The longest recession since World War II apparently is at an end.

Evidence is growing daily that the economy touched bottom either in December or this month and is about to begin the long climb back, according to a number of economic forecasters.

However, with unemployment at 10.8 percent of the work force and only about two-thirds of the nation's industrial capacity now in use, a full recovery from the 18-month recession will take several years at a minimum, economists warn.

The latest evidence was reported yesterday by the Commerce Department, which said that the index of leading indicators rose a strong 1.5 percent in December, the largest increase in more than two years. Changes in the index usually foreshadow movements in the economy.

As further indications that a recovery is at hand, economists cite a December jump in new factory orders for goods, rising prices for several industrial commodities, such as steel scrap, that are extremely sensitive to economic conditions, and a drop in initial claims for unemployment benefits.

Alan Greenspan of Townsend-Greenspan & Co., mentioning all those signs, said, "If the recovery has not begun, it is imminent."

Greenspan estimates that real gross national product, adjusted for inflation, will rise at an annual rate of more than 3 percent during this quarter.

Real GNP fell at a 2.5-percent rate in the fourth quarter of 1982, leaving the level of economic activity slightly lower than it was as long ago as the first quarter of 1979.

Final sales of goods and services rose in the last quarter, while production fell.

This combination led to an unexpectedly sharp decline in business inventories. Now, to keep their stocks of goods from continuing to decline, businesses have had to increase their orders to suppliers, and production is beginning to pick up.

Historically, exactly such a swing in inventories and production has occurred at the end of most recessions since World War II.

Lawrence Chimerine of Chase Econometrics said, "The recovery has begun. The decline in industrial production and real GNP at year-end will likely represent the trough of the recession , as a modest improvement in economic activity is already under way."

Martin Feldstein, chairman of the Council of Economic Advisers, was more restrained, however. The "really sharp" increase in the leading indicators provides "good support for our cautious optimism that an economic recovery will soon be under way," Feldstein said.

Chimerine noted that retail sales have been increasing and that auto sales have not dropped very far from the high level they reached in November, when auto manufacturers began to offer below-market interest rate financing, first at about 10.9 percent on 1982 models but later at 11.9 percent on 1983 models, too.

"Sales of household durables are also continuing to improve, due in part to increased housing activity," Chimerine said.

Chase Econometrics now expects real output to rise at a 3.8-percent rate this quarter, and about 4 percent between the fourth quarter of 1982 and the fourth quarter of this year.

Several other economists have made similar forecasts, which are somewhat more optimistic than the 3-percent increase officially forecast by the Reagan administration.

But even a gain of 4 percent or more during 1983 would be well below the pace of the economic rebounds that have followed most of the post-World War II recessions. The principal reasons for expecting a sub-par recovery are a continued drop in business investment for new plants and equipment and a worsening U.S. trade balance.

The drop in business investment is tied to the enormous amount of unused production capacity now available to meet any demand for more output, and to the high level of long-term interest rates relative to inflation.

Treasury Secretary Donald T. Regan, who this week said "the recovery may well already be under way at this moment," also cautioned that the recovery might not be sustained unless long-term interest rates dropped into the "single-digit" range.

For most business borrowers, that would amount to a fall in rates of at least 2 or 3 percentage points.

Other policy makers in the Reagan administration and at the Federal Reserve are also concerned that long-term interest rates might start to rise again and throw the recovery off the rails.

Greenspan said that if long-term rates were to go up 1 1/2 percentage points, for example, the recovery would be in jeopardy.

For most of this year, the forecasters also say they believe that the worldwide recession will reduce U.S. exports, offsetting part of the domestic recovery's effect on jobs and production.

The continuing high value of the U.S. dollar compared with most other currencies is also a major factor reducing the demand for American goods abroad.

The Commerce Department said that of the 12 indicators making up the leading indicators index, 10 are available for December.

Six of the 10 rose, three fell slightly and one was unchanged, compared with November's figures, and the sum of these changes equals 1.5 percent.

The drop in initial claims for unemployment benefits, new orders for business equipment and an increase in the money supply contributed the most to the rise in the index.