The nation's economy appeared to pick up to a 2.8 percent annual growth rate in the fourth quarter from the summer's 1.6 percent rate, raising hopes that the worst of the slowdown is past.

The Commerce Department reported the improvement in its initial "flash" estimate of the economy's performance from October through December. If that figure is not revised, growth for the year will be 6.7 percent, below the administration's forecast of 7.2 percent real growth over 1983 but still the best gain in output since 1955. Last year, real gross national product increased 3.7 percent.

The Commerce Department also reported an improvement in inflation in the current quarter. Inflation, using a measure of changes in prices and type of output, increased at a 2.9 percent rate, compared with 3.9 percent in the third quarter; for the year, the rate is the same as last year's 3.8 percent, according to yesterday's estimate.

White House spokesman Larry Speakes said, "We appear to be passing through a transitional slowdown and heading for sustained prosperity." He called the report on gross national product and inflation "quite encouraging" and said other recent economic statistics had been "on the positive side."

"This year the economy came in like a lion and is going out like a lamb," Commerce Secretary Malcolm Baldrige said. "The pickup in consumer spending and a drop in interest rates means that the slowdown is mostly behind us. As long as inflation remains moderate, the economy can continue sustainable growth."

However, few economists expect the administration to get its wish for 4 percent economic growth next year, a rate the government needs to keep the federal budget deficit from spiraling beyond about $175 billion next year. High deficits are keeping interest rates from dropping further and feeding the expansion, economists said.

Despite the estimate of a slight uptick in activity in the fourth quarter, the ferocious growth experienced in the first part of the year will not be repeated, economists said. The economy expanded 10.1 percent in the first quarter and 7.1 percent in the second.

The first two quarters of next year are expected to be similar to the last two quarters of this year, economists said. However, the recent dramatic drop in interest rates and signals from the Federal Reserve Board that it wants rates to decline are expected to provide a modest boost to activity in the second half of next year.

The improvement in GNP is a victory for the camp of economists that said the slowdown was merely a lull until a more sustainable rate of growth could be achieved. Another group had said that the economy would fall into a recession.

"We had a lull, as is usually the case in a recovery, and I don't see any excesses in growth on the horizon," said David M. Jones of Aubrey G. Lanston & Co. Inc. Next year, growth should average between 3 percent and 3.5 percent, Jones said, which is enough "to keep the unemployment rate trending down or drifting down, but no faster than that, certainly."

Jones said a big question mark remains about the second half of next year because it is unclear what interest rates will do and whether the Fed will pursue a severe anti-inflation policy that would prevent rates from falling further.

Yesterday's Commerce Department report "tells me that the economy is not likely to weaken much further," said Andrew F. Brimmer of the economic consulting firm Brimmer and Co. "The reduction in interest rates will be a source of stimulus to the economy, such that I believe the third and fourth quarters of next year will show some pickup."

The "flash" estimate of economic activity uses some data from October and November and forecasts for the remainder of the quarter, and thus is subject to revision later. The slight improvement in the fourth quarter was attributed to expected improvements in final sales and in the trade picture, which has been a major drag on the economy's performance this year. The government also said it expected fixed investment by business and government purchases to increase in the fourth quarter, although home purchases will decline.

The Commerce Department revised downward its estimate of third-quarter gross national product from an estimated 1.9 percent reported earlier because business fixed investment, net exports and purchases by federal, state and local governments declined.

It also revised upward its estimates for third-quarter corporate profits. Before-tax profits declined at a quarterly rate of 8.6 percent, compared with an earlier estimate of 9.1 percent. After-tax profits declined at a 5.7 percent rate, compared with a previously stated 7.3 percent rate, Commerce said.

For the year, real gross national product is expected to increase $103.2 billion to $1.6 trillion, an increase from $1.534 trillion in 1983. Nominal gross national product, without adjustment for inflation, is expected to be $3.659 trillion for the year, up from $3.304 trillion last year.

Three-fourths of this year's GNP growth was attributed to final sales, or sales excluding changes in inventories. Most of the final sales increase was because of personal consumption expenditures and business fixed investment, Commerce said.