WASHINGTON — The star actor may be about to depart, but his understudy at the Federal Reserve is expected to keep following the same script — gradually increasing interest rates to make sure inflation does not get out of control.

Many private economists believe outgoing Fed Chairman Alan Greenspan will boost rates at his final two meetings on Dec. 13 and Jan. 31 and that Ben Bernanke, the man tapped to succeed him, will add a final rate increase at his first meeting on March 31.

Analysts said they hold to the view that there will be at least three more rate increases because they believe Bernanke will want to show his inflation-fighting zeal as soon as he takes over and signal his solidarity with the policies of Greenspan. The outgoing chairman gained near mythic status in financial markets during his 18 years as Fed chief.

"The shift in the Fed chair will be seamless," predicted Sherry Cooper, chief economist for Harris Bank of Chicago.

The increase Tuesday was the 12th in the Fed's target for the federal funds rate, the interest that banks charge each other, since the Fed first started tightening credit conditions in June 2004. At that time, the funds rate stood at a 46-year low of 1 percent and banks' prime lending rate, the benchmark for millions of consumer and business loans, was at 4 percent.

Now the funds rate and the prime rate are both at their highest point in 4½ years. Commercial banks followed the Fed's lead on Tuesday and increased their prime lending rate, the benchmark for millions of business and consumer loans, to 7 percent.

The Fed is trying to boost borrowing costs for consumers and businesses gradually as a way to slow the economy enough to keep inflation under wraps. The Fed's concern is that the surge in energy prices that occurred after hurricanes Katrina and Rita shut down Gulf Coast production facilities could spill over into more widespread inflation pressures.

Consumer prices shot up by 1.2 percent in September, the biggest one-month increase in a quarter-century, led by a record rise in energy prices as crude oil briefly topped $70 per barrel and gasoline went over $3 per gallon.

"Higher energy and other costs have the potential to add to inflation pressures," the Fed said in Tuesday's statement. But it added that so far, core inflation, excluding food and energy, "has been relatively low in recent months and longer-term inflation expectations remain contained."

The Fed is closely watching the core inflation figures for any hint that the surge in energy prices is spreading into a bigger problem. For September, the government reported that core inflation remained well-contained with just a small 0.1 percent increase.

"The Fed can remain calm about inflation given what core inflation is doing," said David Wyss, chief economist at Standard & Poor's in New York. "Barring any major shocks to the economy, I think the Fed is close to stopping."

As long as core inflation stays at moderate levels, Wyss and other analysts said, the Fed is likely to feel it can raise the fed funds rate to between 4.5 percent and 5 percent and then move to the sidelines, possibly for the rest of 2006.