What are the best quantitative models for trend detection? I.e. market trend.
I recommend using ARIMA with checks for level shift, trends, and interventions.
You can't just try and model the data with the only intent of identifying a trend. It is more complex than just a single focus. Let me explain....
In order to determine if there is a trend, you need to be careful as the trend may be just a change in the intercept or also known as a "level shift". You also need to be aware that you can't assume the trend started at the beginning of the time series as we are taught in Economics classes so this is an iterative process to determine the beginning and end of the trend. You will also need to determine your threshold of how many periods before you can "call" a trend. You will also need to be adjusting for interventions as they can skew the t-test when trying to identify a trend.
Without more detail it's hard to give you a comprehensive response, but you might for example look at the Hurst exponent to detect if a series displays trending characteristics. There are many R packages which compute the Hurst exponent - in my opinion the best collection can be found in the package fArma.
There are many methods you could use to detect when a specific series is trending. A simple and on-line method is to take an exponential moving average of lagged returns.