FOR A LONG STRETCH OF time, which began in the Arthur Burns era, and continued under his successor as chairman of the Federal Reserve, G. William Miller, the nation's central bank has been following a high-interest-rate policy in an effort to beat back inflation.

The question of when the Fed would take its foot off the brake has been Topic A for Wall Street and the investment community. For when interest rates rise, the market value of bonds falls. Thus, if a $1,000 bond paid 6 percent when issued and market interest rates have risen to 6 1/4 per cent, a new buyer can pay only $960 for that bond to obtain a yield of 6 1/4 percent.

With interest rates sharply higher this year, therefore, the bond market has been weak. Big institutional investors stayed on the sidelines, hoping to spot the peak of the interest rate trend.But smaller investors eagerly put their money into higher-paying bonds. If they hold their investments to maturity, they not only collect the face value of the bonds, but may make a capital gains as well.

High interest rates also have been a depressant for the stock market. Combined with other uncertainties, current interest rates of 8 and 9 percent or more on high-quality corporate and government issues have made stocks look less attractive to some.

For all these reasons, businessmen, bankers, security analysts and investment advisers stay up late at night trying to examine every clue provided by Federal Reserve activity as well as every nuance of Miller's public statements to see if an interest rate turn is at hand - or coming.

Last week, just as Wall Street hit a peak of confusion about the trends, there was a perceptible rally in bond prices - meaning a fractional decline in interest rates. Some traders had decided that they could divine the Fed's foot had come off the brake ever so slightly.

But one man - G. William Miller - knows the story better than anyone. Seated in shirt sleeves and sipping black coffee, Miller repeated his "hope" that "we'll see a peaking of interest rates between now and the end of the year."

CONFIDENT AND POISED after only five months at the helm, Miller then elaborated on prospects in the lengthy interview, and his words on the key question are worth quoting in full:

"I didn't promise any lowering of interest rates or slackening of the discipline in the monetary field in the next few months, but pressures could begin to abate. And some time after the first of the year, we could expect a little more chance that we could not only have topped out, but see the beginning of some decline.

"I think it's premature to assign too much importance to the bond rally that's been going on recently. Rates have dropped a little. But I think that's not necessarily the turning point. It may turn out to be, but I think it's premature. You could see it going the other way for a while.

"But I've said that the rates could be in either direction, but not major ones in the immediate future, because of the kind of market circumstances we now see."

He observed that the Treasury last week had auctioned 3-year notes at 8.46 percent, and within a few days, the yield had dropped slightly. And bank certificate of deposit rates also had dipped a bit. "It's all fractional," Miller smiled, "but before we saw nothing but up."

He warned against the effort to read too much into day-to-day activities of the Fed. "Our purpose is continued restraint and (to) get to the point where our (money) aggregates are within the ranges set by the FOMC (Federal Open Marker Committee)."

Miller said that "as the economy slows, we have to watch not only what's happening in today's money markets, but we have to watch what's happening in the real economy. I think what we've been saying in our monetary policy is we've put a lot of pressure on and we're watching it and nicking it. We're near the vital parts, and we're going to be very careful on how we make the incisions.

"When we opened up the patient," Miller grinned, "we used a firm, large cut. But now that we're near the vital organs, we've got to be very careful not to slip."

In sum, the candid appraisal by the powerful chairman of the Fed means that if the "turning point" isn't actually at hand (and it may well be), it isn't far off. But in any event, dramatic changes in interest rates - up or down - aren't in the cards, and a distinct easing of rates shouldn't be expected until next year.

IN THE COURSE of the interview, Miller made these other assessments of the economy which should be noted with care, given his strong influence on the thinking of the Carter administration:

Over the next year, economic growth in the U.S. will run in the 3 1/4-3 3/4 percent range, well below recent achievements. But Miller would resist setting lower targets - suggested by some as a way to cool inflation. That would run the risk "of falling into a growth recession or real recession," Miller feels.

Assuming that growth will be around 3.5 percent, and that a tight fiscal policy (for which he gives both Carter and Congress high marks) will allow some monetary ease in 1979. Miller says the chances of avoiding a recession "are fairly favorable."

He favors stimulating business investment through accelerated depreciation this year, rather than loosening up capital gains taxation, lining up closer to the White House than to Congress on this issue. Eventually, he thinks capital gains relief, of the kind advocated by Treasury Secretary W. Michael Blumenthal, would be helpful. But right now, he would concentrate on getting the investment share of gross national product from a low 8 percent (Japan's is 20 percent) to about 12 percent via the accelerated depreciation route.

To combat inflation, still the No. 1 problem in his book, he thinks the administration and Congress must be "more courageous" in dealing with so-called structural problems. Thus, he would defer for a year or two the increase in the minimum wage schdueld to go into effect Jan. 1, "or at least also advocates deferral of the rise in Social Security taxes for a year, and a big push on exports.

Miller says that without a successful attack on inflation, "There's not much we can do about the dollar (weakness) in the short run." But Japanese leaders will be glad to know that, in his opinion, the yen at 185 to the dollar has edged too high.

"How about the forecast one hears that some years down the road we'll see a rate of 100 yen to the dollar?" I asked him.

"Not if we get our inflation under control," he said firmly. That process, he grants, will be a long and tedious one. "We built up the inflation problem over about a dozen years," Miller said, "so it's not surprising that it should take us five or six years to finally break it - but it will be worth it."