Well, maybe, maybe not...
If your speculator is an active speculator taking positions in the hope of numerous but small gains over short-term holding periods (an hour, a day, a week), then your speculator will more likely sell when the price of a stock goes up and buy when the price of a stock goes down. Buy low, sell high, right? This tends to work ok as long as the stock being traded continues to fluctuate in a range. Should the stock begin to trend, all bets are off.
There is though, a group that adheres to the 'momentum' school of trading. This group identifies some significant change in the recent rate of change of a stock that suggests that is entering a new up or down trend. This view holds that when you observe such a statistically significant event say, upwards, then you buy even though you are most likely buying at a relatively high price compared to recent history. Of course, a downwards momentum change produces a sell. Often referred to as a 'breakout' of a trading range or a reversal of a previous trend.