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This link states:

Sharp increases in price and sharp increases in volume can mean bulls have been exhausted, all buyers have bought and there is no one else but sellers; the result is bearish

On the same website, however, they say

An increase or decrease in price accompanied by an increase in volume is considered a sign of strength in the prevailing trend.

How do I reconcile these two contradictory statements?

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The first statement is talking about a sudden sharp increase in volume (double or more of average volume) with a sudden increase in price. In other words, there has been a last rush to buy the stock exhausting all the current bulls (buyers), so the bears (sellers) take over, at least temporarily.

Whilst the second statement is talking about a gradual increase in volume as the price up trends (thus the use of a volume oscillator). In other words (in an uptrend), the bulls (buyers) are gradually increasing in numbers sending the price higher, and new buyers keep entering the market. (The opposite is the case for a down-trend).

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These statements aren't necessarily contradictory.

In the first case, investors are bearish because they anticipate selling in the future (because all the interested buyers have bought, so all that remains in the short run are people willing to sell and therefore drive down the price).

In the second case, the trend is strengthened because the increase in volume indicates that the price movement interested a lot of traders. The trend could be bullish or bearish.

The statements aren't contradictory because the second case could very well lead to the first case. For example, if an increase in price is coupled with an increase in volume, this could indicate that the positive trend is strengthening (second case). Traders are becoming more interested in the price move, so they buy.

However, once all of the traders who are willing to enter the market long do so, we're in the first case. Investors realize that all of the traders who were interested in buying have bought, so they become bearish because they expect selling to start soon.

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