The Commerce Department yesterday reported a 0.7 percent increase last month in the government's main barometer of future economic activity, capping a week of favorable economic signals.

The preliminary increase in the February index of leading economic indicators, coupled with an upward revision of the January index, gives credence to the Reagan administration prediction that the economy will grow at a reasonably robust 4 percent in 1986, after sputtering at 2 percent last year.

The performance of the leading indicators was the third favorable economic report this week. The Commerce Department said Thursday that the U.S. merchandise trade deficit narrowed to $12.5 billion in February, reflecting the sharp decline in oil prices and the impact of the declining dollar. On Tuesday, the Labor Department announced that consumer prices fell 0.4 percent in February, the biggest drop in 32 years. Declining oil prices were the major factor in reducing inflation.

If the trade deficit continues to narrow, U.S. manufacturers will pick up an increasing share of consumer demand, which they had been losing to foreign sales during the past few years, according to economist Alan Greenspan, a former chairman of the Council of Economic Advisers. The declining dollar also makes U.S. exports more competitive with foreign goods and should help boost U.S. sales abroad.

The reports were the first positive signals on economic growth that have emerged in recent months, although the news on inflation consistently has been positive, according to Allan Sinai, the chief economist for Shearson Lehman Bros

"The picture is brightening," said Greenspan, who operates his own economic forecasting firm in New York. But he cautioned that it will be late spring or summer before the production increases foreshadowed by the February index will materialize.

Several economists also cautioned that although the overall economy should grow more briskly in 1986 than in 1985 -- helping to increase employment -- the growth rate will mask severe distress in the Southwest United States.

After an energy-led boom in the 1970s and early 1980s, then stagnation for three years, the Southwest faces a severe recession as a result of tumbling oil prices. For each $1 decline in oil prices, the region will experience a $1.5 billion decline in investment in mining and petroleum, according to Roger Brinner of Data Resources Inc.

He said DRI forecasts that the price of oil in 1986 will average $10 less than in 1985 -- meaning that capital spending, and the employment it brings with it, will drop $15 billion in the Southwest.

Overall, however, the economy will benefit from the decline in oil prices -- although the benefits will be diffused and slower in coming than the distress the falling prices will bring to the energy-producing regions.

The big beneficiaries of 1986 will be consumers, according to Sinai. They benefit not only from the decline in oil prices, but also from the decline in interest rates, which have home buyers flocking to refinance mortgages taken out at higher rates.

Businesses will see their costs fall too, according to Brinner, but competition among domestic firms, as well as competition between U.S. companies and foreign companies seeking to maintain the sales they developed during the past few years, will force most businesses to pass along their cost reductions in lower prices.

An increase in contracts and orders for plant and equipment and a rise in stock prices and the money supply were the main forces behind the 0.7 percent increase in the leading indicators index. A decline in the length of the average workweek from 40.9 hours to 40.6 hours, a falloff in building permits and a decline in business and consumer borrowing were the major negatives in the index.

Of the 11 indicators that comprise the preliminary index, five increased and six declined. But the strength of the five that rose overshadowed the six declining statistics.

The Commerce Department had reported that the January index fell 0.6 percent, but yesterday it revised that figure to "no change," mainly on the basis of a sharp rise in business inventories. Data on business inventories, the 12th statistic in the leading indicators index, is never available when the Commerce Department computes its preliminary index.

An increase in inventories generally is considered to be a good sign because it usually demonstrates manufacturers are anticipating an increase in sales and are building their stocks to satisfy demand.

But Sinai cautioned that much of the January buildup in inventories represented excess production of automobiles. He said automobile manufacturers will have to introduce new interest-rate or price concessions to stimulate demand.