Effect of Temperature Shock and Inventory Surprises on Natural Gas and Heating Oil Futures Returns

Table 3

Results for Ljung-Box 𝑄² and ARCH-LM tests.

Commodity	Variables	𝑄^2(3)	𝑄^2(6)	𝑄^2(9)	𝑄^2(12)	ARCH(6)	ARCH(12)
RET𝑁1	Series 1	37.4260	47.8960	48.1930	57.5900	7.4251	4.3999
		(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)
	Series 2	37.7920	47.9380	48.2280	57.8320	7.4365	4.4098
		(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)
RET𝑁2	Series 1	49.2860	49.7660	50.2800	58.3290	7.0381	4.4487
		(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)
	Series 2	48.7730	49.2380	49.7220	57.6940	6.9851	4.4071
		(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)	(0.0000***)
RET𝐻1	Series 1	9.4883	22.1670	29.4190	33.8710	3.1697	2.1361
		(0.0230**)	(0.0010***)	(0.0010***)	(0.0010***)	(0.0043***)	(0.0129**)
	Series 2	9.5893	22.1060	29.3000	33.7370	3.1614	2.1273
		(0.0220**)	(0.0010***)	(0.0010***)	(0.0010***)	(0.0044***)	(0.0133**)
RET𝐻2	Series 1	1.2064	13.6810	22.5980	28.2530	2.3223	2.1579
		(0.7510)	(0.0330**)	(0.0070***)	(0.0050***)	(0.0311**)	(0.0118**)
	Series 2	1.2168	13.4810	22.4570	28.1050	2.2882	2.1480
		(0.7490)	(0.0360**)	(0.0080***)	(0.0050***)	(0.0336**)	(0.0123**)