Trend

Trend
The idea of a trend is so intuitive as to never get a formal definition in technical analysis, even not in the classic Technical Analysis of Stock Trends by Edwards and MacGee. Sperandeo makes the following definition,
An uptrend is a sequence of rallies to successively higher highs, punctuated by pullbacks, with each pullback low ending above the previous pullback low.
and conversely for a downtrend,
A downtrend is a sequence of declines to successively lower lows, punctuated by rallies, with each rally high ending below the previous rally high.
From the definition of a trend, a trend line can be given a precise definition.
An uptrend line is drawn under prices, joining the lowest low to the highest pullback low which does not pass the line through prices in between. The line is then extended past the date of the highest high.
The condition that the line must not pass through prices between the points it joins means that it's not necessarily the most recent low which is joined, but might be only a prior one. When the line is extended to the right, it might then pass through prices, that's a possible indication of a trend change. A downtrend line is defined similarly,
A downtrend line is drawn above prices, joining the highest high to the lowest rally high which does not pass the line through prices in between. The line is then extended past the date of the lowest low.
1-2-3 Rule
Sperandeo identifies a change of an uptrend as
1. Trend line (defined above) broken.
2. Prices no longer making new highs.
3. Prices fall below a previous minor rally low
Or conversely for a downtrend
1. Trend line (defined above) broken.
2. Prices no longer making new lows.
3. Prices fall rise above a previous minor rally high.
Either of 1 or 2 is a probable trend change. Two of the three conditions is an increased probability of a change. All three is the definition of a trend change.
2B Rule
Point 2 above is essentially a failure of prices to carry past a previous rally (or previous selloff). Sometimes prices go just past then immediately reverse. Such a case is Sperandeo's rule 2B,
2B. If prices rise just above the previous rally high but then immediately fall back down.
Or for a downtrend change,
2B. If prices fall just below the previous low but then immediately rise back up.
Sperandeo regards 2B as a powerful pattern, and in assessing the probability of a trend change he weighs it higher than any other single criterion. The advantage of a 2B is that it lets the trader get almost the exact top (or bottom) of a move (with a stop-loss at the failed high or low). Even if it worked only 1 in 3 times the reward side is excellent due to getting in early.
Four day rule
The four day rule is Sperandeo's favourite pattern for a change in intermediate trend. The rule is
In an intermediate trending move, a reversal in the form of 4 days against the trend is highly likely to be a trend change.
This rule is based on his examination of trend changes in the Dow Jones Industrial Average from 1926 to 1985. He defines a variant as the "four-day corollary",
In an intermediate trending move, a sequence of 4 days with the trend followed by 1 against is highly likely to be a trend change.
This rule is looking for a climax over a series of days, instead of a single high-volume climax day.