A government statistic which is supposed to foreshadow economic developments rose sharply for the third consecutive month, confirming that the long pause in economic growth of last summer and fall is over.

The Department of Commerce reported that its index of leading economic indicators rose 1.6 per cent in December, following a 1 per cent November rise and a 0.6 per cent October increase.

John W. Kendrick, the chief economist for the Commerce Department, said the strong performance of the leading indicators confirms the strengthening of the economy since October.

But the economy is sure to show a worse performance in January and February because of the severe cold weather which has struck the eastern two-thirds of the nation.

That cold has forced many plant closings as natural gas suppliers are diverted from industrial use to home heating. While some industries can shift from natural gas to oil, other businesses which use natural gas in the industrial process, such as in textile and carpet making where gas flames are needed, have been forced to reduce the workweek or lay off workers completely.

The severe cold weather also keeps people indoors and is expected to have an adverse impact on retail sales.

Some economists fear that the cold weather will reduce economic growth by a large amount during the winter quarter - say by as much as $3 billion in real, inflation-adjusted terms.

Other economists say that the cold weather has not yet been severe enough to have a lasting impact on industrial production, but agree that is it continues for a long time it could dampen the pace of recovery.

Some analysts say that the economic stimulus package devised by President Carter - including a $50 a person tax rebate - will be eaten up by higher fuel bills, and have suggested that the administration may have to boost the size of the $15 billion package to achieve the results it desires.

Julius Shiskin, Commissioner of Labor Statistics, said the heavy weather-related layoffs in January probably will not be reflected in the January unemployment data his department will release next Friday because the employment survey was conducted in the week beginning Jan. 10, before most of the layoffs began.

The January unemployment rate is likely to reflect the strengthening of the economy in November and December, rather than the weather problems of January.

The Commerce Department said eight of the 11 statistics available to compute the preliminary index of leading indicators rose, two fell and one, the length of the average workweek, stayed constant.

The change in business inventories was not available when the index was computed.

The increase in the amount of cash-like assets was the major contributor to the increase in the overall index, the Commerce Department said.

Other indicators which contributed positively to the index were a decline in the layoff rate, a rise in plant and equipment orders, an increase in sensitive wholesale prices and a jump in net new business formations.

The index of stock prices rose, the money supply adjusted for inflation increased and new orders for consumer goods also rose.

The two statistics which contributed negatively to the index were a decline in the number of building permits issued (an indicator of future construction activity) and a fall-off in the number of companies reporting slower deliveries (the longer it takes to fill an order the busier a plant is supposed to be).

The Department said its index of lagging indicators, which are supposed to show what happened in the past and confirm the predictions of the leading indicators, fell 1 per cent in December.That reflects the pause in economic growth which occured from April through October of 1976.