.7 0.191 0.180 0.620 0.614 1 1 0.8 0.238 0.221 0.762 0.751 1 1 0.9 0.299 0.280 0.870 0.859 1 1 1.0 0.375 0.350 0.941 0.935 1 1

Table 2: Empirical rejection rates for tests of time-invariant transition probabilities for data simulated from process (6). Empirical sizes (rejection rates when λ=0) more than two estimated standard errors from the nominal size (0.05) are set in bold type.